s207
(b) Any one of a set of nuclei that have the same value of the mass number A but different values of the atomic number Z. Nuclei connected by β-decay are isobars since β-decay does not change the value of A. [QPM.3]
...
(b) In the context of particle physics; a resonance is a very short-lived strongly interacting particle. See hadron resonance for further details. [QPM.4]
...
isobar4(a) A line joining points in a fluid that are at the same pressure. [CPM.4]
...
natural frequency 4(a) In the context of a mechanical oscillator; the natural frequency is the (angular)frequency of the oscillator in the absence of any driving or damping forces. For a harmonic oscillator of mass m, subject to a linear restoring force, Fx = −kx, the natural (angular) frequency is ω 0 = k m . [PM.2]
...
ontological interpretation See Bohm's theory. [QPI.4]
...
principle of conservation of angular momentum See conservation of angular momentum. [PM.4]
...
speed4(a) In the context of kinematics; the speed of a specified body is the magnitude of the (instantaneous) velocity of that body. The SI unit of speed is the metre per second (m1s−1). [DM.1; DM.2]
...
collision
A brief interaction between two or more particles or bodies in close proximity. [PM.3]
angular wavenumber
A characteristic property of a wave defined by the relation k = 2π/λ, where λ is the wavelength of the wave. Angular wavenumber is a positive scalar quantity with the SI unit m−1. (See also angular frequency ω.) [DFW.2]
unit circle
A circle of radius 1. Since the radius is a pure number, the unit circle is a mathematical construction rather than a physical one. [DM.3]
inelastic scattering
A collision process in which the nature (or number) of the particles is changed. Inelastic scattering generally involves the conversion of kinetic energy into mass energy. [QPM.4]
magnification
A commonly used shorthand for linear magnification. (See also angular magnification.) [DFW.3]
white dwarf
A compact stellar object with a mass similar to that of the Sun, which, following a fuel shortage, has collapsed to a size similar to that of the Earth. Further collapse is prevented because the mutual gravitational attraction of the matter in the star is opposed by Pauli pressure exerted by its electrons, but the average density of the object will be very high, roughly a million times that of the Sun. [SFP.2]
oscillation
A continuous back and forth (or up and down) motion that can be characterized by an amplitudeand a period. [DM.3]
equipotential
A contour or surface connecting points of equal electric potential. Electric field lines always cut equipotentials at right angles. The equipotentials around an isolated point charge are concentric spheres centred on the charge. The concept may also be extended to other kinds of potential, such as gravitational potential. [SFP.2]
angular coordinate
A coordinate (usually denoted θ0) that determines the angular position of a point in a (plane) polar coordinate system. [DM.3]
plane polar coordinate system
A coordinate systemin which the position of a point in a plane is specified by the ordered pair (r, θ) where r is the distance of the point from a selected origin and θ is the angular displacement, measured at the origin, of the point from a specified reference line that passes through the origin. [DM.3]
interpretation
A detailed account of the physical significance of the various parts of the formalism of a subject. [QPI.4]
transistor
A device for amplifying the power or current of an electrical signal. It usually consists of two p-n junctions arranged as an n-p-n or p-n-p sandwich.[QPM.2]
mirror
A device for reflecting light. See plane mirror, spherical mirror and parabolic mirror. [DFW.3]
direct current motor
A device in which an externally supplied direct current causes a coil of wire to rotate in a magnetic field. For example, if a direct current is fed into a direct current generator, then the Lorentz force acting on the conduction electrons in the coil (which sits in a magnetic field) will cause the coil to rotate about its axis. [DFW.1]
baryon number
A dimensionless quantity, usually represented by the symbol B, that is conserved in all known interactions. All baryons have B = 1, and all antibaryons have B = −1. All quarks have B = 1/3, and all antiquarks have B = −1/3. [QPM.4]
spinning top
A disc (or other heavy axially symmetric object) mounted on an axle. One end of the axle is pointed and acts as a pivot about which the entire object can rotate. [PM.4]
scale height
A distance which characterizes the exponential decay of pressure with altitude in a thin isothermal atmosphere. (See barometric formula). When the altitude increases by the scale height, the pressure decreases by a factor of 1/e. [CPM.4]
node
A fixed point in space at which the disturbance (e.g. displacement of a string) due to a standing wave is zero at all times. (Contrast with antinode.) [DFW.2]
antinode
A fixed point in space at which the disturbance due to a standing wave (e.g. displacement of a string) attains its maximum value. (Contrast with node.) [DFW.2]
47precession
A form of motion, exhibited by gyroscopes, spinning tops and other such rotating bodies, in which a body's angular momentum vector swings around a fixed direction in space, describing a cone. [PM.4]
spontaneous fission
A form of radioactivity with a very long half-life by which some heavy nuclei such as 238U split into two roughly equal fragments and a few neutrons, with the release of energy. [QPM.3]
linear function
A function of the form ƒ(x) = Ax + B, where A and B are constants. [DM.1]
ideal gas
A gas in which the molecular interactions play a completely negligible role. In equilibrium, an ideal gas obeys the ideal gas equation of state and Joule's law for ideal gases. [CPM.1]
optical fibre
A glass fibre used to transmit light signals that can carry coded binary information. The 43principle of operation of optical fibres relies on total internal reflection. [DFW.2]
position-time graph
A graph showing how the position (usually in one dimension) of a particle depends on time. It is conventional to plot the position on the vertical axis and the time on the horizontal axis. The gradient of the position-time graph at any particular time is equal to the velocity of the particle at that time. [DM.1]
bob
A heavy weight attached to the lower end of apendulum or oscillator. [DM.3]
flywheel
A heavy wheel of large moment of inertiaused to store rotational kinetic energy. Flywheels are often used to smooth the output from engines. [PM.4]
translational energy histogram
A histogram in which the height of each bar is proportional to the fraction of particles with translational energies within the width of the bar. [CPM.2]
covalent bond
A kind of bonding that arises between atoms and which can lead to the formation of individual molecules or solids. In a covalent bond, unpaired electrons in the separated atoms are shared to form a pair with opposite spin states. The pair is concentrated between the two atoms and is therefore able to attract each electrically, thus creating the bond. Covalent bonds are directional and may become saturated. [QPM.2]
sigma particle
A kind of elementary particle. A strange baryon with spin 21, and a mass that is about 25% greater than that of the proton. There are three 55kinds of sigma particle, indicated Σ+, Σ−, Σ0 according to charge. [QPM.4]
electron microscope
A kind of microscope that uses electrons and electromagnetic lenses (rather than light and glass lenses) to form very highly magnified images.[CPM.1]
Charles's law
A law stating that; at constant pressure, the volume of a fixed mass of an ideal gas is proportional to its absolute temperature. [CPM.1]
third law of thermodynamics
A law stating that; it is impossible to reduce the temperature of any system to absolute zero by a finite number of operations. [CPM.3]
Joule's law of ideal gases
A law stating that; the internal energy of an ideal gas is independent of pressure or volume. [CPM.1]
Stokes' law
A law stating that; when a sphere of radius R moves through a fluid at constant speed v, the magnitude of the viscous force that opposes the motion isF = 6πηRvwhere η is the coefficient of viscosity of the fluid. [PM.1]
law of reflection
A law stating that; when a wavestrikes a reflecting surface, the incident and reflected rays and the normal to the reflecting surface all lie in the same plane, and the angle of incidence equals the angle of reflection, i.e. i = R. [DFW.2]
cylindrical lens
A lens whose surfaces are parts of cylinders. Such a lens will have focusing properties in the direction perpendicular to the straight side(s) of the cylinder, but have no focusing effect in the direction parallel to the straight side(s). For comparison, see spherical lens. [DFW.3]
ferromagnet
A magnetic material that can become very strongly magnetized even in a relatively weak applied magnetic field. Examples are iron, cobalt, nickel and some associated alloys. [SFP.4]
differentiation
A mathematical process that allows the derivative of a function to be determined. [DM.1]
resistivity
A measure of a material's ability to resist the flow of an electric current. If a uniform wire has resistance R, cross-sectional area A and length l, then the material from which it is made has resistivity ρ = RA/l. The resistivity of a material is a property of the material itself and is independent of the geometrical form or size of any particular sample of the material. The SI unit of resistivity is the Ω1m. 4[SFP.3; QPM.2]
linear magnification
A measure of the enlargement in the size of the image produced by a lens or mirrorrelative to the size of the object. It can be calculated from the equation m = v/u, where v is the image distance and u the object distance. If the image size is less than the object size, m will be less than 1 but greater than 0. [DFW.3]
cross-section
A measure of the probability that a certain kind of scattering will occur at a specified energy. It is often denoted by the symbol σ and has the units of area. Cross-sections are usually expressed in terms of the non-SI unit known as the barn, represented by the symbol b where 11b = 10−281m2. A cross-section can be restricted to elastic scattering or may include both elastic and inelastic contributions, in which case it is known as the total cross-section. [QPM.4]
convection
A mechanism of heat transfer in which a hot body transfers energy to fluid with which it is in contact, causing the fluid to expand and decrease in density so that it rises through overlying denser fluid, thus carrying the transferred energy away from the source of the original heating. [CPM.3]
positron emission tomography
A medical imaging technique involving the annihilation of electrons and positrons. Tomography is a technique for imaging a chosen two-dimensional section, or slice, of an internal organ or tumour, etc., using penetrating radiations, traditionally beams of X-rays. In positron emission tomography, or PET, the penetrating radiation comes from the annihilation of positrons released by a β+-emitting isotope introduced deliberately into the region to be imaged. [QPM.3]
simple solid model
A model of a solid in which independent atoms oscillate in three dimensions about fixed equilibrium positions. [CPM.2]
Pauli's quantum free-electron model
A model of conductivity in metallic solids, formulated by Wolfgang Pauli, in which the free-electron gas in a metal is treated as a quantum gas of fermions. [QPM.1]
Clarke orbit
A name sometimes used to describe the 24-hour equatorial orbit in which a satellite, orbiting in 10the same sense that the Earth rotates, maintains a fixed position as seen from the Earth. This is the orbit used by geosynchronous communications satellites. [DM.3]
cathode
A negative electrode. In a vacuum electronic device (such as a cathode ray tube) electrons are emitted from the cathode and attracted to the anode.causality$The principle that a cause should always precede its effect. Special relativity preserves this logical relationship, provided it is assumed that the speed of light in a vacuum is the maximum speed at which a signal can travel. [DFW.4]
magnetic bottle
A non-uniform magnetic fieldconfiguration that may be used to trap charged particles, especially those in a plasma. [SFP.4]
ordered pair
A pair of quantities, usually presented in the form (x, y), and subject to an interpretation that depends on their order, so that (x, y) has a different meaning from (y, x) as long as y ≠ x. [DM.2]
cyclic accelerator
A particle accelerator in which charged particles follow closed or nearly closed paths so that they can be accelerated repeatedly by the same parts of the machine. [QPM.4]
fermion
A particle with odd half-integer spin (i.e. spin 21, 23, etc.). Fermions obey Pauli's exclusion principle. Consequently, only one fermion can occupy any given quantum state. [QPM.1]
Bose-Einstein condensate
A phase of matter, for a macroscopic system of identical bosons at very low temperature, in which a large number of the particles occupy the same translational quantum state. The condensation occurs abruptly at a characteristic temperature. [QPM.1]
instrumentalism
A philosophical doctrine asserting that the purpose of a scientific theory can only be to predict the results of experiments. [QPI.4]
plane wavefront
A plane on which the phase of a wave has the same value at all points. The existence of such planes is a characteristic of a plane wave. [DFW.2]
cubic function
A polynomial function of the form ƒ(x) = Ax3 + Bx2 + Cx + D. [DM.1]
Archimedes' principle
A principle asserting that; when a body is immersed, partly or wholly, in a fluid, its apparent weight is decreased by the weight of the fluid displaced. [CPM.4]
quasi-static process
A process in which the state of a system changes so slowly that it effectively goes from one equilibrium state to another via a succession of intermediate equilibrium states. [CPM.1; CPM.3]
intrinsic semiconductor
A pure semiconductormaterial that has not been doped. The number of holes in the valence band of an intrinsic semiconductor is equal to the number of thermally excited electrons in the conduction band. [QPM.2]
top
A quantity that is conserved in strong and electromagnetic interactions, but not in weak interactions. [QPM.4]
parameter
A quantity that is constant in a particular case but may vary from one case to another. [DM.3; PM.5]
tight-binding model
A quantum-mechanical model of a solid that starts with the discrete energy levels of a large number N of isolated atoms, and then considers how each discrete level evolves into a band of very closely spaced levels as the atoms are brought together to form the crystalline solid. The tight binding model thus represents an approach to the band theory of solids. [QPM.2]
potential well
A region of space in which the potential energy of a particle is lower than in the surrounding region. In classical physics, a particle within the well that has less energy in total than the potential energy it would have in any region immediately adjacent to the well, will be bound and will remain permanently confined within the well. In quantum physics, such a particle may be able to escape from the well, thanks to the phenomenon of tunnelling. [QPI.2]
Carnot cycle
A reversible cyclic process involving a fixed quantity of ideal gas, and consisting of two isothermal processes linked by two adiabatic processes. [CPM.3]
lever
A rigid beam, supported at one point by a fulcrum, about which it can turn. [PM.4]
square root rule
A rule asserting that; if our best estimate is that a certain outcome will occur N times, we should expect fluctuations of order N , but we should be astonished if the outcome occurred less than N −10 N times or more than N +10 N times. [CPM.2]
40multiplication rule for probabilities
A rule stating that; if a number of outcomes occur independently of one another, the probability of them all happening together is found by multiplying their individual probabilities together. [CPM.2]
fluid
A sample of matter that is able to flow. Both liquids and gases are fluids. [CPM.3]
extrinsic semiconductor
A semiconductor material that has been doped either to increase the number of electrons in the conduction band, making it an n-type semiconductor, or to increase the number of holes in the valence band, making it a p-type semiconductor.[QPM.2]
n-type semiconductor
A semiconductor that is doped with sufficient donors to ensure that a current can be carried by donor electrons in the conduction band.[QPM.2]
components
A set of scalar quantities that can be used to specify a vector. See Cartesian components. [DM.2]
23equivalent circuit
A simple arrangement of circuit components in an electrical circuit that has the same effect as a more complicated arrangement. [SFP.3]
shell
A specified collection of electrons in an atom. In the Bohr model of the atom, each shell consists of electrons moving in Bohr orbits that correspond to a particular value of Bohr's quantum number, n. In Schrödinger's quantum-mechanical model, each shell is composed of electrons in stationary states that correspond to a common value of the principal quantum number, n. [QPI.3]
ideal flow
A state of steady flow in a fluid that has constant density, no viscosity and is free of eddies. [CPM.4]
axis
A straight line along which the values of a position coordinate may be measured. [DM.1]
twin 'paradox'
A supposed paradox arising out of the special theory of relativity concerning the relative ages of twins, one of whom embarks on and then returns from a long trip at a speed close to the speed of light to find his/her sibling much older than him/herself on return. In fact, no paradox exists and the age difference arises as a result of time dilation (and an effective change of inertial frame on the part of the traveller). [DFW.4]
UPT surface
A surface representing the sets of values of internal energy U, pressure P and temperature T that characterize the equilibrium states of a given macroscopic system (such as a sample of matter). The surface is a pictorial representation of the system's internal energy equation. [CPM.1]
relativistic kinetic energy
A term used occasionally as an abbreviation for relativistic translational kinetic energy. [QPM.4]
triatomic
A term used to describe a moleculeconsisting of three atoms bound together by interatomic forces. [CPM.1]
Universe
A term used to describe a system and its environment. [CPM.3]
solid state
A term used to describe any electronic circuit or device containing solid-based (usually silicon) semiconductors. The term is also used to describe the field of physics in which the properties of solids are studied. [QPM.2]
64uni-axial rotation
A term used to indicate rotation about a single fixed axis. [PM.4]
nucleon
A term used to mean either a proton or a neutron. [QPM.3]
work-energy theorem
A theorem stating that; when a single resultant force does work on a system, the kinetic energy of the system increases by an amount that is equal to the work done on the system. [PM.2]
electroweak theory
A theory unifying the electromagnetic and weak interactions. The fact that the weak and electromagnetic interactions are actually different aspects of a single unified force is only expected to become manifest at very high energies. [QPM.4]
weak nuclear force
A very short-range force that is responsible (among other things) for β-decay. It is stronger than the gravitational interaction, but weaker than the electromagnetic or strong interactions. It is one of the four fundamental forces. [RU.1; QPM.4]
plane wave
A wave in which the wavefronts form parallel lines (in two dimensions) or parallel planes (in three dimensions). At any given time, the phase of such a wave will have the same value at all points on a plane that is perpendicular to the direction of propagation of the wave. [DFW.2]
Carnot refrigerator
An 'ideal' refrigerator, the operation of which is based on a (reversed) Carnot cycle. [CPM.3]
tuned circuit
An LC circuit that has been adjusted to a particular natural frequency in order to pick up external radio signals. [DFW.1]
strain energy
An abbreviation for strain potentialenergy. [PM.2]
stimulated absorption
An alternative term for the process known simply as absorption in which an atomabsorbs a photon as an electron within the atom makes a transition from a lower energy level to a higher energy level. [QPI.3]
49quantum
An amount of energy associated with electromagnetic radiation of frequency f, equal to hfwhere h is Planck's constant. This is the amount of energy carried by a single photon of the radiation. [QPI.1]
origin
An arbitrarily chosen reference point from which coordinates are measured in a coordinate system. In one dimension, the origin is the point at which the position coordinate is zero. [DM.1]
13coordinate system
An arrangement of axes (usually in three-dimensions) by means of which the position of any point (or event) can be specified. A Cartesian coordinate system has three mutually perpendicular axes, usually labelled x, y and z. [DM.1; DM.2; DFW.4]
pulsar
An astronomical source of short pulses of radio emission at highly regular intervals, typically in the range 11ms to about 31s. There is very strong evidence that pulsars are highly magnetized, rapidly rotating neutron stars. The observed pulsing is explained by supposing that the neutron star somehow produces a continuous beam of radio emission that sweeps across the observers location (like the beam from a lighthouse) as a result of its source's rotation. [PM.4; SFP.2]
ion
An atom that has become electrically charged, through having lost or gained one or more electrons.[CPM.1; SFP.2]
plum-pudding model of the atom
An atomic model, due to J. J. Thomson in which electrons are contained (like plums in a pudding) in a sphere of positively charged material of about 10−101m radius. [QPI.1]
inductive circuit
An electric circuit containing an inductor. When an alternating current is applied to the circuit, the phase of the voltage across an inductor leads the phase of the current through it by one-quarter of a cycle. [DFW.1]
17direct current
An electric current that maintains a constant direction (although it may vary in magnitude). Contrast with alternating current. [DFW.1]
capacitive circuit
An electrical circuit containing a capacitor. When an alternating current is applied to the circuit, the phase of the voltage across a capacitor lags the phase of the current through it by one-quarter of a cycle. [DFW.1]
capacitor
An element in an electric circuit whose primary function is to separate charge and hence store energy. A parallel plate capacitor consists of two conducting plates, usually separated by an insulating medium of high relative permittivity. Any capacitor will have a certain value of capacitance. When a sinusoidally alternating current passes through a capacitor, the sinusoidally varying voltage across the capacitor lags the sinusoidally varying current by a quarter of a period. [SFP.2]
equation of a circle
An equation of the form x2 + y2 = r2 that describes a circle of radius r, centred on the origin of a Cartesian coordinate system. [DM.3]
light clock
An idealized clock in which a pulse of light bounces back and forth between two parallel mirrors, with the clock 'ticking' every time the light pulse hits either one of the mirrors. Although this would be a pretty impractical clock in real life, it has the advantage that time intervals, as measured by a light clock, depend only on the principle of the constancy of the speed of light, and can therefore be interpreted unambiguously using Einstein's special theory of relativity. [DFW.4]
virtual image
An image where the rays appear to diverge from the image points. Contrast with real image. [DFW.3]
real image
An image where the rays converge to, and pass through, the image points. Contrast with virtual image. [DFW.3]
Bell's inequality
An inequality satisfied by a certain combination of spin component correlation functions according to any theory that exhibits both locality and realism. Quantum mechanics predicts that the Bell inequality will be violated and experiments indicate that this is the case. (See also Bell's theorem.) [QPI.4]
satellite
An object (possibly artificial) that moves in a closed orbit about an astronomical body such as the Earth. [DM.3]
real object
An object from which rays diverge. Contrast with virtual object. [DFW.3]
inertial observer
An observer associated with an inertial frame of reference.
calorie
An obsolescent unit of energy, mostly associated with thermal energy, and equal to 4.1861J. The 'Calorie' (note the upper case C) sometimes referred to in nutritional information, is equal to 10001calories. [CPM.3]
symmetry
An operation that leaves something unchanged. For example, if ƒ(x) = x2 then replacing x by −x leaves the value of ƒ(x) unchanged. [DM.3]
neutron
An uncharged elementary particle with mass 1.675 × 10−271kg (about 0.1% greater than that of the proton), and spin 21. Neutrons are non-strange baryons, and, when free, are unstable, having a mean lifetime of about 151minutes. They are found in the nucleus of every atom (except for the lightest isotope of hydrogen).[CPM.1; QPM.4]
β-particle (beta-particle)
Another name for an energetic electron emitted by the nucleus. [QPM.4]
primary mirror
Another name for the objective mirror in a reflecting telescope. [DFW.3]
Maxwell-Boltzmann speed distribution
Another term for the Maxwell speed distribution. [CPM.2]
allowed transition
Any (radiative) transition corresponding to a change in quantum numbers that satisfies the relevant selection rules. For an electron in a spherically symmetric atom, these rules require that ∆l = ±1 and ∆ml= 0 or ±1. (Contrast with forbidden transition.) [QPI.3]
subshell
Any collection of electrons in an atom, occupying stationary states that correspond to common values of the principal quantum number, n, and of the orbital angular momentum quantum number, l. [QPI.3]
quadratic equation
Any equation that may be written in the form ax2 + bx + c = 0 where a, b, c are constants and a is non-zero. [DM.2]
non-uniform motion
Any form of motion in which the velocity is not constant. [DM.1]
quantum gas
Any gas of weakly interacting indistinguishable particles whose behaviour is influenced by their boson or fermion nature. Examples are the photonsin thermal radiation, and the free electrons in a metallic solid. The translational energy of a quantum gas is not distributed in accordance with the Maxwell-Boltzmann energy distribution, except in the limiting case where the de Broglie wavelength is very much less than the typical distance between particles. Instead it is described by, for example, Planck's radiation law for photons and Pauli's distribution for free electrons. [QPM.1]
conic sections
Any of the curves produced by the intersection of a plane and a cone is called a conic section. The curves that belong to this family include the circle, the ellipse, the parabola and the hyperbola. Each such curve is described by the set of all points (x, y) that satisfy an equation of the formax2 + 2hxy + by2 + 2gx + 2ƒy + c = 012for specific choices of the constants a, b, c, ƒ, g, h. [DM.2]
base unit
Any one of the seven SI units that provide the basis for the definition of all the other (derived) SI units. The seven base units are; metre (m), kilogram(kg), second (s), mole (mol), kelvin (K), ampere (A) and candela (Cd). [DM.1]
magnetic dipole
Any system that produces a magnetic field similar to that of an infinitesimally small bar magnet. A compass needle is a good approximation to a magnetic dipole. Any magnetic dipole experiences a torque in a magnetic field unless it is oriented parallel or antiparallel to the field. The magnitude of the torque depends on the strength of the applied magnetic field and a quantity called the magnetic dipole moment that characterizes the magnetic dipole. [SFP.4]
hadron resonance
Any very short-lived meson or baryon with a mean lifetime of about 10−241seconds. These particles live for too short a time for them to be directly observed, so their existence was first indicated by the presence of peaks in certain inelastic collision cross-sections; hence their peculiar name. [QPM.4]
boundary conditions (of a wave)
Conditions that constrain a wave by specifying its behaviour at its end points. In the case of a standing wave the boundary conditions restrict the possible wavelengths and thereby limit the allowed frequencies. 4[DFW.2]
aberrations
Distortions in optical images produced by the optical systems that form those images. Aberrations arise from a number of well-known causes and are classified accordingly. See, for example, chromatic aberration and spherical aberration. [DFW.3]
degrees of freedom
Each independent term, involving the square of a displacement, velocity, angular displacement or angular velocity, that appears in the expression for the total energy of a particle is said to correspond to a degree of freedom. The number of degrees of freedom, f, is the number of such squared terms. [CPM.2]
visible light
Electromagnetic radiation with a wavelength between about 4 × 10−71m (4001nm, violet) and 7 × 10−71m (7001nm, red) or a frequency between about 8 × 10141Hz and 4 × 10141Hz. [DFW.2]
antiparticle
Elementary particles that have the same mass and spin as certain known particles, but the opposite signs for other attributes, such as electric charge. For example, the electron and positron have the 4same mass and both have spin 21, but the former has a negative charge −e, while the latter has positive charge +e. [QPM.4]
transuranic elements
Elements with atomic number Z > 92 (uranium) which are made artificially. [QPM.3]
cosmic ray
Energetic particles that reach the Earth from outer space. [QPM.4]
angular position
Expressed relative to a point O and an arbitrarily chosen straight line through O, the angular position θ of a point P is the angle (measured in the anticlockwise direction) from the chosen straight line to the line linking O to P. [PM.4]
coherence length
For an electron in a superconductor, the distance across which the wavefunction spreads with sufficient amplitude that it will interact with a second electron to bind and form a Cooper pair. The coherence 11length is long in pure well-formed metallic crystals, but it is reduced by electron scattering and can be very short in alloys and polycrystalline compounds. The main significance of the coherence length is that when it is shorter than the penetration depth for a magnetic field, the bulk of the superconductor can be threaded by flux lines to give a type II superconductor. [QPM.2]
fictitious forces
Forces with no basis in physical reality, but which can, nonetheless, be used to account for the motion of bodies observed from non-inertial frames of reference. By introducing such fictitious forces, the bodies can be made to conform to Newton's laws of motion, even though those laws do not, strictly speaking, apply in non-inertial frames. (See centrifugal force and Coriolis force.) [PM.1]
absorption (and emission) of radiation
General processes whereby energy carried by Electromagnetic radiation may be added to, or taken from, the total energy of the system responsible for the emission or absorption. A particular case is that in which an electron makes a radiative transition between two energy levels in an atom. When an electron makes a transition from a lower energy level E1 to a higher energy level E2, the atom increases its total energy by an amount E2− E1. In the case of a radiative transition, the atom obtains this energy by absorbing a single photon of energy E2− E1. Similarly, an atom can emit a photon of energy E2− E1in a radiative transition when one of its electrons makes a transition from a higher energy level E2 to a lower energy level E1. [QPI.3]
energy distribution function
Generally taken to be the same thing as the translational energy distribution function. [CPM.2]
generations
Groupings of four fundamental spin 21particles that play an important role in the standard model of particle physics. According to the model there are three such generations, each of which contains two quarks and two leptons. The first generation consists of the electron, electron neutrino, up quark and down quark (or in symbols, e−, νe, u, d). [QPM.4]
hidden variables
Hypothetical and currently unmeasurable physical variables that are supposed by some to account for our present need to use probabilities in an unavoidable way in quantum mechanics. Bell's theorem places strong constraints on viable hidden variable theories. Bohm's theory is a hidden variable theory that satisfies those constraints. [QPI.4]
strings
Hypothetical extended objects that are consistent with quantum theory and involve supersymmetry. It was hoped that they would provide a plausible superunified theory. [QPM.4]
specular reflection
If a particle bounces off a planar surface at the same angle as it approached the surface, it is said to have undergone specular reflection. [CPM.2]
defects
Imperfections in the regular arrangement of atoms in real crystals due to a variety of effects including; vacancies (missing atoms), dislocations, chemical impurities and polycrystal boundaries. [QPM.2]
acceptors
Impurity atoms added to a semiconductor to produce a p-type material. They have fewer valence electrons than are required for bonding and therefore absorb one or more electrons from the valence band of the semiconductor, creating holes there. In silicon, the acceptor atoms are often boron. [QPM.2]
donors
Impurity atoms added to a semiconductor to produce an n-type material. They have more valence 18electrons than are required for bonding and therefore release one or more electrons into the conduction band of the semiconductor, thus creating free electrons there. In silicon, the donor atoms are often arsenic or phosphorus. [QPM.2]
defect scattering
In Pauli's quantum free-electron model in metals, electrical resistivity is caused by the scattering of electron waves by defects in the crystal lattice and by thermal scattering. The defect scattering makes a contribution to the resistance that is roughly independent of temperature and proportional to the defect density. [QPM.2]
effective focal length
In a telephoto lens system, two lenses separated by a certain distance behave optically in the same way as a single lens with a much longer focal length. Similarly, in a Cassegrainian telescope, the converging primary mirror and the diverging secondary mirror behave optically in the same way as a single converging mirror with a much longer focal length. This longer focal length in each case is achieved within a smaller physical length of the device, and is said to be the 'effective (or equivalent) focal length of the system'. [DFW.3]
impact parameter
In any scattering process, the impact parameter b is the length of the perpendicular drawn from the centre of the target to the original line of approach of the projectile. [QPI.1]
external force
In the context of a given system, an external force is a force that acts on the system (or part of the system) but which has a reaction that acts outside of the system. [PM.3]
deformed nuclei
In their state of lowest energy, most nuclei tend to be spherically symmetric partly because of their surface energy which, for a given mass number, is a minimum for a sphere. For some heavy nuclei however, weak shell-effects overcome the effects of the surface energy and favour a rugby-ball shape. Such nonspherical nuclei are said to be deformed. [QPM.3]
type I superconductors
Materials from which magnetic flux is completely excluded in the superconducting state, displaying the Meissner effect. Typical type I superconductors are pure metals with a long coherence length. [QPM.2]
spectral lines
Narrow lines seen in the spectrum of a substance. The lines correspond to those particular wavelengths of electromagnetic radiation that may be absorbed or emitted by atoms or molecules of the substance as a result of transitions occurring between energy levels. (See also spectrometer.) [QPI.1]
thermal neutrons
Neutrons that are collectively in thermal equilibrium with their surroundings. Inside a nuclear reactor such neutrons typically have thermal energies of about 0.081eV. [QPM.3]
trigonometric ratios
Numerical quantities (the most important of which are abbreviated sin1θ, cos1θ and tan1θ) that are defined in terms of ratios of the side lengths of a right-angled triangle that has an interior angle θ. Given such a triangle, in which the hypotenuse (longest side) has length r, the side opposite the angle θhas length y, and the third side, adjacent to the angle θ, has length x; the three basic trigonometric ratios (formally called the sine, cosine and tangent) are defined by sin1θ = y/r, cos1θ = x/r, tan1θ = y/x. 4[DM.2]
quantum physics
One of the major subdivisions of physics that should be compared and contrasted with classical physics. Quantum physics encompasses quantum mechanics and quantum field theory, along with a host of other quantum phenomena. Amongst its characteristic features are indeterminacy and the intrinsic use of probability, along with the appearance of Planck's constant. [RU.1]
classical physics
One of the major subdivisions of physics that should be compared and contrasted with quantum physics. Classical physics is often taken to consist of those subjects, such as mechanics, electromagnetism and thermodynamics, that were already well-defined by the year 1900, along with their direct developments in the twentieth century. [RU.1]
strange quark
One of the six types of quark. It is the only quark to have non-zero strangeness. [QPM.4]
top quark
One of the six types of quark. It is the only quark to have non-zero top (or topness). [QPM.4]
primary cosmic rays
Particles, mainly protons, arriving at the top of the Earth's atmosphere and coming directly from space. Such particles have a range of energies, but the most energetic protons can have energies in excess of 10181eV. [QPM.4]
resonant photons
Photons with an energy E that is exactly equal to the energy of a specified radiative transition in an atom. The photons are said to be resonant with the specified transition. [QPI.3]
grand unified theories (GUTs)
Quantum field theories of the fundamental interactions that attempt to truly unify the strong, weak and electromagnetic interactions within a single theoretical framework. [QPM.4]
superunified theories
Quantum field theories that attempt to unify all four fundamental interactions. No satisfactory self-consistent theory exists at present. [QPM.4]
electromagnetic radiation
Radiation comprising any part of the electromagnetic spectrum. [DFW.2]
periodic motion
Repetitive motion characterized by the requirement that r(t + T0) = r(t) for some fixed value of T and all values of t. [DM.3]
Fitzgerald-Lorentz contraction
See Lorentz contraction. [DFW.4]
length contraction
See Lorentz contraction. [DFW.4]
gamma factor
See Lorentz factor. [DFW.4]
energy distribution law for photons
See Planck's radiation law. [QPM.1]
cavity radiation
See blackbody radiation. [QPM.1]
negative lens
See diverging lens. [DFW.3]
convex mirror
See diverging mirror. [DFW.3]
negative mirror
See diverging mirror. [DFW.3]
hyperopia
See long-sightedness. [DFW.3]
magic nuclei
See magic numbers. [QPM.3]
cascade particle
See xi particle. [QPM.2]
β+-decay
See β-decay. [QPM.3]
β−-decay
See β-decay. [QPM.3]
law of conservation of angular momentum
Seeconservation of angular momentum. [PM.4]
law of conservation of linear momentum
Seeconservation of linear momentum. [PM.3]
ultrasound
Sound with a frequency above the limits of hearing of the human ear (i.e. greater than about 201kHz). [DFW.2]
bifocal spectacles
Spectacles in which the top part of each 'lens' has a different focal length to the bottom part, thereby enabling a prescription for both close viewing and distant vision to be incorporated into the one pair of spectacles. They are often required by people as they get older and begin to suffer from presbyopia. [DFW.3]
right-handed coordinate system
Starting with the palm of your right hand flat, extend the thumb so that it is approximately at right angles to the first finger, then bend the second finger so that it is at right angles to the plane of the palm. Your thumb, first and second fingers should then be mutually at right angles (at least approximately). A three-dimensional Cartesian coordinate system is said to be right-handed if, by rotation alone, it may be brought into alignment with the extended thumb, first and second fingers of your right hand in such a way that the z-axis points in the same direction as the thumb, the x-axis points in the direction of the first (index) finger, and the y-axis points in the direction of the second finger. Any three-dimensional Cartesian coordinate system that is not right-handed must be left-handed. [DM.2]
aperture
That part of a lens through which light can be transmitted, or that part of a mirror from which light can be reflected. This may correspond to the full diameter of the lens (or mirror), or, if the lens is used with an adjacent aperture stop (as in a camera, for instance), to the effective diameter of the lens as limited by the stop. [DFW.3]
system
That part of the Universe which is the subject of an investigation. (See also environment.) [CPM.3]
crystalline lens
That part of the human eyelens system which, being made up of over 201000 layers of transparent cellular material, can have its shape changed (under the action of the ciliary muscle) and thereby change the eyelens's overall focal length. (See also cornea and aqueous humour.) [DFW.3]
aperture stop
The (usually adjustable) iris diaphragm through whose central aperture light is admitted to the body of a camera or similar device. When it is adjustable, it can be used to alter the total exposure to which the film is subjected in a given time. [DFW.3]
Rydberg constant
The Bohr model predicts that the wavelength of the spectral line emitted by a hydrogen atom when its electron makes a radiative transition from an energy level with Bohr quantum number n to an energy level with Bohr quantum number q is given by4 ⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧−→ =2 22 21n qq nRλn qwhere the constant R is known as the Rydberg constant. The value for R predicted by Bohr's theory R = (1.096178 × 1071m−1)agrees to within 6 parts in 101000 with the experimentally measured value (1.097137 × 1071m−1). [QPI.1]
absolute temperature scale
The SI scale of temperature measured in kelvin (K). On this scale, the lowest conceivable temperature, absolute zero, is 01K, and the triple point temperature of H2O is 273.161K. (See also temperature scale.) [CPM.1]
tesla
The SI unit of magnetic field, represented by the symbol T, and defined by the relation 11T = 11kg1s−21A−1. [SFP.4]
Schrödinger's equation3See time-dependent and timeindependent Schrödinger's equation.second
The SI unit of time, represented by the symbol s. The second is one of the seven SI base units, and is defined as 919216311770 periods of a certain kind of electromagnetic radiation emitted by caesium-133 atoms. [DM.1]
translational quantum states
The allowed quantum states of a particle moving with translational motion and confined to a container with rigid walls. [QPM.1]
molar heat capacity
The amount of energy required to raise the temperature of 11mole of a specified substance by 11K (generally under specified conditions, such as constant pressure, or constant volume). The SI unit of molar heat capacity is the J1K−11mol−1. [CPM.3]
intensity (of a wave)
The amount of energy, carried by a wave, per unit time per unit area perpendicular to the direction of motion. It is proportional to the square of the amplitude of the wave. [DFW.2]
visual angle
The angle subtended at the eye by an extended object (or image). It is a way of expressing the object's apparent size. [DFW.3]
driving frequency
The angular frequency, Ω, of the periodic force used to supply energy to a driven damped harmonic oscillator. [PM.2]
antiquark
The antiparticle of a quark. [QPM.2]
Rutherford model of the atom
The atomic model put forward by Ernest Rutherford, in which the electrons are assumed to orbit outside a tiny core or nucleus which contains all the positive charge and almost all the mass of the atom. [QPI.1]
visual axis (of the eye)
The axis within the eye that links the centre of the eyelens system to the fovea. [DFW.3]
domain wall
The boundary between two neighbouring domains in a ferromagnetic material and is typically only a few atoms in thickness. [SFP.4]
Fermi level
The boundary line on an energy-level diagram between filled states and unfilled states for a system of fermions in thermal equilibrium at 01K. The Fermi level occurs at an energy equal to the Fermi energy EF. [QPM.1]
statics
The branch of dynamics that deals with systems at rest. [PM.4]
fluid statics
The branch of fluid mechanics that studies fluids that are in a state of rest, and the forces they exert on immersed solid objects. Fluid statics is also called hydrostatics, even if the fluid involved is not water. [CPM.4]
kinematics
The branch of mechanics concerned with motion and its description, but not its causes. [DM.1; PM.1]
relativistic physics
The branch of physics dealing with situations in which Einstein's special theory of relativity or general theory of relativity must be applied. [DFW.4]
particle physics
The branch of physics that concerns the fundamental constituents of matter, and the manner in which those constituents interact. In practice, particle physics uses the methods of quantum physics to study all structures of sub-nuclear size, including protons and neutrons (which are known to contain quarks) and electrons (which have no known internal structure). The 'real' particles that are the concern of particle physics are sometimes referred to as 'elementary particles', in order to distinguish them from the 'ideal' particles of classical physics.pascal$The SI unit of pressure, represented by the symbol Pa, and defined by the relation 11Pa = 11N1m−2. [PM.1; CPM.1]
electromagnetism
The branch of physics that encompasses all electrical and magnetic phenomena, including the interactions of charges and magnets with electricand magnetic fields, and the production and propagation of electromagnetic waves. [RU.1; SFP.4]
32interference fringes
The bright and dark regions that make up the observed interference pattern caused by the constructive and destructive interference of two or more coherent waves. (See also single-slit diffraction pattern and double-slit diffraction pattern.) [DFW.2]
grating spacing
The centre-to-centre separation of adjacent slits in a diffraction grating. [DFW.2]
impulse
The change of momentum produced when a given force (not necessarily constant) acts over a given time. If the force F is constant and it acts for a time interval ∆t, then the impulse that it imparts will be F1∆t. [PM.3]
locality
The characteristic of a physical theory which implies the absence of faster than light connections that would enable a result obtained at one point at time t, to influence a result obtained at any other point, a distance d away, at any time earlier than t + d/c. [QPI.4]
spherical symmetry
The characteristic of a system whereby some property (e.g. its density) depends only on the distance from a specified point (usually the centre of the system). [PM.1; QPI.3]
electromagnetic spectrum
The complete range of electromagnetic radiation, ranging from gamma rays at short wavelengths (high frequencies) through X-rays, ultraviolet radiation, visible light, infrared radiation and microwaves to radio waves at long wavelengths (lowfrequencies). [DFW.2]
isothermal condition
The condition PV = I that may be used to specify a particular isothermal process in a given quantity of ideal gas. The parameter I = nRT will have a constant value for any particular isothermal process, but will have different values for isothermal processes that take place at different temperatures. [CPM.3]
far-point adjustment
The condition in which a magnifying glass, microscope or telescope positions the final image (to be observed by the eye) at infinity (i.e. at the normal eye's far-point). The angular magnificationis slightly greater in near-point adjustment than in farpoint adjustment, but the eye is more relaxed in this latter adjustment. [DFW.3]
53rotational equilibrium
The condition in which a system is free from any net external torque, so that∑ = 0iGi.The angular momentum of such a system will be constant. [PM.4]
reverse bias
The condition in which an external voltage is applied across a p-n junction so as to increase the electric field in the depletion layer and suppress the diffusion current flowing across that layer. In reverse bias, the positive terminal of the external voltage source is connected to the n-type material and the negative terminal to the p-type. [QPM.2]
earthed
The condition of a body connected to Earth by means of a conductor. The electric potential of such a body is equal to that of the Earth. [SFP.2]
mechanical equilibrium condition
The conditions∑ = 0iFi$And4∑ = 0iΓ i.which ensure that a system is free from any net external force and any net external torque. Both the linear momentum and the angular momentum of such a system will be constant. [PM.4]
Avogadro's hypothesis
The conjecture, now well established, that; equal volumes of different gases, at the same temperature and pressure, contain the same number of molecules. [CPM.1]
Planck's constant
The constant h (= 6.626 × 10−341J1s) introduced by Max Planck to explain the radiation emitted by blackbodies. It also appears in Einstein's theory of the photoelectric effect and in the Planck-Einstein formula. In fact, it appears in practically every equation of quantum mechanics but never in those of classical physics. [RU.1; QPI.1]
15damping constant
The constant of proportionality bthat relates the strength of the damping force to the velocity of the oscillator in the case of a damped harmonic oscillator. (Note that some authors use the term damping constant to mean b/m.) [PM.2]
spring constant
The constant of proportionality ksbetween the restoring force Fx and the extension x for an ideal spring that obeys Hooke's law; Fx = −ksx. [PM.1]
coefficient of dynamic viscosity
The constant of proportionality η in the relation=AFxx∆∆×vηbetween the magnitude of the viscous force per unit area, F/A, acting on each of two adjacent layers of fluid, and the magnitude of the velocity gradient at the interface between those layers. (Note that ∆vx/∆xprovides an approximation to the exact velocity gradient dvx/dx.)The value of η depends on the relative difficulty with which a given fluid flows, and hence the resistance that an object encounters in moving through that fluid. According to Stokes' law, when a sphere of radius Rmoves through a fluid of viscosity η at constant speed v, the force which opposes that motion is of magnitude F = 6πηRv. The coefficient of dynamic viscosity is sometimes simply referred to as the coefficient of viscosity, or just the viscosity of the fluid. The SI unit of coefficient of viscosity is N1s1m−2. [PM.1; CPM.4]
phase difference
The difference between the phase of two or more waves or oscillations, under specified conditions. Two or more waves are said to be 'in phase' at a particular point if their phase difference at that point is always zero. Two oscillations with the same frequency, such as x1 = A1sin(ω0t + φ1)$And4x2 = A1sin(ω0t + φ2)are said to be 'in phase' if their phase difference φ2− φ1is zero. 4[DM.3; DFW.2]
path difference
The difference in length of two specified routes. If the two routes join different points in a coherent source to the same point in an image, then constructive or destructive interference can take place between waves following those routes. 4[DFW.2]
induced current
The electric current produced as a result of electromagnetic induction. An induced current may be produced as a result of the relative movement between a conducting wire and a magnetic field, or by a changing magnetic field. [DFW.1]
valence electrons
The electrons in the outer shells or subshells of atoms that are responsible for chemical bonding and the conduction of electricity in metals. [QPM.2]
electrostatic potential energy of two point charges (in free space)
The electrostatic potential energy Eel of a point charge q1 due to its electrostatic interaction with another point charge q2, separated from it by a distance r in a vacuum, isrq qEπ 0=4 ε1 2el ,where ε0 is the permittivity of free space and, by convention, Eel is taken to be zero when r = ∞.4[SFP.2]
Fermi energy
The energy EF of the highest occupied state in a system of fermions in thermal equilibrium at 01K. For a system of fermions in thermal equilibrium at temperature T > 01K, the Fermi energy EF is the energy at which the Fermi occupation factor equals 21. [QPM.1]
kinetic energy
The energy that a body possesses by virtue of its motion. See translational kinetic energy and rotational kinetic energy. [RU.1; PM.2]
environment
The environment of a system is the rest of the Universe, not including the system. [CPM.3]
equation of continuity
The equation that describes the law of conservation of mass in an ideal fluid. [CPM.4]
Maxwell speed distribution
The equilibrium speed distribution function for molecules in a gas at (absolute) temperature T:m kTkTmf2 / 23/ 22e2( ) 4vv v−⎟×⎠⎞⎜⎝⎛π= πwhere m and v are the mass and speed of the molecules, and k is Boltzmann's constant. The product ƒ(v)1∆v is the probability of a single molecule having translational energy between v and v + ∆v. [CPM.2]
eyepiece
The eyepiece lens in a microscope or telescope. [DFW.3]
resultant force
The force obtained by combining two or more other forces using the operation of vectoraddition. When two or more forces act on a particle, their net effect is the same as that of their resultant force acting alone. 4[PM.1]
quadratic equation formula
The formulaab b acx242− ± −=that determines the two solutions to any quadratic equation expressed in the form ax2 + bx + c = 0. [DM.2]
fractional frequency
The fraction of times a specified outcome occurs in a finite set of attempts. [CPM.2]
compressibility
The fractional decrease in volume of a substance per unit increase in the pressure acting on it, under specified conditions (e.g. at constant temperature). [CPM.1]
isobaric expansivity
The fractional increase in volume of a system when its temperature is increased at constant pressure. [CPM.1]
cyclotron frequency
The frequency, fC, of the circular or helical motion of a charged particle in a uniform magnetic field. It depends only on the magnitude of the particle's charge to mass ratio |1q1|1/1m and the magnetic field strength B:mq Bfπ| |=2C. [SFP.4]
circle
The geometrical figure formed from all points in a plane that are at a common distance from a given point. The given point is called the centre of the circle, and the common distance is called the radius of the circle. (See also equation of a circle.) [DM.3]
gravitational field due to a point mass
The gravitational field due to a point mass is spherically symmetric around the mass. If a mass M is placed at the origin, the gravitational field at a point specified by the position vector r isg( ) r rˆ2r−GM =where rˆ is a unit vector in the direction of r and G is the universal gravitational constant. Thus, the magnitude of the gravitational field depends only on the distance r from the point mass and is directed towards that mass. [SFP.1]
weight
The gravitational force that acts on an object as a result of its mass. The term is usually used in the context of objects that are close to the Earth's surface, in which case, the weight acts vertically downwards and has magnitude mg, where m is the object's mass and g is the magnitude of the acceleration due togravity. [PM.1]
heat capacity at constant volume
The heat capacityof a body when its volume is kept constant. [CPM.3]
molar internal energy
The internal energy per moleof a pure substance. The SI unit of molar internal energy is the J11mol−1. [CPM.1]
time of flight
The interval of time between the launch of a projectile and the end of its flight. [DM.2]
Poiseuille flow
The kind of steady flow exhibited by an ideal fluid passing through a pipe. [CPM.4]
translational kinetic energy
The kinetic energyassociated with the translational motion of a body. For a particle of mass m travelling with speed v, the translational kinetic energy is221Etrans = mv .For a rigid body of mass M,22CM1Etrans = Mvwhere vCM is the speed of the body's centre of mass. In the case of a molecule, the translational energy is associated with motion of the centre of mass of the molecule, and does not include energy associated with 63molecular vibrations or rotations (See also relativistic translational kinetic energy.) [PM.2; CPM.2]
field of view
The lateral extent of an object that can be satisfactorily imaged by an optical system. If the system has a large field of view, it means that it can accommodate an object that subtends a large visual angle, αOB. [DFW.3]
arc length
The length of an arc, measured along the arc itself. [DM.3]
objective lens
The lens in a microscope or refracting telescope that receives the incident radiation from the object. Often just called the objective. The objective lens of a telescope is sometimes simply referred to as the objective. 4[DFW.3]
absolute zero of temperature
The lowest conceivable temperature for any system. It is represented by the value 01K on the absolute temperature scale, and corresponds to a temperature of −273.151°C on the Celsius temperature scale. In classical physics, where temperature is a measure of molecular agitation, absolute zero corresponds to all particles being at rest. [CPM.1]
gravitational mass
The mass of a body as determined by the relation Fgrav = GMm/r2. (Contrast with inertial mass.) [PM.1]
work function
The minimum energy required to remove an electron from a solid. [QPI.1]
moment of inertia
The moment of inertia about a given axis for a system of particles, or for a rigid body, is a measure of the distribution of the system's massabout that axis. For a system of particles with masses miat perpendicular distances ri from the axis, the moment of inertia I is=∑imiriI2.A similar expression applies to a rigid body, but in that case, the continuous nature of the mass distribution means that the sum must usually be replaced by a definite integral. The SI unit of moment of inertia is the kg1m2. [PM.4]
relativistic momentum
The momentum of a body according to the special theory of relativity. For a particle of (rest) mass m, travelling with velocity v, the relativistic momentum is1 ( )2 2cm− v=vpAt speeds which are small compared with the speed of light, c, this reduces to the Newtonian expression p = mv. [PM.3; DFW.4; QPM.4]
elliptical orbit
The most general path followed by one particle moving in a closed path around another due to their gravitational interaction. [DM.3]
determinism
The notion that the past completely determines the present, and hence the future. [RU.1]
number density
The number of particles per unit volume, usually represented by the symbol n. The SIunit of number density is m−3. 4[CPM.1]
atomic number
The number of protons in a specified nucleus. The atomic number is usually represented by the symbol Z, and is equal to the difference between the mass number A and the neutron number N, so Z = A −N. All atoms of the same element have the same atomic number. The positive charge on the nucleus is Ze. For a neutral atom, Z is also equal to the number of electrons in the atom. 4[CPM.1; QPI.1; QPI.3; QPM.3]
adiabatic accessibility index
The parameter A that appears in the adiabatic condition for an ideal gas, PV0γ = A, and which determines whether one equilibrium state can be reached from another by an adiabatic process. The adiabatic accessibility index is related to the entropy of the gas, and therefore has a constant value in any reversible adiabatic process. [CPM.3]
streamline
The path of a particle in a fluid. [CPM.4]
interference
The phenomenon arising from thesuperposition of two or more waves derived from an extended, but coherent source. (See also constructive and destructive interference.) [DFW.2]
air resistance
The phenomenon giving rise to aerodynamic drag, whereby the motion of an object through air is opposed. [PM.1]
total internal reflection
The phenomenon in which light, travelling in a medium of relatively high refractive index (e.g. glass), is reflected when it strikes an interface between that medium and a second medium of relatively low refractive index (e.g. air) at an angle of incidence greater than the critical angle. [DFW.2]
universality
The phenomenon whereby different systems may exhibit common behavioural features. [PM.5]
boundary layer separation
The phenomenon whereby the boundary layer of a fluid becomes detached from the solid surface around which it forms. [CPM.4]
realism
The philosophical claim that there is a real world that humans have a common ability to perceive, but which exists independently of those perceptions. Philosophers recognize a number of variations on this basic theme. In the context of quantum mechanics, realism is that characteristic of a theory which implies that microscopic entities possess properties whether or not they are measured. [RU.1; QPI.4]
spectra
The plural of spectrum.
conservation of mechanical energy
The principle that in an isolated system, in which only conservative forces act, the total mechanical energy (i.e. the sum of the kinetic and potential energies) is constant. [PM.2]
conservation of charge
The principle that the total electric charge of any system remains constant, provided that no matter enters or leaves the system. Thus, if a certain amount of positive charge is created in a process, an equal amount of negative charge must also be created. [SFP.1]
central problem of relativity
The problem of determining the coordinate transformation that links two inertial frames of reference in standard configuration. The solution is the Lorentz transformation. [DFW.4]
charge sharing
The process by which an uncharged body can be charged by receiving some of the chargefrom a charged body with which it makes contact. (Compare with induction in electrostatics.). [SFP.1]
resolution
The process of finding a vector's components, along specified directions, from the magnitude and direction of the vector. [DM.2]
heating
The process of transferring heat to or from a system. [CPM.1]
refraction
The process whereby the direction of propagation of a wave passing from one medium to another, is changed as a result of its change of speed. When waves are refracted at a boundary between two media, they obey the law of refraction (Snell's law). [DFW.2]
accommodation
The process whereby the eye adjusts its focal length so as to bring objects at different distances into sharp focus on the retina. [DFW.3]
distance
The quantity that describes the magnitude of the displacement of one point from another. For example, in one dimension, the distance between two points with position x1 and x2 iss = |1sx1| = |1x2− x11|. [DM.1]
decoherence effect
The rapid destruction of coherence between the different parts of the wavefunction of a macroscopic system as a result of the interaction between that system and its environment. This is widely supposed to be responsible for the absence of macroscopic superpositions of the sort made famous by Schrödinger's cat. [QPI.4]
velocity gradient
The rate of change of a component of velocity in a fluid in a chosen direction. [CPM.4]
pressure gradient
The rate of change of pressure with respect to position in a given direction (e.g. dP/dz). [CPM.4]
relative velocity
The rate of change of the displacement of a particle or body from a specified reference point or body. Note that the chosen reference point or body is not required to be stationary. [DM.1]
performance (of a refrigerator)
The ratio of the net amount of heat absorbed by the circulating fluid to the net amount of work done on that fluid. [CPM.3]
efficiency (of a heat engine)
The ratio of the net amount of work done by an engine to the net amount of heat transferred to the engine. [CPM.3]
wavenumber
The reciprocal of the wavelength of a wave, σ = 1/λ. For comparison, see angular wavenumber. [DFW.2]
internal resistance
The resistance of the chemicals and junctions inside a battery. The voltage supplied by the battery is given by V = VEMF − ir, where VEMF is the battery's electromotive force, i is the current drawn from the battery and r is the internal resistance of the battery. [SFP.3]
Cartesian components
The scalar quantities required to specify a vector relative to a Cartesian coordinate system. For example, a vector v may be specified relative to a three-dimensional Cartesian coordinate system, with axes x, y and z, by determining the projection of v in the x-, y- and z- directions. These projections are the Cartesian components vx, vy, and vz, and we can write v = (vx, vy, vz). The term 'Cartesian components' is often abbreviated to 'components'. [DM.2]
thermal scattering
The scattering of electrons caused by the thermal vibrations of lattice ions in a metal. This makes a contribution to the resistivity of the material which increases as the temperature rises and the thermal agitation of the lattice ions increases. (See also defect scattering.) [QPM.2]
simple harmonic motion equation
The second-orderdifferential equationd2x(t)/dt2 = −ω02x(t)which has the general solution x(t) = A1sin(ω0t + φ). [DM.3]
process
The sequence of changes taking place in a system as it makes a transition from one state to another. [CPM.3]
energy bands
The sets of closely spaced energy levels, occupied by electrons in solids, that are separated from one another by energy gaps according to the band theory of solids. [QPM.2]
resolving power of the eye
The smallest angle of separation of two point-source objects at which the eye can still distinguish them as two distinct objects. [DFW.3]
distance of closest approach
The smallest distance between an incident particle and its target. It is exemplified by the smallest distance between an α-particle and the centre of a target nucleus in a head-on collision, i.e. one with an impact parameter of zero. [QPI.1]
image
The spatial pattern of light produced by a lensor mirror, which is as accurate a reproduction as possible (apart from a scaling factor and a possible change of orientation) of the pattern distribution within the object. See real image and virtual image. [DFW.3]
blackbody spectrum
The spectrum (intensity of radiation in a small wavelength range ∆λ at each wavelength λ) emitted by a blackbody. [QPI.1]
instantaneous speed
The speed of an object at a particular instant. See speed. [DM.1]
most probable speed
The speed that is most likely for a collection of molecules, corresponding to the peak in the speed distribution function. [CPM.2]
square
The square of a quantity is the result of multiplying the quantity by itself, for examplex2 = x × x. [DM.1]
dark adapted
The state of the eye, brought about by subjecting it to a lengthy period of extremely low light level, in which the pupil has dilated to its maximum diameter (typically about 81mm). [DFW.3]
spectroscopy
The study of spectra, particularly for the purposes of chemical analysis. It was an area of much scientific activity in the second half of the nineteenth century. Its techniques were further extended and refined throughout the twentieth century and remain crucial to chemical analysis and to many other areas of physical investigation. [QPI.1]
dynamics
The study of the relation between forcesand changes in motion. [PM.1]
mechanical energy
The sum of kinetic energy and potential energy of a body or system. [PM.2]
tangent
The tangent to a curve at a point P is a straight line touching the curve at P, but not crossing it. The tangent to a graph has the same gradient as the graph at the point of contact. 4[DM.1]
state variable
The term used to describe any property of a system that depends only on the equilibrium state of the system, and not on how that equilibrium state was reached. (See function of state.) [CPM.3]
function of state
The term used to describe any property of a system that depends only on the equilibrium state of the system, and not on how that equilibrium state was reached. Examples include internal energy and entropy. [CPM.3]
transient currents
The time-varying electric currents(usually of short duration) that build up or decay away in electrical circuits as a result of one-off events, such as the opening or closing of a switch. An example arises when a solenoid is connected to (or disconnected from) a source of constant EMF, such as a battery. Both the growth and decay of the current are described by exponential functions which take the form( ) (1 e )bat Rt/ LRVi t−− ⎟⎟⎠⎞⎜⎜⎝⎛=for growth of current, andRt LRVi tbat /( ) e−⎟⎟⎠⎞⎜⎜⎝⎛=for decay of current. The time constant for each of these processes is L/R, where L is the coefficient of selfinductance of the solenoid, and R is the resistance of the circuit. [DFW.1]
relativistic energy
The total energy of a body according to the special theory of relativity. For a free particle of (rest) mass m travelling with speed v1 ( )2 22cmc E− v= .The relativistic energy of such a particle is the sum of its relativistic translational kinetic energy and its mass energy. [DFW.4; QPM.4]
mass number
The total number of protons and neutrons in a specified nucleus. The mass number is usually represented by the symbol A, and is equal to the sum of the atomic number Z and the neutron number N, so A = Z + N. 4[CPM.4; QPI.3; QPM.3]
relativistic translational kinetic energy
The translational kinetic energy of a body according to the special theory of relativity. For a particle of relativistic energy Eand rest energy E0, the relativistic kinetic energy is E − E0 and is therefore given by.(1 )22 22trans mccmc E −−=vAt speeds which are small compared with the speed of light, c, this reduces to the Newtonian expression Etrans = mv2/2. [DFW.4 QPM.4]
cornea
The transparent front part of the eye casing. It is a component of the complete eyelens system; together with the aqueous humour, it contributes the major part of the eye's focusing power: the cornea + aqueous humour combination acts as a fixed focal lengthconverging lens with a power of about 401dioptres. [DFW.3]
centre of mass
The unique point associated with any given rigid body (which does not necessarily lie within the body) with the property that if any unbalanced force acting on the body has a line of action that passes through the centre of mass, then the only effect of that force will be to cause translational acceleration of thebody. If the total external force acting on a body is F, the acceleration of the centre of mass is a = F/m, where m is the total mass of the body. So, if the body experiences no net external force (e.g. if it is isolated), its centre of mass moves with constant velocity. The centre of mass can therefore be regarded as the point at which Newton's laws for particle motion can most easily be applied to rigid bodies. [PM.1]
turbulence
The unsteady and chaotic flow that occurs in fluids at Reynolds numbers a few thousand or greater. [CPM.4]
upthrust
The upward force on a body that is partly or wholly immersed in a fluid. The existence of the upthrust is implied by Archimedes' principle. [CPM.4]
molar volume
The volume per mole of a pure substance. The SI unit of molar volume is the m31mol−1. [CPM.1]
de Broglie wavelength
The wavelength (given by the de Broglie formula) which de Broglie's theory of wave-particle duality assigns to a material particle of given momentum. [QPI.1]
magic numbers
There are more stable nuclei with either the atomic number Z or neutron number N equal to one of the numbers 2, 8, 20, 28, 50, 82 and 126, than might be expected. These nuclei are called magic nuclei. The numbers are called magic numbers and can be understood in the context of the nuclear shell model. [QPM.3]
cosmic background radiation
Thermal radiation at a temperature of about 31K which bathes the whole Universe. It reaches its peak intensity in the microwave part of the spectrum and is sometimes referred to as cosmic microwave background radiation for that reason. It is thought to consist of the cooled remnant of the high temperature thermal radiation that was in thermal equilibrium with cosmic matter for the first 30010001years or so of the Universe's existence. The cooling is a direct consequence of the expansion of the Universe. [QPM.1]
energy levels
These are the allowed energies of a particle in a quantum-mechanical system. If the particle is in a bound state, the energy levels are discrete. If the particle is not bound they form a continuum. Do not confuse energy levels with quantum states. [QPI.1]
Magnus effect
This effect whereby a spinning object, moving through a fluid, experiences a transverse force, perpendicular to its direction of motion and to its angular velocity. [CPM.4]
Newtonian mechanics
This is a branch of physics which attempts to explain the motion of objects in terms of the forces acting on them. It is based on Newton'slaws of motion and incorporates other important principles, such as the laws of conservation of energy, conservation of linear momentum, and conservation ofangular momentum. [PM.1]
Boltzmann's constant
This is k = 1.381 × 10−231J1K−1,the constant that relates temperatures to characteristic energies. In classical physics, the average translational energy of a molecule in a gas that is in thermal equilibrium at (absolute) temperature T is given by 3kT/2. [CPM.1]
element
Traditionally, a substance which cannot be divided by chemical means, heating or the passage of an electric current. More specifically, a sample of any given element consists of matter entirely composed of atoms with the same number of protons in their nuclei. [CPM.1]
space-time conjunction
Two events that occur together in space and time. All observers will agree that the events constitute a conjunction, though different observers may assign different coordinates to that conjunction. [DFW.4]
epilayers
Very thin layers of one kind of crystalline material grown on top of another crystal. These layers may be the same except for a different doping or they may consist of totally different materials. [QPM.2]
equivalent lens
When two or more thin lenses are placed in contact (i.e. the separation between the lenses is negligible compared with their focal lengths), they can be treated as a single equivalent lens with a focal lengthfequiv, given by 1/1fequiv = 1/1f1 + 1/1f2 + ..., or an equivalent power Pequiv, given by P1 + P2 + .... This latter format is very convenient in ophthalmology. [DFW.3]
(b) In the context of state space; the trajectory of an evolving system is the path it traces out in state space. [PM.5]
...
ellipse
A closed curve shaped like a flattened circle. In Cartesian coordinates, the standard form of the equation of an ellipse centred on the origin is12222+ =byaxwhere a and b are constants, called respectively the semimajor axis and the semiminor axis, that characterize a particular ellipse. The ellipse is a member of the family of curves known as conic sections. (See also eccentricity and focus (of an ellipse).) [DM.3]
superelastic collision
A collision in which the kinetic energy increases, typically as a result of the release of potential energy. [PM.3]
relativistic collision
A collision involving sufficiently high speeds that its analysis requires the use of the relativistic relations for momentum and energy rather than their Newtonian counterparts. Relativistic collisions are often inelastic and are characterized by the creation of new particles and an associated increase in mass energy (at the expense of kinetic energy). [PM.3]
electrode
A conducting plate at which charged particles (usually electrons) are collected or emitted in a cell, battery, vacuum electronic device, etc. A positive electrode is called an anode, a negative electrode is called a cathode.electrolyte$A liquid that conducts electricity by virtue of the presence of ions in solution. [SFP.3]
solar wind
A continuous (though not steady) stream of charged particles, mostly protons and electrons, emanating from the Sun. The solar wind helps shape the Earth's magnetosphere. [SFP.4]
spherical polar coordinate system
A coordinate system in which the position of a point is given by the three coordinates (r, θ, φ) where r is the distance from the origin, θ is the angle that the position vector r of the point makes to the z-axis, and φ is the angle between the x-axis and the projection of r on to the xy-plane. This coordinate system is particularly useful for systems that exhibit spherical symmetry, since the quantities associated with that system depend only on r and not on θ or φ. [QPI.3]
parabola
A curve which may be described by an equation of the form y = ax2 + bx + c where a, b and care constants, and a is non-zero. The parabola belongs to the family of curves known as conic sections, and is produced by the intersection of a cone and a plane inclined parallel to one of the sloping sides of the cone. [DM.2]
cyclotron
A cyclic accelerator in which a vertical magnetic field is used to bend the path of particles that circulate within two horizontal 'dee'-shaped metal cavities. The dees are separated by a small gap and are maintained at opposite voltages so that a horizontal electric field exists between them. In order to ensure that the electric field always causes the particles to speed up rather than slow down, it is necessary to apply an alternating voltage to the dees. The cyclotron is not suitable for accelerating particles to relativistic energies. [QPM.4]
short-sightedness
A defect of vision in which the far point of the eye is considerably closer than infinity (and the near point much closer than the normal near point of 2501mm). As a result the eye is unable to focus on distant objects (the eye is too strong, and light from an object located further away than the far point would be focused in front of the retina). Short-sightedness is known technically as myopia. (See also presbyopia.) [DFW.3]
long-sightedness
A defect of vision in which the near point of the eye is considerably further away than the normal near point of 2501mm (and the far point 'beyond infinity'). As a result the eye is unable to focus on near objects (the eye is too weak, and light from an object located at the normal near point would be focused beyond the back of the eyeball). Long-sightedness is known technically as hyperopia or hypermetropia. [DFW.3]
presbyopia
A defect of vision, common in older age, caused by the eye muscles weakening and the eyelens tissues stiffening. The most noticeable effect is to cause loss of close vision (though in practice the whole range of accommodation is reduced), thus requiring the prescription of reading glasses or bifocal spectacles. Compare with long-sightedness and short-sightedness. [DFW.3]
model
A description of a system or process that aims to capture the essence of the true situation but incorporates various simplifications or idealizations. In physics, models are often of a mathematical nature, and are frequently designed to make mathematical analysis tractable. [DM.1]
bubble chamber
A device for detecting elementary particles, based on observing the trails of tiny bubbles left by charged particles as they pass through a superheated liquid (i.e. a liquid that is temporarily above its boiling temperature). 4[QPM.4]
interferometer
A device that can be used to measure lengths or changes in length (hence speed) very accurately by means of interference effects. (See also Michelson-Morley experiment.) [DFW.2]
heat engine
A device that converts heat into work. [CPM.3]
free-body diagram
A diagram used in the analysis of mechanical systems that shows only a body of interest and the forces that act upon it. [PM.1]
lepton number
A dimensionless quantity that is conserved in all known interactions. It is usually given the symbol L and all leptons (and antileptons) have nonzero lepton number. Now regarded as the sum of the electron number, muon number and tauon number, the lepton number of the electron and the electron neutrinois L = 1, while that of the positron is L = −1. [QPM.4]
centrifugal force
A fictitious force that may be used to account for certain aspects of the motion of bodies observed from a rotating (non-inertial) frame of reference. The effect of the centrifugal force is to cause bodies to accelerate radially outwards from the axis of rotation. By introducing such fictitious forces, the motion of the bodies may be made to conform with the predictions of Newton's laws, which do not, strictly speaking, apply in such frames. (See also Coriolis force.) [PM.1]
uniform field
A field that has the same value (and, in the case of a vector field, the same direction) at all points within some specified region of space. [SFP.1]
electromagnetic wave
A fluctuating pattern of electric and magnetic fields, in which each field takes the form of a wave. At any point in an electromagnetic wave, the electric and magnetic fields are mutually perpendicular, and each field is also perpendicular to the direction of propagation of the wave. The existence of such waves is implied by Maxwell's equations, which also predict that the waves will travel through a vacuum at the speed of light. Electromagnetic waves of appropriate wavelength (or frequency) may be used to model each of the kinds of electromagnetic radiationthat comprise the electromagnetic spectrum. [DFW.2]
impulsive force
A force that acts for a short time, such as the force between colliding rigid bodies. (See impulse.) [PM.3]
viscous force
A force that tends to reduce the relative velocity of two neighbouring layers of a fluid. The magnitude of the force is proportional to the area of the interface between the two layers, and to the magnitude of the velocity gradient at the interface. [CPM.4]
non-conservative force
A force which is not a conservative force, and which, therefore, cannot be associated with a unique potential energy at every point. The work done by such a force when its point of application moves from one place to another is dependent on the path followed. Frictional forces are examples of non-conservative forces. [PM.2]
uniform motion
A form of motion in which the velocity does not change with time. See uniform motion equations. [DM.1; DM.2]
translational motion
A form of motion that causes every point of a rigid body to move the same distance in the same direction, and which should be contrasted with rotational motion. [PM.1]
electron capture
A form of β-decay in which a nucleus absorbs one of its orbiting electrons, causing a proton to become a neutron and a neutrino to be emitted. [QPM.3]
quadratic function
A function of the form ƒ(x) = ax2+ bx + c with a, b and c all constants. [DM.1]
response function
A function that specifies how rapidly one property of a macroscopic system varies with respect to another under specified conditions. Response functions are usually defined in such a way that they characterize the material under study, and are independent of the shape and size of any particular specimen. Examples include the isobaric expansivityand the isothermal compressibility. [CPM.1]
vitreous humour
A gelatinous material within the eye which fills the central volume of the eyeball between the eyelens and the retina. [DFW.3]
decay
A general process whereby an (unstable) particle can spontaneously change into two or more other particles. 4[QPM.4]
speed-time graph
A graph showing the speed of a body (plotted vertically) against time (plotted horizontally). [DM.1]
upsilon particle
A kind of elementary particle. A meson, represented by the symbol ϒ, consisting of a bottom and an antibottom quark (b ). b 4[QPM.4]
psi particle
A kind of elementary particle. A relatively long-lived meson (represented by the symbol ψ) consisting of a charm and an anticharm quark (cc ). The discovery of the psi particle (as a very narrow resonance) provided the first direct evidence of the existence of the charm quark. 4[QPM.4]
solar cell
A large area p-n junction used to generate electrical power by absorbing energy from light, normally sunlight. [QPM.2]
Lorentz force law
A law stating that; a particle of charge q, moving with velocity v at a point specified by the position vector r, is subject to a force F = q[e(r) + v × B(r)]
converging lens
A lens that is thicker at its centre than it is at its edges. Such a lens is also called a convex lens, or a positive lens, and has the property that it will increase the convergence (or reduce the divergence) of an incident wavefront. In the real-is-positive convention, a converging lens always has a positive focal length. [DFW.3]
diverging lens
A lens that is thinner at its centre than at its edges. It has the property that it will increase the divergence (or reduce the convergence) of an incident wavefront. Also called a concave lens, or a negative lens. In the real-is-positive convention, a diverging lens always has a negative focal length. [DFW.3]
spherical lens
A lens whose surfaces are parts of spheres. Contrast with cylindrical lens. [DFW.3]
thin lens
A lens whose thickness is small compared with its focal length. [DFW.3]
wavefront
A line (in two dimensions) or a surface (in three dimensions) that connects points in a wave that have the same phase. [DFW.2]
semimajor axis
A line segment from the centre of an ellipse to a point on the ellipse, such that the line has the maximum possible length. [DM.3]
semiminor axis
A line segment from the centre of an ellipse to a point on the ellipse, such that the line has the minimum possible length. [DM.3]
line of action
A line that passes through the point of application of a force, and is parallel to the direction in which the force acts. [PM.1]
sound wave
A longitudinal wave with a frequencybetween about 201Hz and 2010001Hz, that might be the direct cause of the phenomenon perceived as sound. Such waves can travel through a gas, liquid or solid. [DFW.2]
pressure
A macroscopic property of a system (such as a fluid), defined as the magnitude of the perpendicular force per unit area exerted by the system on a planar surface. In the case of a fluid, the pressure can be determined at any point by introducing pressure detectors that move with the fluid. The SI unit of pressure is the pascal (Pa), where 11Pa = 11N1m−2. [PM.1; CPM.1; CPM.4]
quadratic map
A map in which each value has two possible predecessors. All quadratic maps exhibit chaos. [PM.5]
optic nerve
A mass of connected nerve fibres which links the retina of the eye to the brain. [DFW.3]
Pythagoras' theorem
A mathematical result, concerning the lengths of the sides of a right-angled triangle, which states that: the square of the hypotenuse is equal to the sum of the squares of the other two sides. (The hypotenuse is opposite the right angle and is always the longest side.) [DM.2]
thermal conductivity
A measure of a material's ability to conduct heat. The thermal conductivity κ of a material is numerically equal to the rate at which heat would flow through a slab of the material of length 11m and cross-sectional area 11m2, when the temperature difference across its ends is 11K. The units of thermal conductivity are W1m−11K−1. [QPM.2]
eccentricity
A measure of how much an ellipsedeparts from a circle. The eccentricity e of an ellipse with semimajor axis a and semiminor axis b is given by2 21a bae = − . [DM.3]
Drude's free-electron model
A model in which the free electrons in a metal are treated as a classical gas with a Maxwell-Boltzmann energy distribution. The electrons are assumed not to interact with one another but to occasionally collide with the lattice ions. [QPM.1]
logistic map
A non-linear rule (for turning one set of values into another) that may be written in the form, xn+1 = kxn(1 − xn). [PM.5]
non-linear map
A non-linear rule for turning one set of values into another. An example of such a non-linear rule is y = kx(1 − x) (the basis of the logistic map) but almost any other rule would serve as an example provided it could not be written in the form y = mx + c, where m and c are constants. [PM.5]
Cooper pair
A pair formed from two electrons in quantum states with similar wavefunctions, but characterized by wave propagation in opposite directions, k and −k, and opposite spin states. All the conduction electrons in a superconductor are bound in Cooper pairs at 01K, but the pairing gradually disappears as the temperature rises towards the superconducting transition temperature TC, due to thermal excitation across the superconducting energy gap. [QPM.2]
strange particle
A particle that possesses a non-zero value of strangeness. Examples include the kaons (K+, K−, K0, 0K ), the lambda (Λ0), the sigmas (Σ+, Σ−, Σ0) and the xi or cascade particles (Ξ−, Ξ0). [QPM.4]
Hohmann transfer orbit
A path, ideally part of an elliptical orbit, along which a space vehicle can travel from one planet to another with minimum expenditure of fuel. [DM.3]
virtual photon
A photon that is exchanged in a fundamental electromagnetic interaction. Such photons appear as exchange particles in Feynman diagrams and are not required to comply with the usual (relativistic) relationship between energy and momentum for a massless particle. 4[QPM.4]
three-dimensional infinite square well
A potential (energy) well in three-dimensional space used to model a container with rigid walls. [QPM.1]
kilo
A prefix used to indicate the standard SI multipleof 103. [DM.1]
milli
A prefix used to indicate the standard SI submultiple of 10−3. [DM.1]
correspondence principle
A principle asserting that; in the classical limit (usually associated with large quantum numbers and therefore with macroscopic as opposed to microscopic systems), the predictions of quantum mechanics agree with those of classical physics. [QPI.2]
principle of energy conservation
A principle asserting that; the total energy of the Universe (i.e. a systemand its environment) is constant. [CPM.3]
principle of entropy increase
A principle asserting that; there exists a function of state, known as entropy, which increases during any naturally occurring change of an isolated macroscopic system. [CPM.3]
principle of dynamic similarity
A principle asserting that; two fluid flows referring to geometrically similar situations, with the same Reynolds number, are similar when each is described in terms of the appropriate scaled variables. [CPM.4]
iteration
A procedure in which a rule is used to generate a sequence of results by using the output from one application of the rule as all or part of the input to another application of the same rule. [PM.5]
deep inelastic scattering
A process in which very high-energy electrons collide with protons and behave (by undergoing relatively large deflections) as though they are striking point-like targets. The implication is that the point-like objects being struck are quarks within the proton. [QPM.4]
colour
A property of quarks that is an essential part of the gauge theory of the strong interaction. Consequently, the theory is called quantum chromodynamics, or QCD. [QPM.4]
spin magnetic quantum number
A quantum number, conventionally represented by the symbol ms, that determines the z-component, Sz, of the intrinsic angular momentum of a particle:Sz = ms".For a particle with spin 21s = (such as an electron) mscan take only two values, 21± ; for a particle with spin 1 (such as a photon), ms can take the values, ±1 or 0. [QPI.3]
spin angular momentum quantum number
A quantum number, conventionally represented by the symbol s, that characterizes the magnitude S of the intrinsic angular momentum of a particle:4 S = s(s +1) ".The spin angular momentum quantum number is often referred to as simply the spin; hence the electron is said to have spin 21, and the photon spin 1. Spin is an inherently quantum property. [QPI.3; QPM.4]
Schmidt telescope
A reflecting telescope that utilizes a Schmidt plate to overcome the spherical aberration of a spherical mirror. [DFW.3]
Keplerian telescope
A refracting telescope that uses converging lenses for both the eyepiece and the objective. (See also telescope.) [DFW.3]
domain
A region in a ferromagnetic material in which the alignment of atomic magnetic dipoles is practically perfect. In an unmagnetized sample of iron, a typical domain is a few micrometres (10−61m) across. When the iron is magnetized, domains in which the atomic magnetic dipoles are aligned parallel to the applied magnetic field grow, while others shrink. [SFP.4]
strange attractor
A region of state space into which trajectories are attracted, and within which they exhibit chaotic behaviour. [PM.5]
graph
A representation of a function in pictorial form. In the case of a function y(x), the usual procedure is to plot the values of y vertically and the values of xhorizontally. [DM.1]
Hund's rule
A rule describing the order in which quantum states are filled in heavy atoms. It asserts that, in the ground state of an atom, the total spin of the electrons always has its maximum possible value (subject to the Pauli exclusion principle). This means that if two outer-shell electrons have several degeneratestates available to them (corresponding to different values of ml), they will have parallel spins and will therefore occupy states with different values of ml. Thus, in carbon the ground state electronic structure is and not [QPI.3]
right-hand rule
A rule for determining the sense in which the vector product a × b is perpendicular to the vectors a and b. The rule is the following: point the flattened palm and fingers of your right hand in the direction of vector a. Then, keeping your palm and fingers parallel to a, twist your wrist until you can bend your fingers to point in the direction of vector b. Your extended thumb will then point in the direction ofa × b. [PM.4]
linear map
A rule for turning one set of values into another that could form the basis of a linear function. [PM.5]
normalization rule
A rule or condition imposed on a function or a set of related values with the aim of simplifying the interpretation of that function or those values. An example is the requirement that the sum of the probabilities of all the alternative outcomes of a process should equal 1. [CPM.2]
geostationary satellite
A satellite that maintains a fixed position relative to any point on the Earth's surface. (See also Clarke orbit.) [DM.3]
elastic scattering
A scattering process in which the beam and target particles do not change their nature. [QPM.4]
fractal
A self-similar pattern in which enlarging a small part of the pattern produces a new pattern that is similar to the original pattern. [PM.5]
p-type semiconductor
A semiconductor that is doped with sufficient acceptors to ensure that a current can be carried by holes in the valence band. [QPM.2]
Maxwell's equations
A set of equations assembled by James Clerk Maxwell to describe the behaviour of electric and magnetic fields. The equations can be expressed in words as follows:1 The electric flux, due to an electric field, through a closed surface is proportional to the charge contained inside it. (This is related to Coulomb's law.)2 The magnetic flux due to a magnetic field through a closed surface is zero. (This embodies the idea that magnetic monopoles do not exist.)3 The magnitude of the rate of change of the magnetic flux, due to a magnetic field, through a surface is equal to the magnitude of the EMF along the boundary of the surface; the direction of the EMF opposes the change causing it. (This is essentially an expression of Faraday's law and Lenz's law.)4 The average magnetic field along the boundary of a surface depends on the current per unit area inside the surface and on the rate of change of the electric field across the surface. (This recognizes current as one source of magnetic field, and introduces a changing electric field as another.)Equations 3 and 4 embody the two key concepts of electromagnetic induction, namely that 'a changingmagnetic field causes an electric field' and 'a changing electric field causes a magnetic field'. These two effects can be used to predict the existence of electromagnetic radiation, which travels at a fixed speed in a vacuum given by 1 0µ0c = ε , where ε0 and µ0 are the permittivity of free space and the permeability of free space, respectively. [DFW.1]
constant acceleration equations
A set of equations relating the displacement, velocity and acceleration of a uniformly accelerating particle. For a particle accelerating along the x-axis, the equations are221s u t a tx= x+ xu a tx= x+ xvx x x xu 2a s2 2v = +where sx is the displacement of the particle at time tfrom its initial position at time t = 0; the initial velocity (at time t = 0) is ux, and vx is the final velocity at time t.The acceleration is ax and must be constant for the equations to apply. [DM.1]
crystalline solid
A solid in which the equilibrium positions of the constituent atoms form a regularly repeating pattern that exhibits long-range order. Such solids may form spontaneously when a large number of atoms or molecules condenses to form a solid, since they represent the structure of maximum binding energy, and hence of greatest stability. [CPM.1; QPM.2]
ionic solid
A solid, such as sodium chloride, containing positive and negative ions held together by ionic bonds in a crystalline structure. [QPM.2]
torque wrench
A spanner-like tool for applying a specified torque. [PM.4]
equilibrium
A system is said to be in a state of equilibrium if its measurable properties remain constant in time. [RU.1]
monatomic
A term indicating that the basic particles of a pure substance (usually a gas) are single atomsrather than molecules containing two or more atoms. [CPM.2]
elastic
A term used to describe the ability of a body to recover fully from a distortion, as long as it is not stretched too far. [PM.1]
kinetic theory of gases
A theory that accounts for the behaviour of gases in terms of the movement of the molecules of which the gas is composed. [CPM.2]
fovea
A tiny area in the eye, on the back of the retina, where the visual detectors are more densely packed than average. The most acute vision is achieved by focusing the image onto this area of the retina. [DFW.3]
deterministic chaos
A type of behaviour characterized by: (i) Deterministic rules that describe how the state of a system at a particular time determines the state of the system at a later time. (For simple systems the rules may be written down, but many real systems are too complex to allow this.) (ii) Unpredictable outcomes, because a small uncertainty in the initial state of a system causes differences in subsequent behaviour that increase exponentially with time, so after a sufficiently long time the state will be effectively unpredictable. [PM.5]
dislocation
A type of defect in a crystal where, for example, an incomplete sheet of atoms terminates along a line. The movement of dislocations accounts for metals being ductile. [QPM.2]
α-decay (alpha-decay)
A type of radioactive decay in which a nucleus spontaneously emits an α-particle. [QPM.3]
γ-decay (gamma-decay)
A type of radioactive decayprocess in which a nucleus spontaneously emits a γ-ray. This process often involves the decay of an excited daughter nucleus produced by a prior α-decay or β-decay. [QPM.3]
stable equilibrium
A type of static equilibrium in which a system displaced slightly from its original position has a tendency to return to that position. This is the kind of static equilibrium exhibited by a uniform spherical body resting at the bottom of a hollow. [PM.4]
unstable equilibrium
A type of static equilibrium in which a system displaced slightly from its original position, has a tendency to move further away from that position. This is the kind of static equilibrium exhibited by a uniform spherical body resting at the top of a hill. [PM.4]
measured average value
A typical value of some quantity obtained by multiplying each possible value of the quantity by its fractional frequency and adding together all the resulting terms. [CPM.2]
dioptre
A unit used to express the power of a lens and defined as 11D = 11m−1. [DFW.3]
unit vector
A vector of magnitude 1 that serves to indicate a specific direction. Given a displacement vector r, the unit vector in the direction of r is rˆ = r/r. (Note that the magnitude of any unit vector is 1, not 11m, nor even 11unit.) [PM.1; SFP.1]
momentum
A vector quantity, useful in various situations as a measure of a body's tendency to continue in its existing state of rotational or translational motion. See angular momentum and linear momentum for further details. [PM.3]
simple pendulum
A weight (also known as a bob) suspended by a light inelastic string. [DM.3]
principal focus
An alternative name for the focal point of a lens or mirror. (See also prime focus.) [DFW.3]
prime focus
An alternative name for the focal point, particularly of an objective mirror in a reflecting telescope. It is the first point to which parallel rays converge before (possibly) encountering other lenses or mirrors. [DFW.3]
Einstein-Podolsky-Rosen argument
An argument (in the modified form due to Bohm) concerning observations at two separate locations of the spincomponents of a pair of particles in an entangled state. The EPR argument shows that, quantum mechanics as conventionally formulated, includes non-local features and uses this to argue that quantum mechanics is incomplete. (See also Bell's theorem.) [QPI.4]
inductor
An element in an electrical circuit that has a significant coefficient of self-inductance. Inductors often take the form of a solenoid or a coil of wire. [DFW.1]
point object (or source)
An idealized object (or source of light) in an optical system; it has no appreciable spatial extent and thus gives rise to spherical wavefronts. A point object subtends a visual angle of zero. [DFW.3]
test particle
An idealized particle that can be imagined as having such a small mass or charge that it can be introduced into a gravitational field or an electric field, for the purposes of measuring that field, without causing any significant change in the field. [SFP.1]
time-of-flight mass spectrometer
An instrument that measures the masses of ions by giving them a definite translational energy and measuring the time they take to cover a given distance. [CPM.1]
SI
An internationally agreed system of units of measurement. The system employs seven base units(including the metre and the second0) and an unlimited number of derived units obtained by combining the base units in various ways. The system also uses certain standard SI multiples and SI submultiples and recognizes a number of standard symbols and abbreviations. (SI is one of those symbols and stands for Système International.) [DM.1]
magnifying glass
An optical device that, in its simplest form, consists of a single converging lens. In one mode of use, the magnifying glass is held close tothe eye; this permits an increase in the visual anglesubtended by an object by allowing it to be held much closer to the eye than the normal near point while still remaining in focus. The magnifying glass forms an enlarged virtual image of the otherwise too-close object at some point between the eye's near point (near-point adjustment) and far point (1far-point adjustment). This device is sometimes called a simple microscope. [DFW.3]
conservation law
Any law that expresses the constancy in time of a physical quantity (such as energy or momentum) under specified circumstances. Such laws are often referred to as conservation principles. [RU.1; QPM.4]
gluon
Any member of the family of eight spin 1 exchange particles that are, according to quantum chromodynamics (QCD), responsible for mediating the strong interaction. Gluons may be exchanged between quarks or between other gluons (but they have no direct connection with leptons). [QPM.4]
isotope
Any one of a set of atoms that have the same value of the atomic number Z (and hence represent the same element), but different values of the mass number A (and hence different values of the neutron number N). The various isotopes of a given element thus represent different 'versions' of the atom of that element. The mass number and atomic number of an isotope are 33indicated by writing them as a superscript and subscript, respectively, before the relevant chemical symbol. For example, the isotope of silicon with A = 27 and Z = 14 is written Si 2714 . Less formally, this isotope may be referred to as silicon-27. [CPM.1; QPI.3; QPM.3]
quantum system
Any system which is analysed using the formalism of quantum mechanics. [QPI.4]
type II superconductors
Materials from which magnetic flux is not completely excluded in the superconducting state. Typical type II superconductors are very impure alloys or compounds with a complex polycrystalline structure. In all cases the electrons have a very short coherence length. The high-temperature superconductors are an extreme form of type II material. [QPM.2]
down quark
One of the six types of quark. [QPM.4]
selection rules
Rules that govern whether particular radiative transitions are allowed or forbidden. For example, the allowed changes in the quantum numbersof an electron in an atom are restricted to ∆l = ±1 and ∆ml = 0 or ±1. There is no restriction on the change in the value of n. [QPI.3]
Planck's law
See Planck-Einstein formula. [QPI.1]
α-
See alpha.
inductance
See coefficient of self-inductance and coefficient of mutual inductance. [DFW.1]
self-inductance
See coefficient of self-inductance. [DFW.1]
law of conservation of energy
See conservation of energy. [RU.1; PM.2]
principle of conservation of linear momentum
See conservation of linear momentum. [PM.3]
law of conservation of mass
See conservation of mass. [RU.1]
uniform acceleration equations
See constant acceleration equations. [DM.1]
energy gaps
See energy bands. [QPM.2]
general relativity
See general theory of relativity. [DFW.4]
theory of general relativity
See general theory of relativity. [DFW.4]
slope of a graph
See gradient of a graph, which is a synonym. [DM.1]
GUTs
See grand unified theories. [QPM.4]
simple microscope
See magnifying glass. [DFW.3]
elementary particle
See particle.elimination$The process whereby a chosen variable that is common to two or more equations is removed from those equations, in order to produce a relationship between the remaining variables. [DM.1]
periodic time
See period. [DM.3]
superposition
See principle of superposition. [DFW.3]
de Broglie wave
See probability wave. [QPI.2]
constant of proportionality
See proportionality.
pp chain
See proton-proton chain. [QPM.3]
QCD
See quantum chromodynamics. [QPM.4]
QED
See quantum electrodynamics. [QPM.4]
myopia
See short-sightedness. [DFW.3]
s.h.m.
See simple harmonic motion.short-range order$The phenomenon exhibited by some forms of matter, particularly liquids and amorphous solids, in which the near neighbours of a typical atom show some signs of regularity and order in their spatial arrangement, but that order does not extend beyond those near neighbours. (Contrast with longrange order, and see also radial density function.) [CPM.1]
relativity
See special theory of relativity and general theory of relativity. [DFW.4]
56special relativity
See special theory of relativity. [DFW.4]
negative (photographic)
The 'reversed' image produced on photographic film in which bright parts of the object are rendered black (because this is where the exposed silver halide grains are converted into opaque silver) and dark parts of the object are rendered light. [DFW.3]
pupil
The (apparently black) hole at the centre of the eye's iris through which light is admitted to the eye. In a typical human eye, the pupil diameter can be varied from about 21mm (in bright light conditions) to about 81mm (when the eye is dark adapted). [DFW.3]
induced EMF
The EMF produced as a result of electromagnetic induction in accord with Faraday's law. An induced EMF may be produced as a result of the relative movement between a conducting wire and a magnetic field, or by a changing magnetic field. [DFW.1]
farad
The SI unit of capacitance, represented by the symbol F, where 11F = 11C1V−1. [SFP.2]
coulomb
The SI unit of electric charge, represented by the symbol C, where 11C = 11A1s. It follows that the coulomb is the charge transferred by a steady current of one ampere flowing for one second. [SFP.1]
significant figures
The accurately meaningful digits in the value of a physical quantity. The number of significant figures in a value such as 121000 may be ambiguous unless the value is expressed in scientific notation, in which case 1.2 × 104 would indicate 2 significant figures, whereas 1.2000 × 104 would indicate 5 significant figures.silver halide3A generic term used to describe the group of salts in which silver is combined with an element from the halogen group (namely, fluorine, chlorine, bromine, iodine). Photographic emulsions commonly use one of the silver halides AgCl (silver chloride), AgBr (silver bromide) or AgI (silver iodide) as the photosensitive agent. [DFW.3]
iris
The adjustable diaphragm in the human eye, located just in front of the crystalline lens, which gives the eye its characteristic hue. The hole at the centre of the iris, through which light enters the eye, is the eye pupil. [DFW.3]
positron
The antiparticle to the electron. It is represented by the symbol e+. [QPM.4]
drip lines
The boundary lines in the Z-N plane (a plot of atomic number against neutron number), between which all nuclei are expected to be found. [QPM.3]
integral calculus
The branch of mathematics concerned with the analysis and evaluation of (definite) integrals. [PM.2]
calculus
The branch of mathematics concerned with the way in which small changes in one quantity determine, or are determined by, changes in related quantities. [DM.1]
relativistic mechanics
The branch of mechanicsdealing with situations in which Einstein's special theory of relativity or general theory of relativity must be applied. [DFW.4]
space
The collection of all possible positions. [DM.2]
coplanar
The condition in which two or more geometrical objects (e.g. lines or circles) lie in the same plane. [DM.3]
thermal contact
The condition that exists between a system and its environment (or between two bodies) when heat may be exchanged between them. A system that cannot exchange heat with its environment is said to be thermally isolated. [CPM.3]
universal gravitational constant
The constant G = 6.673 × 10−111N1m21kg−2 that appears in Newton'slaw of universal gravitation. [PM.1; SFP.1]
direction of propagation
The direction in which a travelling wave transports energy. [DFW.2]
equilibrium separation
The distance between two particles when they are in equilibrium. An example is the equilibrium distance between two atoms in a diatomic molecule. [CPM.1]
molar latent heat of vaporization
The energy per mole required to vaporize a liquid into a gas, whilst the temperature remains fixed at the boiling temperature.The SI unit of molar latent heat of vaporization is the J11mol−1. 4[CPM.1]
Boltzmann factor
The factor e−E/kT that appears in Boltzmann's distribution law and in the Boltzmann occupation factor. [CPM.2; QPM.1]
ultraviolet catastrophe
The failure of the classical formula for the blackbody spectrum, which fails to show a maximum and wrongly predicts that the energy density in the blackbody spectrum tends to infinity as the wavelength decreases. [QPI.1]
isothermal compressibility
The fractional decrease in volume of a system when the pressure exerted on it is increased at constant temperature. [CPM.1]
gradient of a graph
The gradient of a graph of y (plotted vertically) against x (plotted horizontally) is a measure of how rapidly y changes in response to a change in x, at any point on the graph. If the graph is a straight line, then the gradient is the same at all points, and is given by the ratio ∆y/∆x where ∆y is a change in yand ∆x is the corresponding change in x. If the graph is a curved line, the gradient at any point P on the curve is defined as the gradient of the tangent to the curve at P. The gradient is also equal to the derivative of y with respect to x, dy/dx, evaluated at the point P. [DM.1]
gravitational field
The gravitational field g(r) is a vector quantity that determines the gravitational forcethat would act on any mass placed at the point specified by the position vector r. It is defined as the gravitational force per unit test mass, so if Fgrav is the gravitational force on mass m at point r, then g(r) = Fgrav/m. The gravitational field has both magnitude and direction at each point in space, so it is an example of a vector field, and gravitational fields due to different sources add vectorially at every point. For an important example of a gravitational field see gravitational field due to a point mass. At any point, the gravitational field component in a given direction is equal to minus the gradient of the gravitational potential, Vgrav, in that direction. For example, the x-component and the radial component are given respectively by gx = −dVgrav/dx and gr = −dVgrav/dr. The SI unit of gravitational field is N1kg−1 or (equivalently) m1s−2. [SFP.1, SFP.2]
19eddy currents
The induced currents set up in a solid piece of metal, such as the iron core of a solenoid or transformer. Eddy currents generally dissipate energy, and are deemed to be wasteful. However, they are utilized to good effect in devices such as the induction furnace, where the energy dissipated is used to melt a sample of metal. [DFW.1]
inertial mass
The mass of a body as determined by using Newton's second law via the relation m = F/a. (Contrast with gravitational mass.) [PM.1]
pumping
The mechanism by which a population inversion is maintained on a laser transition in an appropriate medium. There are many different ways to achieve this, such as electrical discharges, irradiation with light, possibly combined with collisional transfer of population to the upper laser level. [QPI.3]
Brownian motion
The microscopic random motion exhibited by small particles suspended in gases or liquids. Einstein recognized that Brownian motion is a result of the incessant bombardment of the observed particle by molecules in the surrounding fluid. [CPM.1]
dimension of a coordinate system
The minimum number of coordinates needed to specify uniquely the position of every point in the region covered by a coordinate system. [DM.1]
escape speed
The minimum speed with which a projectile must be launched if it is to escape completely from the Earth (or any other designated body). Ignoring air resistance, the escape speed from the Earth is given byvescape = E2ERGMand is equal to 1.1 × 1041m1s−1. [PM.2]
period
The minimum time needed for a repetitive action to recur. If the action can be described by a periodic function ƒ(t), then the period T is the smallest value such that ƒ(t + T0) = ƒ(t) for all t. An example is the time T for a simple harmonic oscillator (described by x = A1sin(ω0t + φ)) to complete one full cycle. Other examples include the period of an elliptical orbit, the period of rotation of a spinning body, and (in the context of waves) the time interval between one part of a wave passing a fixed point and the next identical part of the wave passing the same fixed point. [DM.3; DFW.2]
objective mirror
The mirror in a reflecting telescopethat receives the incident radiation from the object. Often simply called the objective. [DFW.3]
horizon of predictability
The number of iterations of an iterated map that must occur before a small change in the initial value leads to significant differences in the sequence of iterates. [PM.5]
diffraction pattern
The pattern of interference fringesproduced by the superposition of waves that have been diffracted by an object such as a diffraction grating. Maxima and minima of intensity in the pattern are caused by constructive interference and destructive interference, respectively. [DFW.2]
period doubling
The phenomenon whereby the period of the limit cycle of a system undergoes a sequence of doublings as the system approaches a state of chaos. [PM.5]
electromagnetic induction
The phenomenon, described by Faraday's law and Lenz's law, by which a changing magnetic flux through a circuit gives rise to an induced EMF around the circuit, and hence an induced current in the circuit. [DFW.1]
retina
The photosensitive surface, on the inner wall of the eyeball, on which the eye focuses its images of the 'outside world'. [DFW.3]
doping
The practice of adding a small carefully controlled amount of impurity to an intrinsic semiconductor material in order to make it an extrinsic semiconductor. [QPM.2]
conservation of linear momentum
The principle that the total linear momentum of any isolated system is constant. [PM.3]
conservation of angular momentum
The principle that, in any system, the total angular momentum about any point remains constant as long as no net external torque about that point acts on the system. [PM.4]
normalization
The process by which a function is scaled (i.e. multiplied by an appropriate constant) so that the resulting normalized function satisfies a specified normalization rule. For example, in the case of the timeindependent wavefunction ψ(x) of a particle confined to the x-axis, normalization is achieved when the area under a graph of |1ψ(x)1|2 against x is equal to 1. [QPI.2]
recombination
The process by which an electron in the conduction band of a solid falls to the valence bandto fill an empty state or hole there, releasing an energy approximately equal to the energy gap. This energy appears in the form of lattice vibrations or, in a lightemitting-diode, as an optical photon. [QPM.2]
magnetization
The process that causes a material, subjected to an applied magnetic field, to produce a magnetic field of its own. [SFP.4]
tension
The property of a stretched elastic body that tends to restore the body to its natural length. Measured in newtons, it is responsible for the tension forces that such a body exerts. [PM.1]
energy
The property of a system that measures its capacity for doing work. The SI unit of energy is the joule, represented by the symbol J where 11J = 11N1m. [PM.2]
ductile
The property, particularly associated with metals, that allows a solid material to be hammered or bent into a new shape and to flow to a limited extent if the applied stress is sufficiently great. [QPM.2]
capacitance
The quantity that describes the ability of a conductor or a system of conductors to store charge by altering its electrostatic potential relative to some agreed reference point. In the case of a two-plate capacitor the capacitance is the ratio of the charge q on one of the plates to the potential difference V between that plate and the other plate: C = q/V. The capacitance of a given capacitor is determined by the geometry and composition of the device and is independent of q and V. Thus, in the case of the parallel plate capacitor again, the capacitance is εrε0A/d, where A is the area of the plates, d is their separation, ε0 is the permittivity of free spaceand εr is the relative permittivity of the medium between them. The SI unit of capacitance is the farad, represented by the symbol F, where11F = 11C1V−1. [SFP.2]
quantum chromodynamics
The quantum field theoryof the strong interaction, so called because it involves the property known as colour. It is often abbreviated to QCD. [QPM.4]
cyclotron radius
The radius of the circle described by a particle undergoing cyclotron motion in a uniform magnetic field. [SFP.4]
depth of field
The range of distances within the object field over which an acceptably in-focus image is produced at a fixed image (or film) plane. [DFW.3]
high-temperature superconductors (HTS)
The type II superconductors, based on complex oxide structures, which have a superconducting transition temperature TCmuch larger than was considered to be possible before 1986. The HTS title is most suitably applied to those materials with a TC above 771K, the boiling temperature of liquid nitrogen. [QPM.2]
instantaneous velocity (vector)
The velocity of an object at a particular instant. See velocity. [DM.2]
wave mechanics
The version of quantum mechanicsdeveloped by Erwin Schrödinger, building on de Broglie's idea of wave-particle duality, and giving a central role to the concept of a wavefunction that satisfies the time-dependent Schrödinger equation. [QPI.2]
axis of rotation
A line that remains at rest in a specified rotation. [PM.4]
adiabatic process
A process in which no heat is transferred. (See also adiabatic condition.) [CPM.3]
adiabatic system
A system in a state of thermal isolation, so that no heat may be transferred to it or from it. [CPM.3]
2action
A term sometimes used to describe one of the forces in a Newton's third-law pair, the other member of the pair being referred to as a reaction. (Beware: action also has other technical meanings, quite different from that given here.) [PM.1]
astronomical unit
A unit of distance, equal to the mean distance between the Earth and the Sun. The astronomical unit is represented by the symbol AU, and its value is given by 11AU = 1.49598 × 10111m. [PM.5]
absolute temperature
Any temperature measured on the absolute temperature scale. [CPM.1]
Bell's theorem
Based on the fact that quantum mechanics predicts that Bell's inequality will be violated, Bell's theorem asserts that: any theory which exhibits both locality and realism cannot replicate all the predictions of quantum mechanics. [QPI.4]
angular acceleration
The (instantaneous) rate of change of angular velocity, dw/dt. It is a vector quantity, sometimes represented by the symbol a, and its SI unit is the rad1s−2. [PM.4]
Avogadro's constant
The number of basic particles (atoms, molecules, ions, etc.) per mole of any substance, Nm = 6.022 × 10231mol−1. This is equal to Avogadro's number per mole. [CPM.1]
amplitude
(a) In the context of an oscillation; the amplitude is the magnitude of the maximum displacement of the oscillator from its equilibrium position. In the particular case of a simple harmonic oscillator described by the equation x(t) = Asin(ωt +φ)the amplitude is represented by the parameter A. [DM.3] (b) In the context of a wave; the amplitude is the maximum magnitude of the disturbance that constitutes 3the wave (e.g. the displacement of a string from its equilibrium position). In the particular case of a simple travelling wave described by the equation y(x,t) = Asin(kx−ωt +φ)the amplitude is represented by the parameter A. [DFW.2]
(b) In more general contexts the principle of superposition asserts that; for certain equations, the linear superposition of any number of solutions to the equation is also a solution to the equation. The equations (including differential equations) to which this principle applies must have a mathematical property known as linearity. The time-dependent Schrödinger equation of quantum mechanics is one of these equations, as is the wave equation of classical physics. Hence the applicability of the principle to waves and timedependent wavefunctions. [QPI.4]
...
(b) In the context of an LC circuit; the natural frequency is the frequency of charge oscillations in the absence of resistance or driving signal. For an LC circuit of inductance L and capacitance C, the natural frequency is ƒ = 1/2π LC 4[DFW.1]
...
(b) In the context of an optical system; a focus is a point at which rays diverging from a single point are brought together again. (See also focal point.) [DFW.3]
...
(b) In the context of optics, the power of a lens is a measure of the 'ray-bending' ability of the lens. It is defined as the reciprocal of the lens's focal length (i.e. P = 1/ƒ). If ƒ is expressed in metres, then P will be measured in dioptres. According to the real-is-positive convention, a diverging lens will have a negative focal length and hence a negative power; a converging lenswill have a positive power. [DFW.3]
...
(b) In the context of particle physics; groups are mathematical structures that characterize certain quantum field theories. Well-known examples include SU(2) and SU(3). [QPM.4]
...
(b) In the context of waves; the speed v of a travelling wave is the product of the wavelength λ and frequency ƒof the wave, so v = ƒλ. (This also represents the speed at which a point of constant phase travels in the direction of propagation of the wave, and may therefore be referred to as the 'phase speed' of the wave.) The speed of light in a vacuum is represented by the symbol c and has a value of 3.00 × 1081m1s−1. [DFW.2]
...
. The magnetic field has both magnitude and direction at each point in space, so it is an example of a vector field, and magnetic fields due to different sources add vectorially at every point. An important example of a magnetic field is that due to an infinitely long, straight wire carrying a steady current i, in which case the magnetic field at a distance r from the wire acts in the plane perpendicular to the wire (in the direction specified by the right-hand grip rule) and has magnituderiB rπ=2( )µ0where µ0 is the permeability of free space. Other important examples include the magnetic field at the centre of a single coil of radius R, carrying a steady current i (in which case the magnitude is Bcentre = µ0i/2R), and the field along the axis of an infinitely long cylindrical solenoid with N/l turns per unit length (in which case the magnitude is B = µ0Ni/l). The SI unit of magnetic field is the tesla, represented by the symbol T, where 11T = 11kg1s−21A−1. (See also magnetic field strength.) [SFP.4]
...
31induction4(a) In the context of electrostatics; induction is the phenomenon whereby a charged object, brought close to an electrically neutral object (without touching it), will cause positive and negative charges in the neutral object to separate, leading to a net attraction between the charged object and the neutral one. (Contrast with charge sharing.) [SFP.1]
...
Boltzmann's principles of statistical mechanics Two principles, formulated by Ludwig Boltzmann at the foundation of statistical mechanics. The principles assert that:1 The only allowed configurations are those with fixed energy, E.2 Each of the allowed configurations are equally likely. 4[CPM.2]
...
If the (constant) acceleration is specified by the vector a = constant, then221s =ut + atv =u+atwhere u is the initial velocity, v is the velocity at time t, and s is the displacement from the initial position (not necessarily the origin) at time t. [DM.2]
...
In quantum mechanics, identical particles are indistinguishable, and a configuration of a system of identical particles is defined by giving the numbers of particles in each quantum state. [QPM.1]
...
energy distribution law for free electrons in metalsSee Pauli's distribution. [QPM.1]
...
focus4(a) In the context of an ellipse; when the equation of the ellipse is written in the standard form, the foci of the ellipse are the two points lying on the xaxis, with x-coordinates ±ae. [DM.3]
...
gravitational potential4 The gravitational potential Vgrav(r) at a point specified by the vector r is the gravitational potential energy per unit mass at that point. So, if Egrav is the gravitational potential energy of a mass m at a point r, the gravitational potential at that point isgrav grav1( ) EmV r = .Gravitational potential has a scalar value at every point in space, so it is an example of a scalar field. The SI unit of gravitational potential is the J1kg−1. An important example of a gravitational potential field is that due to a point mass M located at the origin of a coordinate system:28Vgrav = −GM/rwhere G is the universal gravitational constant and r is the distance from the point mass. Note that, by convention, the gravitational potential energy has been taken to be zero at r = ∞ in this case.Another important example of a gravitational potential field is that close to the surface of the Earth:Vgrav = ghwhere g is the magnitude of the acceleration due to terrestrial gravity and h represents height above the Earth's surface. Note that in this case the gravitational potential has been taken to be zero at the Earth's surface. [SFP.2]
...
groups4(a) In the context of atoms; groups are the vertical columns in the Periodic Table of the elements. The elements in a group are all characterized by the same outer-shell electronic structure. [QPI.3]
...
microscope3An optical device that, in its simplest form, uses an objective lens to produce an enlarged, real image of an object well inside the normal near point of the eye, this real image is viewed through an eyepiece lens, which forms a further enlarged virtual image at some point between the eye's near point (near-point adjustment) and far point (far-point adjustment). This device is sometimes called a compound microscope. [DFW.3]
...
particle4(a) In the context of classical physics; a particle is an object that has no spatial extent and can therefore be thought of as existing at a single point in space. It has no size, shape or internal motion though it may have intrinsic properties such as mass and charge, as well as position, velocity and acceleration. Although the concept of a classical particle is an idealization, the centre of mass of an extended body moves just like a particle with the same mass as the body, subject to the combined effect of the external forces acting on the object. [DM.1; PM.1]
...
power4(a) In the context of mechanics, power is the property of a system that measures the rate at which work is done and energy transferred. (Care must be taken to specify whether the energy is transferred to or from the system.) The SI unit of power is the watt (W), where 11W = 11J1s−1. The instantaneous power delivered by a force F acting on a body moving with velocity v is given by= = F •vtWPdd. [PM.2]
...
principle of superposition4(a) In the context of waves, the principle of superposition asserts that; if two or more waves meet at a point in space, then at each instant of time the net disturbance at that point is given by the sum of the disturbances created by each of the waves individually. [DFW.2]
...
radiation4(a) Specifically, a mechanism of heattransfer in which energy is transferred from one body to another (possibly through a vacuum) by means of light or some other form of electromagnetic radiation. [CPM.3]
...
ray3A directed line drawn perpendicular to a series of successive wavefronts. It can be thought of as giving the local direction of propagation of the wave. See reversibility of light paths. [DFW.2]
...
resonance4(a) In the context of a driven damped oscillator; resonance is the condition in which the oscillator develops oscillations of maximum amplitude for a given level of damping. For a lightly damped harmonic oscillator, this occurs when the driving 52(angular) frequency Ω is close to the system's natural frequency ω00. This is also close to the condition in which the rate at which energy is transferred to the oscillator by the driving force is a maximum. [PM.2]
...
spectrum4(a) In the context of the electromagnetic radiation emitted by atoms or molecules; a spectrum is any detailed representation of the way in which the intensity of the radiation is distributed with respect to wavelength or frequency. A spectrum may be obtained experimentally, as a band of light, using a spectrometeror some similar instrument. Alternatively the spectrum may be presented as a graph.(b) In more general contexts; the term spectrum may be used to refer to any spread or distribution of one quantity with respect to another.
...
time-independent Schrödinger equation For confined particles, the solutions of Schrödinger's time-dependent equation involve standing waves and it is therefore possible to write the relevant wavefunctions as a product of a function of space y0(x) (for one dimension) and a function of time φ(t). Thus Y0(x, t) = y00(x)0φ(t). The functions y0(x) are themselves the solutions of a differential equation — Schrödinger's time-independent equation62( ( )) 0.2ddtot pot 2 22+ − y =yE E xmx "4[QPI.2]
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trajectory4(a) In the context of projectile motion; the trajectory of a projectile is its path through space. For a projectile modelled as a particle that moves in the absence of air resistance, the trajectory is a parabola. [DM.2]
...
where e(r) and B(r) are, respectively, the electric and magnetic fields at the point r. [SFP.4]
...
film (photographic)
A 'device' for recording photographic images; it consists of a photosensitive emulsionof suspended silver halide crystals deposited onto a transparent base material (typically a plastic polymer) for stability. [DFW.3]
shutter-speed
A (somewhat colloquial) term used to describe, in effect, the length of time for which a camera's shutter is open. It is usually expressed as the reciprocal of the 'open time'; for example, a shutter speed of 60 means that the shutter is open for 1/601s. [DFW.3]
Schmidt camera
A Schmidt telescope which has a photographic detector at the prime focus of the objective mirror in order to capture a real image. Such devices typically have an undistorted image over a large field of view. [DFW.3]
rigid body
A body that can be regarded as a system of particles whose mutual separations remain fixed. In a rotating rigid body, all parts rotate at the same angularvelocity w (i.e. at the same angular speed w about the same axis of rotation). [PM.1]
telephoto lens
A camera lens system used when photographing distant objects. It comprises a converging lens placed a small distance in front of a diverging lensin such a way that the effective focal length of this twolens system is much greater than the distance from the front lens to the image plane. Since the image size is proportional to the equivalent focal length of the system, a reasonable degree of magnification can be achieved without the need for an excessively long lens barrel. [DFW.3]
parallel plate capacitor
A capacitor consisting of two parallel conducting plates of area A, a distance dapart and separated by an insulating material of relative permittivity εr. Its capacitance is given by: C = εrε0 A/d, where ε0 is the permittivity of free space. [SFP.2]
three-body problem
A celebrated problem in Newtonian mechanics concerning the motion of three bodies (e.g. the Sun, Moon and Earth) that interact gravitationally, but are otherwise isolated. No general solution to this problem, for arbitrary initial conditions, is known. [PM.1]
proton-proton chain
A chain of nuclear reactions, the net effect of which is that hydrogen nuclei (protons) undergo nuclear fusion to become helium nuclei with the release of energy. This cycle occurs in the central region of the Sun and is the main source of the Sun's energy. [QPM.3]
angular displacement
A change in angular position in a specified sense, measured from a specified point. [DM.3]
superconducting energy gap
A characteristic amount of energy that separates the ground state of a superconductor from the lowest excited state. The BCS theory predicted the existence of this superconducting energy gap, and that its value would depend strongly on temperature, rising from 01J at the superconducting transition temperature TC to about 3.5kTC at absolute zero. The experimental confirmation of these predictions gave early support to the BCS theory. The energy gap is, in effect, the binding energy of a Cooper pair. [QPM.2]
angular frequency
A characteristic property of an oscillating system, defined by the relation ω = 2π/T, where T is the period of oscillation of the system. Since the frequency of an oscillator is defined by ƒ = 1/T, it follows that ω = 2πƒ. In the context of a simple harmonic oscillator, described by the equation x = A1sin(ω0t + φ), the angular frequency is represented by the parameter ω. The concept of angular frequency may be extended to the case of a wave, simply by taking T to be the period of the wave. Angular frequency is a positive scalar quantity with the SI unit s−1. (See also angular wavenumber.) [DM.3; DFW.2]
point charge
A charged particle (usually in a context where the mass of the particle is irrelevant). Although the concept of a point charge is an idealization, charged bodies whose sizes are negligible compared with the distances between them may be modelled as charged particles. [SFP.1]
fixer
A chemical solution which when used on developed film renders the unexposed silver halidecrystals soluble in water, thus enabling them to be removed from the film. [DFW.3]
developer (photographic)
A chemical that is used to convert the exposed transparent crystals of silver halidein photographic film into opaque black grains of metallic silver, while leaving the unexposed crystals intact. When the film is then treated with fixer and washed, a negativeimage of the photographed object is produced. [DFW.3]
trigonometric functions
A class of periodic functionsthat includes the sine, cosine and tangent functions, as well as their inverse functions arcsin, arccos and arctan. The trigonometric functions generalize the corresponding trigonometric ratios, and can be defined by various means. For example, suppose a point P lies on a unit circle whose origin coincides with the origin of a Cartesian coordinate system. If a line from P to the origin is at an angle θ, measured anticlockwise, to the xaxis, then the x-coordinate of P determines the value of the cosine function cos(θ0) and the y-coordinate of P determines the value of the sine function sin(θ0). [DM.3]
cylindrical solenoid
A coil of wire wound uniformly in such a way that successive turns are of the same diameter and coaxial. A 'long' solenoid is one in which the length greatly exceeds the diameter. When a current flows through such a long coil, a uniform magnetic fieldis produced inside the coil, parallel to its long axis, and of magnitude B = µ01|1i1|1N1/1l, where N/l is the number of turns per unit length. The direction of the current is determined by the right-hand grip rule. [SFP.4]
elastic collision
A collision in which kinetic energy is conserved. [PM.3]
inelastic collision
A collision in which kinetic energyis not conserved. [PM.3]
completely inelastic collision
A collision in which the colliding bodies stick together, resulting in the maximum loss of kinetic energy consistent with conservation of momentum. [PM.3]
real-is-positive convention
A consistent convention that can be used when calculating the relationships between the focal length of a lens or mirror and the corresponding object and image distances. According to this convention: converging lenses and converging mirrors have positive focal lengths, whereas diverging lenses and diverging mirrors have negative focal lengths; real objects and real images are assigned positive distance values, whereas virtual objects and virtual images have negative distance values; and the lens equation has the form 1/v + 1/u = 1/ƒ. [DFW.3]
surface energy
A contribution to the binding energy per nucleon in the semi-empirical model of nuclei. Surface effects become progressively more important in the model as smaller and smaller nuclei are considered. This is because medium-sized and smaller nuclei have a higher proportion of surface nucleons, and these have fewer neighbours and so are less strongly bound than nucleons that are completely surrounded by neighbouring nucleons. The consequent reduction in binding energy per nucleon gives a good description of the fall-off of the B/A curve for small A. [QPM.3]
volume energy
A contribution to the binding energy per nucleon in the semi-empirical model of nuclei. The volume energy is calculated by assuming that; all nucleons are completely surrounded by other nucleons, that each nucleon interacts only by the strong nuclear force with its nearest neighbours, and that all asymmetry effects can be neglected. (For other contributions see Coulomb energy and surface energy.)4 [QPM.3]
symmetry energy
A contribution to the binding energy per nucleon in the semi-empirical model of nuclei. There are actually two contributions that come under the heading of symmetry energy. One contribution is due to the asymmetry effect. The other contribution is due to the Pauli exclusion principle which in this context lowers the total energy when Z = N. [QPM.3]
Coulomb energy
A contribution to the binding energy that arises in the context of the semi-empirical model of atomic nuclei, due to the electrostatic repulsion between all pairs of protons. This contribution has little effect for small nuclei where the strong nuclear force dominates, but the Coulomb repulsion is a long-range force and the associated energy becomes increasingly important in large nuclei. [QPM.3]
lens
A device (usually a specially shaped piece of glass, or other material with a refractive index different from that of its surroundings) that is able to convert plane wavefronts into spherical wavefronts or, equivalently, make incident parallel rays converge to a point or appear to have diverged from a point. (See also converging lens and diverging lens.) [DFW.3]
Josephson junction
A device consisting of two pieces of superconductor separated by a very thin layer of insulator. Cooper pairs are able to tunnel through the insulator and pass between the superconductors. The insulator is usually an oxide coating that is just a few molecules thick. The current through a superconducting Josephson junction can be controlled to provide very fast low-power switching, which may eventually find applications in large computers. [QPM.2]
cloud chamber
A device for detecting elementary particles, based on observing the trails of tiny droplets left by charged particles as they pass through a supersaturated vapour (i.e. a vapour that is temporarily above its condensation point ). [QPM.4]
(b) In the context of electromagnetism; induction is the phenomenon whereby changing magnetic flux gives rise to an induced EMF. This phenomenon is more properly referred to as electromagnetic induction.induction furnace
A device for melting samples of metal, which is reliant on the eddy currents generated by electromagnetic induction within coils of wire. [DFW.1]
battery
A device for producing an electromotive forceand thus supplying electric current. It consists of two or more electrical cells connected together. [SFP.3]
camera
A device for recording optical images on film. Its principal components are a lens, a timing shutter, an adjustable aperture stop, and some form of filmtransport mechanism. With the advance of digital electronics, an increasing number of cameras are being designed to focus their image onto a photosensitive electronic detector array, which then enables the optical pattern information to be digitized and stored in a form readable by a computer. [DFW.3]
transformer
A device for transforming an EMF of one value to another. The operation of a transformer relies on the principle of mutual induction between two coils of wire with a common magnetic flux linkage. For 100% flux linkage, the EMFs in the two coils are related by the ratio of the number of turns on each:.( )( )1212NNV tV t=If the number of turns on the secondary is greater than the number of turns on the primary, the device is a stepup transformer; if the number of turns on the secondary is less than the number of turns on the primary, the device is a step-down transformer. [DFW.1]
alternating current motor
A device in which an externally supplied alternating current causes a coil of wire to rotate in a magnetic field. For example, if an alternating current is fed into an alternating current generator, then the Lorentz force acting on the conduction electrons in the coil of wire (which sits in a magnetic field) will cause the coil of wire to rotate about its axis. [DFW.1]
direct current generator
A device in which an externally supplied torque causes a coil of wire to rotate in a magnetic field, thus inducing an electric current in the coil that can be used to produce a direct current in an external circuit. The direct current is drawn off by means of a single split metal ring attached to either end of the coil and connected via brushes to the external circuit. The way in which the current is drawn off distinguishes this device from an alternating current generator. [DFW.1]
alternating current generator
A device in which an externally supplied torque causes a coil of wire to rotate within a magnetic field, thus inducing an electric current in the coil that can be used to produce an alternating current in an external circuit. The alternating current is drawn off by means of two metal rings attached to either end of the coil, and connected via brushes to the external circuit. The way in which the current is drawn off distinguishes this device from a direct current generator. [DFW.1]
(b) In the context of particle physics; a particle (also known as an 'elementary particle' in this context) is a piece of matter that is of sub-nuclear size. Such particles include protons and neutrons, as well as electrons and quarks, and may or may not be truly fundamental constituents of matter.particle accelerator
A device in which charged (elementary) particles are accelerated to high energies. There are two distinct types, known as linear accelerators and cyclic accelerators. [PM.3; QPM.4]
spectrometer
A device that uses a diffraction grating(or prism) to spread the light from a source into its constituent wavelengths, thus producing a spectrum that can be examined and measured. Measurements of the spectral lines seen in such a spectrum can greatly assist the analysis of the material from which the light originated, or any material through which the light has passed on its way to the spectrometer. [DFW.2]
refrigerator
A device that uses externally supplied work to transfer heat from a cooler to a hotter body. [CPM.3]
laser
A device that uses the phenomenon of stimulated emission to amplify a light wave, producing an intense, coherent source of light in the form of a narrow beam. The word 'laser' is an acronym for Light Amplification by the Stimulated Emission of Radiation. [QPI.3]
mass spectrometer
A device which uses electric and magnetic fields to separate particles (usually ionized atoms or molecules) of different mass (strictly charge to mass ratio) and to measure the masses of these particles. [SFP.4]
rectifier
A device, usually consisting of a p-n junction, that allows an electric current to pass in one direction only. 4[QPM.2]
Feynman diagram
A diagram representing the interactions of particles in a quantum field theory. In conjunction with the appropriate Feynman rules, such diagrams can be used to predict physical quantities such as cross-sections. [QPM.4]
second-order differential equation
A differential equation involving a second derivative but no higher derivative. [DM.3; PM.1]
Reynolds number
A dimensionless quantity characterizing the flow of a fluid and defined byviscositydensity × characteristic speed×characteristic length Re =[CPM.4]
electron number
A dimensionless quantity that is conserved in all known interactions. The electron has an electron number of 1, and so has the electron neutrino. [QPM.4]
muon number
A dimensionless quantity that is conserved in all known interactions. The muon has a muon number of 1, and so has the muon neutrino. [QPM.4]
tauon number
A dimensionless quantity that is conserved in all known interactions. The tauon has a tauon number of 1, and so has the tauon neutrino. [QPM.4]
bottom
A dimensionless quantity that is conserved in strong and electromagnetic interactions, but not in weak interactions. See bottom quark. [QPM.4]
charm
A dimensionless quantity that is conserved in strong and electromagnetic interactions, but not in weak interactions. [QPM.4]
aerodynamic drag
A dissipative force arising from air resistance that opposes the motion of an object through air. For objects of moderate size and speed, moving through the atmosphere close to the Earth's surface, the magnitude of the aerodynamic drag is proportional to the square of the object's speed. For very small objects moving very slowly, the magnitude of the drag is proportional to the object's speed. [PM.1]
observer
A fictional individual dedicated to the use of a specific frame of reference to measure quantities such as position, time, speed, velocity and acceleration. An observer is usually thought of as being at rest in his or her frame of reference, but is not necessarily at the origin, or any other particular position. The observer associated with a specified frame of reference is essentially an experimenter dedicated to the use of that frame. [PM.1; DFW.4]
Coriolis force
A fictitious force that may be used to account for certain aspects of the motion of bodies observed from a rotating (non-inertial) frame of reference. The effect of the Coriolis force is to cause bodies moving towards or away from the axis of rotation to be deflected at right angles to their direction of motion. (This is exemplified by the rightward deflection of air masses travelling north or south in the Earth's Northern Hemisphere.) By introducing such fictitious forces the motion of the bodies may be made to conform with the predictions of Newton's laws, which do not, strictly speaking, apply in such frames. (See also centrifugal force.) [PM.1]
ideal fluid
A fluid that exhibits ideal flow. An ideal fluid is incompressible and has no viscosity, and its motion is steady and free of eddies. [CPM.4]
contact force
A force arising from the direct physical contact of one body with another. Such forces are ultimately electrical in nature since they actually arise from the electrical repulsion between atoms in the surfaces of the bodies. [PM.1]
restoring force
A force tending to restore a body to some former position, often a position of equilibrium. Such a force acts in the direction opposite to the displacement of the particle from that former position. [PM.1]
linear restoring force
A force tending to return an object to some former position, with the property that its magnitude is proportional to the displacement from that position. [PM.1]
drag
A force that acts on a body moving through a fluid. Drag acts in a direction that is opposite to the body's direction of motion. [CPM.4]
lift
A force that acts on a body moving through a fluid. Lift is perpendicular to the body's direction of motion and arises from the difference in pressure across the body due to Bernoulli's principle. [CPM.4]
conservative force
A force with the characteristic that the work it does when its point of application moves from one point to another, is independent of the route followed between those two points. (This is equivalent to the requirement that the work done by the force when its point of application moves around a closed loop is zero.) The gravitational force on a body of fixed mass is an example of such a force. [PM.2]
in parallel
A form of connection in electrical circuits. Two or more components, such as resistors, are said to be connected in parallel if one end of each is connected to a common point in the circuit while the other end of each is connected to some other common point, so that the voltage across each is the same. The effective resistance of a set of resistors connected in parallel is given by=∑R i i R1 1eff. [SFP.3]
in series
A form of connection in electrical circuits. Two or more components, such as resistors, are said to be connected in series if they are connected in a line so that the same current goes through each. The effective resistance of a set of resistors connected in series is given by=∑iReff Ri. [SFP.3]
uniformly accelerated motion
A form of motion in which the acceleration does not change with time. See constant acceleration equations. [DM.1; DM.2]
rotational motion
A form of motion that involves turning about a line called the axis of rotation, and which should be contrasted with translational motion. (Any displacement of a rigid body may be regarded as arising from a translational motion of a point in that body together with a rotational motion about an axis passing through that point.) [PM.1]
uniform circular motion
A form of two-dimensional periodic motion, in which the Cartesian coordinates of a particle moving around the origin at fixed distance R, and with fixed angular speedω, may be represented by(x, y) = (R1cos(±ω0t + θ0), R1sin(±ω0t + θ0)).where the + sign indicates motion in the anticlockwise sense, and θ0 is the angular position of the particle at time t = 0. [DM.3]
density of states function
A function D(E) that describes, in the classical continuum approximation, the way in which the states of a quantum gas are distributed with respect to energy. The function is such that the number of quantum states with energies in the range between E and E + ∆E is D(E)1∆E. For a gas of distinguishable molecules, D(E) = B E , for a gas of photons Dp(E) = CE2 and for a gas of electrons De(E) = 2B E , where B and C are constants. (See also density of states function for electrons and density of states function for photons.) [QPM.1]
speed distribution function
A function f0(v) which, when multiplied by a small range of speeds, ∆v, indicates the fraction f00(v)1∆v of some specified population of particles with speeds between v andv + ∆v. The speed distribution function for a classical gas is given by the Maxwell-Boltzmann speed distribution. [CPM.2]
translational energy distribution function
A function g(E) which, when multiplied by a small range of translational energies, ∆E, indicates the fraction g(E) ∆E of some specified population of particles with translational energies between E and E1+1∆E. The translational energy distribution function for a classical gas is given by the Maxwell-Boltzmann energy distribution. [CPM.1]
radial density function
A function specifying the average number of particles per unit volume at a given distance from a chosen reference particle. Peaks and troughs in this function reveal short-range order in liquids and long-range order in crystalline solids. [CPM.1]
exponential function
A function that may be written in the form v(t) = v0eα1t, where v0 and α are constants. Any function of the form y = ax, where a is a positive constant, may be written as y = ekx since it is always possible to find a constant k such that ek = a, and we can then write ax = (ek)x = ekx. [PM.2]
46polynomial
A function that may be written in the form ƒ(x) = A + Bx + Cx2 + Dx3 + ...,where A, B, C, etc. are constants. Special cases of polynomial functions include constants, linear functions, quadratic functions and cubic functions. [DM.1]
distribution function
A function which, when multiplied by a small range of a given variable, tells us the fraction of particles for which the given variable has values in the given range. Gases are commonly described in terms of their speed distribution function or translational energy distribution function. (See Maxwell-Boltzmann energy distribution for an example.) [CPM.2]
even function
A function ƒ(0y) that satisfies the condition ƒ(0y) = ƒ(−y) for all values of y. [DM.3]
odd function
A function ƒ(0y) that satisfies the condition ƒ(0y) = −ƒ(−y), for all values of y. [DM.3]
periodic function
A function, ƒ(t) say, with the property that, for all values of t, ƒ(t + T0) = ƒ(t) for some particular value of T. The smallest value of T that satisfies this requirement is said to be the period of the function. For example, the periodic functions sin(θ) and cos(θ) are each periodic with period 2π. [DM.3]
electric charge
A fundamental property of matter that determines the electric and magnetic interactions of particles. It obeys the principle of conservation of charge. There are two types of charge, positive and negative. Protons in atomic nuclei are positively charged (with charge e) and electrons are negatively charged (with charge −e). According to Coulomb's law, charges experience electrostatic forces; like charges repel and opposite charges attract. According to the Lorentz force law, charges moving across a magnetic field experience magnetic forces in a direction perpendicular both to their direction of motion and to the magnetic field. The SIunit of electric charge is the coulomb (C). [SFP.1]
matter
A general term for material substances, irrespective of their form.Maxwell-Boltzmann energy distribution$The equilibrium translational energy distribution function for molecules in a gas at (absolute) temperature T:38E kT EkTg E/3/ 2e2 1( )−⎟×⎠⎞⎜⎝⎛π=where E denotes the translational kinetic energy of a molecule, i.e. E = Etrans = mv2/2 where m and v are the mass and speed of the molecule. The product g(E)1∆E is the probability of a single molecule having translational energy between E and E + ∆E. Consequently, if the total number of molecules in the gas is N, the quantityG(E) ∆E = Ng(E) ∆E represents the total number of molecules with energy between E and E + ∆E. [CPM.2; QPM.1]
Schmidt plate
A glass plate used to introduce a predistortion into parallel wavefronts in order that they can be focused to a single point by a spherical mirror. The effect is therefore to greatly reduce the effects of spherical aberration. A reflecting telescope utilizing a Schmidt plate is referred to as a Schmidt telescope. [DFW.3]
displacement-time graph
A graph showing how the displacement of a particle from a given reference point depends on time. It is conventional to plot the displacement on the vertical axis and the time on the horizontal axis. The gradient of the displacement-time graph at any particular time is equal to the velocity of the particle relative to the reference point at that time. [DM.1]
velocity-time graph
A graph showing how the velocity (usually in one dimension) of a particle depends on time. It is conventional to plot the velocity on the vertical axis and the time on the horizontal axis. The gradient of the velocity-time graph at any particular time is equal to the acceleration of the particle at that time. [DM.1]
path of stability
A graphical feature seen when the lifetime of each known nucleus is indicated on a Z-N plane (a plot of atomic number Z against neutron number N). The points corresponding to stable and very long-lived nuclei, i.e. those naturally abundant on Earth, all lie close to a narrow curving path — the path of stability. [QPM.3]
valley of stability
A graphical feature seen when the total energy per nucleon for each known nucleus is plotted above the corresponding point in the Z-N plane. The plotted points all lie very close to a surface called 65the valley of stability, with the valley floor lying directly above the path of stability in the Z-N plane. [QPM.3]
triangle rule
A graphical method of determining the resultant a + b of two given vectors a and b. Any vector can be represented graphically by an arrow, with a length that represents the magnitude of the vector and an orientation that represents the direction of the vector. To construct the arrow representing the resultant a + b, first draw an arrow to represent the vector a, then, starting from the head of the arrow you have just drawn, draw a second arrow to represent the vector b. The resultant a + b will then be represented by an arrow drawn from the tail of the arrow representing a to the head of the arrow representing b. The arrows representing a, b and a + b will thus form a triangle. [DM.2]
Schrödinger's cat
A hapless beast enclosed in a box along with a radioactive nucleus and a fiendish device that will break open a phial of poison gas when the decay of the nucleus is detected. This set-up was introduced into quantum physics by Erwin Schrödinger to highlight the difficulties of making sense of macroscopic superposition states such as the state in which the cat has some probability of being alive and some probability of being dead. (See also decoherence effect.) [QPI.4]
gyroscope
A heavy, rotating disc mounted in such a way that it is free to rotate about its centre of mass. In the absence of external torques, the axis of the gyroscope maintains a fixed orientation in space; this causes the gyroscope to have important applications in the navigation and stabilization of ships, planes and space vehicles. [PM.4]
neutron star
A highly compact stellar body composed of neutron-rich matter. Neutron stars have a typical density of order 10151kg1m−3 (about 1012 times the density of water). Measured neutron star masses are typically 1.4 times the mass of the Sun, and their radii are thought to be about 8 to 101km. Neutron stars are formed when massive stars with degenerate cores that are supported normally by electron Pauli pressure, collapse under their own weight. When the degenerate core of a highly evolved star acquires a mass that is greater than about 1.4MSun, the Pauli pressure is insufficient to prevent its sudden collapse. The core undergoes extreme compression in which electrons and protons combine to yield neutrons and neutrinos. This results in an extremely violent supernova explosion, and leaves behind a neutron star that is prevented from further collapse by neutron Pauli pressure. [PM.4; SFP.2]
plasma
A highly ionized gas, that is electrically neutral overall but consists almost entirely of charged particles (electrons and positive ions). Plasma is sometimes described as the fourth phase of matter. On the Earth's surface it is only found in small-scale devices, such as discharge tubes and nuclear reactors. However, on the large scale, plasma is the commonest form of visible matter in the Universe; stars and interstellar space contain large amounts of matter in the plasma state. [CPM.1 SFP.3]
speed histogram
A histogram in which the height of each bar is proportional to the fraction of particles with speeds within the width of the bar. [CPM.2]
ether
A hypothetical medium once supposed to permeate all of space and to be essential for the propagation of electrical and magnetic effects, including light, from one place to another. The concept of a material ether has been strongly disfavoured by physicists since the early twentieth century, partly as a result of the Michelson-Morley experiment of 1887. [RU.1; DFW.2; DFW.4]
gravitational potential energy of two point massesThe gravitational potential energy of a point mass m1due to its gravitational interaction with another point mass m2, separated from it by a distance r isrGm mE1 2grav−=where G is the universal gravitational constant and, by convention, Egrav is taken to be zero when r = ∞.graviton
A hypothetical spin 2 massless particle that occurs as the exchange particle in some attempts to formulate a quantum field theory of gravity.4 [QPM.4]
ionic bond
A kind of bonding that arises between atoms and which can lead to the formation of individual molecules or solids. In an ionic bond, one or more valence electrons are transferred from one atom to a more strongly electronegative partner. The oppositely charged ions formed in this way are attracted electrostatically, thus creating the bond. The ionic bond is not directional and does not saturate. [QPM.2]
hydrogen bonding
A kind of bonding that arises between molecules in which hydrogen atoms have formed covalent bonds with strongly electronegativeatoms such as oxygen and fluorine. The bonding electrons are pulled towards the electronegative atom leaving the hydrogen end of the molecule with a positive charge. This makes the molecule a weak permanent electric dipole and allows the molecules to bond to one another with the negative end of one molecule linked to the positive hydrogen end of another by electrostatic attraction. Hydrogen bonding of this kind is important in ice. [QPM.2]
mixed bonding
A kind of bonding that is intermediate between ionic bonding and covalent bonding. Except for the covalent bonding of identical atoms (as in the diatomic chlorine molecule Cl2), the usual views of ionic and covalent bonding — involving either the entire transfer of valence electrons or the completely even sharing of a pair of valence electrons — are somewhat idealized. In practice bonding is more realistically viewed as a mixture of these types, with uneven sharing of electrons and some Coulomb attraction of ion pairs. [QPM.2]
electron neutrino
A kind of elementary particle that has no known substructure and is therefore regarded as a truly fundamental particle. It is the partner to the electron in the first generation of leptons. It has spin 21, no charge and a mass of less than 0.00010151MeV/c2. [QPM.4]
muon neutrino
A kind of elementary particle that has no known substructure and is therefore regarded as a truly fundamental particle. It is the partner to the muonin the second generation of leptons. It has spin 21, no charge and a mass of less than 0.171MeV/c2. [QPM.4]
electron
A kind of elementary particle with charge −1.602 × 10−191C, mass 9.109156 × 10−311kg, and spin 1/2. The electron is a stable lepton. As far as is known, it has no internal structure, and is therefore regarded as a truly fundamental particle. Electrons are constituents of all atoms, and are responsible for many familiar properties of matter including bonding, chemical reactions and electrical conduction. [CPM.1; QPM.4]
tauon
A kind of elementary particle, similar to an electron, but with a mass of 17771MeV/c2 ( about 3477 times that of the electron). Tauons are unstable leptonsthat may occur with either positive or negative charge, the positive tauon (τ+) being the antiparticle of the negative tauon (τ−). [QPM.4]
muon
A kind of elementary particle, similar to an electron, but with a mass that is about 207 times that of the electron. Muons are unstable leptons that spontaneously decay with a mean lifetime of 2.2 × 10−61s in a frame of reference in which they are at rest. Some muons are naturally produced in the upper atmosphere as a result of cosmic rays from outer space interacting with atoms. Since these particular muons are travelling with respect to the Earth at a speed around 98% of the speed of light, their mean lifetime is extended by about a factor of five as measured in a frame of reference fixed to the Earth. This is an example of time dilation and an effect of special relativity. Muons may occur with either positive or negative charge, the positive muon (µ+) being the antiparticle of the negative muon (µ−). [DFW.4; QPM.4]
kaon
A kind of elementary particle. A spin 0 mesonwith approximately half the mass of a proton. There are four kinds of kaon, denoted K+, K−, K0, K0 according to charge (and strangeness). Kaons were the first strange particles to be discovered. [QPM.4]
pion
A kind of elementary particle. A spin 0 mesonwith mass of about 1401MeV/c2 (about one-quarter of a proton's mass). There are three kinds of pion, denoted π+, π−, π0 according to charge. [QPM.4]
lambda particle
A kind of elementary particle. A strange baryon with spin 21, and a mass that is about 20% greater than that of the proton. The lambda particle is electrically neutral and is represented by the symbol Λ0. [QPM.4]
xi particle
A kind of elementary particle. A strange baryon with spin ½, and a mass that is about 40% greater than that of the proton. There are two kinds of xi particle, denoted Ξ−, Ξ0 according to charge. Xi particles have strangeness −2, which causes them to decay in several steps; hence their alternative name — cascadeparticles. 4[QPM.4]
red giant
A late stage in the evolution of a star, during which the star's surface temperature is somewhat lower (accounting for its redder colour) and its radius considerably larger (accounting for its giant status) than at most other stages. [SFP.2]
Bragg's law
A law stating that; a beam of X-rays can be reflected from parallel planes of atoms in a crystalwhennλ = 2d1sin1θwhere n is an integer (the order of the reflection), λ is the X-ray wavelength, θ is the angle between the beam 8direction and the normal to the atomic planes, and d is the separation of atomic planes in the crystal. [QPM.2]
Newton's first law of motion
A law stating that; a body remains at rest or in a state of uniform motion unless it is acted on by an unbalanced force. Newton's first law presupposes the use of an inertial frame ofreference. Given that such a frame is used, the law implies that a particle moving along the x-axis, that is free from any unbalanced force, will obey the uniform motion equations: sx = uxt, vx = ux and ax = 0. 4[PM.1]
Newton's second law of motion
A law stating that; an unbalanced force acting on a body of fixed mass will cause that body to accelerate in the direction of the unbalanced force, and that the magnitude of the force is equal to the product of the mass and the magnitude of the acceleration: F = ma. Newton's second law presupposes the use of an inertial frame of reference. Given that such a frame is used, the law implies that a particle of mass m subject to an unbalanced force with component Fx in the x-direction will obey the equation Fx = max. For a system of particles, or an extended body, the law implies that the resultant external force is equal to the total mass times the acceleration of the centre ofmass. Newton's second law may be expressed in terms of momentum as follows. The resultant force acting on a body is equal to the rate of change of the body's momentum: F = dp/dt. For a system of particles or an extended body this implies that the total external force is equal to the rate of change of the total linear momentum. [PM.1]
law of terrestrial gravitation
A law stating that; at any location on Earth, all objects that are subject only to the effect of gravity have the same downward acceleration g, irrespective of their mass and composition. In Newtonian mechanics, a directconsequence of this law is that close to the Earth's surface, any body of mass m experiences a gravitational force (the body's weight) which acts vertically downwards and has magnitude mg, where g is the magnitude of the acceleration due to gravity(approximately 9.811m1s−2). [PM.1]
Boyle's law
A law stating that; at constanttemperature, the pressure of a fixed mass of an ideal gas is inversely proportional to its volume. [CPM.1]
law of universal gravitation
A law stating that; every particle of matter attracts every other particle of matter with a gravitational force, whose magnitude is directly proportional to the product of the masses of the particles, and inversely proportional to the square of the distance between them. It follows from this that, if a particle of mass m1 is separated by a distance r from a second particle of mass m2, then the gravitational force on the second particle due to the first is directed towards the first particle and has magnitude21 221rGm mF = ,where G = 6.673 × 10−111N1m21kg−2 is the universal gravitational constant. By introducing a dimensionless unit vector rˆ = r/r parallel to the displacement vector rfrom the first particle to the second, the force on the second particle, due to the first, may be writtenF rˆ21 221r−Gm m= . [PM.1; SFP.1]
Boltzmann's distribution law
A law stating that; for a (classical) gas in thermal equilibrium at absolute temperature T, the probability of finding a given molecule in a given phase cell of energy E is p = Ae−E/kT, where A has the same value for all phase cells, no matter what their energy. [CPM.2]
Newton's third law of motion
A law stating that; if body A exerts a force on body B, then body B exerts a force on body A, and that these two forces are equal in magnitude but act in opposite directions. In vector notation, the law implies that FAB = −FBA, where FAB is the force on A due to B, and FBA is the force on B due to A. Such a pair of forces is sometimes called a Newton's third-law pair. [PM.1]
second law of thermodynamics
A law stating that; in the neighbourhood of any equilibrium state of a macroscopic system there are states that areadiabatically inaccessible (Carathéodory's version.)Or: the entropy of the Universe tends to a maximum. (Boltzmann's version.)Or: no cyclic process is possible which has, as its sole result, the complete conversion of a positive quantity of heat into work. (Kelvin's version.)Or: no cyclic process is possible which has, as its sole result, the transfer of a positive quantity of heat from a cooler body to a hotter one. (Clausius's version.)Any of these may be used to justify the introduction of a function of state known as entropy, that never decreases in any isolated system. It thereby provides the basis for the general principle of entropy increase. [RU.1; CPM.3]
Planck's radiation law
A law stating that; the energy distribution function for photons in blackbody radiationat (absolute) temperature T, is given by Gp(E) = Dp(E)FB(E) where Dp(E) is the density of states function for photons and FB(E) is the Bose occupation factor. The quantity Gp(E) ∆E represents the number of photons in the radiation with energy between E and E + ∆E. [QPI.1; QPM.1]
Faraday's law
A law stating that; the magnitude of the induced EMF around the boundary of a surface is equal to the magnitude of the rate of change of the magnetic flux through that surface. In symbols24.dd ( )( ) indttV tφ| | = 4[DFW.1]
Lenz's law
A law stating that; when a changing magnetic flux generates an induced EMF, the effect of that EMF is to oppose the change that caused it. Although Lenz's law, like Faraday's law, is phrased in terms of EMFs, the induced EMF will, in general, give rise to an induced current, which in turn will give rise to a magnetic field. It is usually the effect of this (induced) magnetic field that needs to be considered when working out the direction in which the induced current will flow. [DFW.1]
first law of thermodynamics
A law stating that; when a system undergoes a change from one equilibrium state to another, the sum of the heat transferred to the system and the work done on the system will depend only on the initial and final equilibrium states and not on 25the process by which the change is brought about. This law justifies the introduction of a function of state, called the internal energy, that is conserved in any isolated system. It thereby provides the basis for the general principle of conservation of energy and is often represented by the equation ∆U = Q + W. [RU.1; CPM.3]
34law of refraction
A law stating that; when a wave travels from one medium in which its speed is v1to another in which its speed is v2 (such that v1≠ v2), the angle of incidence i and the angle of refraction r are related by:1221sinsinnnri= =vvwhere n1 and n2 are the refractive indices of the two media. This law is also known as Snell's law. [DFW.2]
Coulomb's law (in free space)
A law that describes the electrostatic force on a stationary charged particle, due to another stationary charged particle, located some distance away, in a vacuum. Coulomb's law can be represented mathematically by the equationF rˆ4201 2elrq qπε= ,where Fel is the force on one of the particles, q1 and q2are the charges, r is the distance between them, ε0 is the permittivity of free space and rˆ is a unit vector directed towards the particle on which the force is acting from the other (source) particle. Thus, rˆ = r/r, where r is the position vector of the particle on which the force is acting, when the origin is taken to be at the position of the source particle. In agreement with Newton's third law, the existence of this force implies that there is also a force −Fel acting on the source particle. This is consistent with the rule that: like charges repel and unlike charges attract. [SFP.1]
aurora
A luminous atmospheric phenomenon, observed in high latitudes. It arises from plasmaparticles from the solar wind which become trapped in the Earth's magnetic field and oscillate between the magnetic North and South Poles. Near the poles these charged particles excite the oxygen and nitrogen molecules in the upper atmosphere causing them to emit light seen as the beautiful auroral display. [SFP.4]
conductor
A material that allows electric charge to flow with relative ease. Conductors contain free electric charges that are able to move throughout the whole body of the material under the influence of applied electric fields or potentials. The free charges are often electrons (e.g. in metals), but can also be positive charges such as ions in a solution. (Contrast with insulator.) [SFP.1]
insulator (electrical)
A material that conducts electric currents very poorly, or not at all. Insulators contain no free charges because all the electrons are bound to particular atoms of the material. (Insulators are also known as dielectrics.) In the context of the band theoryof solids, insulators have an energy gap between the valence band and the conduction band of more than about 31eV. There is no clear-cut distinction between an insulator and a semiconductor since the electrical conductivity depends on temperature. [SFP.1, QPM.2]
moderator
A material used in a nuclear reactor to reduce the average speed of the fast neutrons released by induced fission reactions. The neutrons are slowed and eventually brought into thermal equilibrium by repeated collisions with the light nuclei of the moderator, which is usually composed of carbon in the form of graphite or hydrogen in the form of water. The resulting thermal neutrons can then cause further induced fission reactions thereby sustaining a chain reaction. [QPM.3]
semiconductor
A material with an energy gapbetween the valence band and the conduction band of between about 0.11eV and 31eV. Such a material is an insulator at very low temperatures, but conducts electricity near room temperature, and typically has a room temperature electrical conductivity between about 10−4 and 1021Ω−11m−1. [QPM.2]
operator
A mathematical entity (such as the derivative operator, d/dt) that acts on a function and thereby changes it into another function. In the case of the derivative operator, the function upon which it acts is transformed into the derivative of the function. [DM.1]
definite integral
A mathematical expression indicating the limit of a sum, usually as some particular quantity becomes vanishingly small. Definite integrals can be thought of as representing the (signed) area under a given curve between given limits, and may be evaluated using a technique called integration. [PM.2]
electrical conductivity
A measure of a material's ability to conduct electricity, defined as the reciprocal of the material's resistivity ρ; so σ = 1/ρ. The electrical conductivity of a material is numerically equal to the electric current that would flow in a slab of the material of length 11m and cross-sectional area 11m2 when a potential difference of 11V is maintained across its ends. The units of σ are Ω−11m−1. [QPM.2]
entropy
A measure of the disorder of a system. The entropy S associated with a given macroscopicequilibrium state of a system is related to the number of microscopic configurations W which correspond to that state. The relationship is expressed by Boltzmann's equation S = k logeW, where the constant k is Boltzmann's constant. The second law of thermodynamics implies that the entropy of an isolated system is a function of state, that never decreases, so ∆S ≥ 0, the equality holding in the case of a reversibleadiabatic process. (If a system is not isolated, ∆S may be positive or negative, but we may still say that ∆SUniv≥ 0, where the equality now holds for any reversible process.) The difference in entropy between two equilibrium states of a system may be evaluated by using the fact that the reversible transfer of an amount of heat Qrev to a system at fixed absolute temperature Twill increase the entropy of that system by an amount ∆S = Qrev/T. In the case of an ideal gas with pressure Pand volume V, this implies that00,m e0,m elog log SPPnCVVS nCP V+⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛=where S0 is the entropy of an arbitrarily chosen reference state with pressure P0 and volume V0. 4[RU.1; CPM.3]
37magnetic flux
A measure of the extent to which a given magnetic field 'passes through' a given surface. In the case of a uniform magnetic field and a flat surface, the flux through the surface is φ = AB1cos1θ, where A is the area of the surface, B is the magnitude of the magnetic field and θ is the angle between the normal to the surface and the direction of the magnetic field. Alternatively, the magnetic flux is given by the scalar product φ = A1•1B, where A is a vector perpendicular to the surface with a magnitude equal to the area of the surface, and B is the magnetic field. The magnetic flux through a solenoid consisting of N turns of wire may be written Φ = NAB = Nφ, where N is the number of turns on the solenoid, and φ is the magnetic flux through a single turn. The total magnetic flux through any closed surface will always be zero (a fact that is related to the non-existence of magnetic monopoles). Magnetic flux is measured in the SI unit of weber (Wb). The concept of flux may be generalized to non-magnetic situations; for instance, considering an electric field rather than a magnetic field leads to the idea of electric flux, which is also of some use in electromagnetism. [DFW.1]
light-gathering power
A measure of the extent to which a telescope can increase the apparent brightness of an object (relative to its brightness when viewed directly by eye) by collecting the light over a large area and concentrating it into an area less than or equal to the area of the eye pupil. For a telescope with an objectiveaperture diameter of Do and set up in far-point adjustment, the light-gathering power is given by (Do0/0Dp)2, where Dp is the diameter of the eye pupil. (This assumes that the diameter of the 'exit beam' at the eyepiece lens is less than or equal to Dp, so that all the light leaving the telescope can enter the eye.) [DFW.3]
Q-factor
A measure of the quality of a damped oscillator, calculated by dividing the total energy stored in the oscillator at any time by the energy lost per oscillation and multiplying the result by 2π, soaverageenergy lossper oscillation2π× totalstored energy Q = .A damped oscillator with a high Q-factor will complete many oscillations before most of its energy is dissipated. A low Q oscillator will complete very few. [PM.2]
phase
A measure of the stage in its cycle that an oscillator has reached at a specified time, or the stage that a wave has reached at a specified time and position. In the case of a simple harmonic oscillator described by x(t) = A1sin(ω0t + φ), the phase is ω0t + φ, where ω is the angular frequency and φ is the phase constant or initial phase. Similarly, in the case of a travelling waverepresented by the equation y(x, t) = A1sin1(kx − ω0t + φ), the phase is (kx - ω0t + φ), where k is the angular wavenumber. Two waves are said to be 'in phase' if their phases are equal at a particular point in space and instant of time; they are said to be 'out of phase' if their phases differ by exactly π radians at that point and instant. [DM.3; DFW.2]
conduction (of heat)
A mechanism of heat transfer in which collisions between atoms or molecules cause energy to be transferred from regions where the average molecular speed is relatively high (corresponding to high temperature) to regions where the average molecular speed is somewhat lower (corresponding to low temperature). [CPM.3]
shutter
A mechanism that can be opened and closed for a predetermined length of time so as to control the light entering a camera body to expose the film. [DFW.3]
carbon dating
A method of dating pieces of organic archaeological or fossil material by measuring the amount of radioactive 14C present in the material. It is assumed that the 14C was taken in by the material from the atmosphere when it was part of a living organism and has since undergone radioactive decay according to the exponential decay law. [QPM.3]
echo location
A method of determining the position of an object relative to a source of sound. The method is based on distance measurements derived from the time taken for a sound wave to travel from its source to an object and then return to its source after being reflected by the object. [DFW.2]
configuration
A microscopically detailed description of the condition of a system, sufficiently detailed for the purposes of statistical mechanical analysis. In classical statistical mechanics, the configuration of a gas is defined by specifying which molecules are in which phase cells. The configuration of a system, such as a gas, is also known as its microstate. [CPM.2; CPM.3]
converging mirror
A mirror that increases the convergence (or reduces the divergence) of an incident wavefront. Such a mirror will have a concave shape but will behave like a converging (i.e. convex) lens; also called a positive mirror. In the real-is-positive convention, a converging mirror always has a positive focal length. [DFW.3]
diverging mirror
A mirror that increases the divergence (or reduces the convergence) of an incident wavefront. Such a mirror will have a convex shape but will behave like a diverging (i.e. concave) lens. Also called a negative mirror. In the real-is-positive convention, a diverging mirror always has a negative focal length. [DFW.3]
parabolic mirror
A mirror whose surface has a parabolic shape and so does not suffer from spherical aberration. Contrast with spherical mirror and plane mirror. [DFW.3]
spherical mirror
A mirror whose surface shape is part of the surface of a sphere. Contrast with parabolic mirror and plane mirror. [DFW.3]
plane mirror
A mirror with a flat, plane surface (no curvature). Such a mirror will reflect light (and produce same-size images) but has no focusing properties. Contrast with spherical mirror and parabolic mirror. [DFW.3]
limit cycle
A mode of behaviour in which the sequence of values arising from the iteration of a mapsettles down to an oscillation that repeats itself after a certain number of steps. [PM.5]
simple gas model
A model of a gas that treats the molecules of the gas as structureless particles in random motion. The molecules collide with one another and with the walls of their container, subject to the laws of Newtonian mechanics. Gravity and intermolecular forces between collisions are neglected and all collisions are taken to be elastic. [CPM.2]
thin isothermal atmosphere
A model of a planetary atmosphere in which the atmosphere is at constant temperature and is thin enough for any variation in gravitational acceleration to be neglected. [CPM.4]
semi-empirical model
A model of the atomic nucleusthat attempts to provide insight into the systematic behaviour of nuclei in general on the basis of a mixture of empirical measurements of nuclear radii and binding energies, and an analogy between an atomic nucleus and a water droplet. (See also Coulomb energy, surface energy and volume energy.) [QPM.3]
nuclear shell model
A model of the nucleus based on the observation that many nuclear properties vary with atomic number and neutron number in a slow and regular fashion suggesting the existence of energy shells for nucleons analogous to the electron shells in atoms. (See also magic numbers.) Shell effects in nuclei are not as strong as in atoms. [QPM.3]
spectroscopic notation
A notation in which the value of the orbital angular momentum quantum number of an electron in an atom is labelled by a letter, namely: l = 0 states are labelled s; l = 1 states p; l = 2 states d; l = 3 states f; l = 4 states g, and thereafter letters are used alphabetically for increasing l. The principal quantum number n is written explicitly as a number before the letter denoting the value of l. Thus3s is spectroscopic notation for n = 3, l = 04d is spectroscopic notation for n = 4, l = 2. [QPI.3]
Feigenbaum constant
A numerical constant, represented by the symbol δ, that arises in various ways in the study of chaos. In particular, in the limit where the periods of limit cycles are large, the intervals between successive period doublings get exponentially smaller as some parameter k increases, each interval being smaller than the previous interval by a factor δ, which has the valueδ = 4.66912011609110219901671185312031820146612011617 2581185157714751768163217451651...4[PM.5]
probability
A numerical measure of relative likelihood of the possible outcomes of a process. It is conventional to use a probability of 1 as an indication of certainty. According to this convention, the probability of any particular outcome will be a number between 0 (impossibility) and 1 (inevitability), and will be the fraction of times that outcome is expected to happen in the long run. [RU.1; CPM.2]
relative atomic mass
A numerical measure of the mass of a given species of atom, obtained by dividing the mass of the atom m by the atomic mass unit; so Mr = m/11amu, where 11amu is one-twelfth the mass of a carbon-12 atom. The relative atomic mass is a dimensionless quantity. [CPM.1]
relative molecular mass
A numerical measure of the mass of a given species of molecule, obtained by dividing the mass of the molecule m by the atomic mass unit; so Mr = m/11amu, where 11amu is one-twelfth the mass of a carbon-12 atom. The relative molecular mass is a dimensionless quantity. [CPM.1]
light-emitting-diode (LED)
A p-n junction device under forward bias that produces light via the recombination process, when electrons and holes meet in the depletion region. The photons produced typically have an energy equal to that of the semiconductor energy gap. [QPM.2]
Helmholtz pair
A pair of identical conducting coils that are positioned coaxially with their centres separated by a distance equal to their radius. When the same current flows in the same sense through each, a magnetic field is produced which has a high degree of uniformity over a considerable region around the midpoint between the coils. [SFP.4]
Einstein temperature
A parameter, θE, arising in Einstein's theory of heat capacities, that determines, at any given absolute temperature T, the extent to which the molar heat capacity of a specified elemental solid departs from the value 3R predicted by the classical Dulong-Petit law. The Einstein temperature of a given crystalline solid is given by θE = hfv/k, where h is Planck's constant, fv is the frequency of vibration of the atoms in the solid, and k is Boltzmann's constant. [QPI.1]
free particle
A particle for which the potential energy function Epot(x) is constant. A free particle therefore experiences no forces. [QPI.2]
45photon
A particle of electromagnetic radiation. More properly, a quantum of the electromagnetic field. For monochromatic radiation of frequency ƒ the quantum of energy is, according to Planck's law, E = hƒ where h is Planck's constant. Each photon of that radiation will carry just one quantum of energy and will also carry momentum p of magnitude p = h/λ, where λ is the wavelength of the radiation. The notion that electromagnetic radiation might be treated as a collection of particles was, to some extent, prefigured by Einstein's explanation of the photoelectric effect in 1905. More direct support was provided in 1923 by the Compton effect, but the term 'photon' was not actually introduced until 1926, by G. N. Lewis. Viewed as an elementary particle, the photon is the exchange particlefor the electromagnetic interaction. It has spin 1, no charge, zero mass, and is stable. It is often represented by the symbol γ. [RU.1; QPI.1, QPM.4]
bound particle
A particle that is trapped in a potential well because its total energy is less than its potential energy at every point on the boundary of the well. In classical physics, a bound particle is rigorously confined to the region in which the potential energy is less than the total energy. In quantum mechanics, tunnelling can occur, and the particle can stray beyond the classically allowed region; nevertheless, the wavefunction of the particle usually decreases rapidly beyond the classically allowed region, so the probability of tunnelling is generally quite small. In quantum mechanics, the energy levels of a bound particle are discrete. [QPI.2]
exchange particle
A particle that, according to our current understanding, is responsible for one of the fundamental forces. In the context of gauge theories, they are also known as gauge bosons. [QPM.4]
unbound particle
A particle whose total energy Etot is everywhere greater than its potential energy Epot, is said to be unbound. If, in addition, Epot is constant, the particle is said to be free. [QPI.2]
boson
A particle with integer or zero spin (i.e. spin 0, 1, 2, etc.). Bosons do not obey Pauli's exclusion principle. Consequently, any number of bosons may occupy any given quantum state. 4[QPM.1; QPM.4]
simple harmonic motion
A particular form of oscillatory motion about a specified equilibrium position, characterized by the fact that the accelerationis always directed towards the equilibrium position and is proportional to the displacement from that point. In one dimension, any simple harmonic motion may be described by an equation of the form d2x(t)/dt2 = −ω02x(t)which has the general solution x(t) = A1sin(ω0t + φ), where A is the amplitude of the motion, ω is its angular frequency, and φ is the phase constant (or initial phase) of the motion. [DM.3]
synchrotron
A particular kind of cyclic acceleratorsuitable for elementary particles that are moving at relativistic speeds. The particles are accelerated in bunches and are made to move in closed paths of large fixed radius (typically several kilometres) by a number of separate bending magnets. Since the beam consists of distinct bunches of particles, rather than a continuous beam, it is possible to adjust the frequency of the applied 60accelerating fields to the speed of the particles. [QPM.4]
adiabat
A pathway on the PVT surface of a system (or on one of its projections, such as a PV-diagram) that corresponds to a reversible adiabatic process. [CPM.3]
isotherm
A pathway on the PVT surface of a system(or on one of its projections, such as the PV-diagram) that represents an isothermal process. [CPM.3]
wave
A periodic disturbance that may convey energy from one point to another without any particle of the medium through which it travels being permanently displaced. Waves may be standing or travelling, solitary or continuous, and transverse or longitudinal. According to its type, a wave may be characterized by a frequency or wavelength, a plane of polarization and a direction of propagation. The speed of a (travelling) wave is jointly determined by its frequency and wavelength in accordance with the relation v = fλ. [DFW.2]
gas
A phase of matter that has a low density and is able to flow and adopt the size and shape of any empty container. The molecules in gases have relatively large kinetic energies, and move around freely, occasionally colliding with one another or with the walls of their container. [CPM.1]
liquid
A phase of matter that is able to flow, but does not expand to fill the whole volume of any empty container. The liquid phase of any substance is generally denser than the corresponding gas phase. The moleculesin liquids exhibit short-range order and move around mainly in the vicinity of their neighbours, but occasionally take longer jumps to join other groups of molecules. [CPM.1]
solid
A phase of matter which exhibits rigidity, and is not able to flow. The atoms or molecules in a solid oscillate around fixed equilibrium positions. In a crystalline solid, the atoms exhibit long-range order. [CPM.1]
time dilation
A phenomenon arising in Einstein's special theory of relativity, often summed up by the statement 'moving clocks run slow'. If the time interval between two ticks of a clock is recorded as ∆T0 in a frame in which the clock is at rest, then the time interval between the same two ticks, measured from a frame of reference in which the clock is moving at speed V, has the dilated value.1 /2 20V cTT−∆∆ =A consequence of this is that unstable particles observed to be travelling at speeds close to that of light, live much longer than identical particles that are observed at rest. Time dilation is built into the Lorentz transformation. [DFW.4; QPM.4]
Lorentz contraction
A phenomenon arising in Einstein's special theory of relativity, often summed up by the statement 'moving rods contract in the direction 36of their motion'. If the length of a rod is recorded as L0in a frame of reference in which the rod is at rest, then the length of the same rod, measured from a frame of reference in which the rod is moving at speed V in a direction parallel to the original measurement, has the contracted value1 .220cVL = L −Lorentz contraction is built into the Lorentz transformation. [DFW.4]
bond directionality
A phenomenon associated with the covalent bond between atoms (but not with ionic or metallic bonds) whereby the resulting molecules have a definite geometric structure. This arises because the paired valence electrons that form the covalent bonds are not free to move away from the bonded atoms but are strongly attached to them. This becomes apparent when one atom is bonded to two or three others and there are definite angles between the bonds. [QPM.2]
bond saturation
A phenomenon associated with the covalent bond that limits the number of atoms that may be directly bonded to any selected atom. This arises because the pairing of all unpaired electrons in the selected atom prevents the formation of any additional covalent bonds. [QPM.2]
operationalism
A philosophical doctrine asserting that only observationally defined quantities should be allowed to enter at any stage into a theory. [QPI.4]
positivism
A philosophical doctrine asserting, in its most extreme form, that no sentence is meaningful unless it can be directly verified by means of the senses. This view was fashionable at the time when quantum mechanics was first being developed and had some influence on the Copenhagen interpretation. [QPI.4]
event
A physical occurrence of very short duration, which occurs in a very small region of space. Ideally it occurs at a point in space and at an instant in time. [DFW.4]
observable
A physical property of a system that might be measured in a suitable experiment. Examples include position, momentum and energy. [QPI.4]
scalar field
A physical quantity to which a definite value can be ascribed at every point throughout some region of space. Examples include the temperature field in a room and the electric potential field between the plates of a capacitor. [SFP.1]
field
A physical quantity to which a definite value can be ascribed at every point throughout some region of space. Scalar fields (e.g. temperature, pressure and electric potential fields) are specified by a scalar value at every point; vector fields (e.g. electric fields, magnetic fields and gravitational fields) are specified by a vector value at every point. Historically, fields were introduced into physics as a means of accounting for the propagation of forces and other measurable phenomena without having to admit the possibility of action at a distance. [RU.1; SFP.1]
Z-N plane
A plot of atomic number Z against neutron number N for nuclei. The Z-N plane may be used in various way to highlight systematic variations in the properties of nuclei. (See path of stability and valley of stability for examples.)Z0particle$A type of elementary particle. A neutral spin 1 exchange particle, with a mass about 97 times that of the proton. The existence of the Z0 particle was predicted by the theory of the electroweak interaction. [QPM.4]
anode
A positive electrode. In a vacuum electronic device (such as a cathode ray tube), the anode is given its charge by external means and therefore attracts electrons.antibaryon$The antiparticle of a baryon. [QPM.4]
α-particle (alpha-particle)
A positively charged subatomic particle with about four times the mass of a hydrogen atom. Alpha-particles are composite particles consisting of two protons bound to two neutrons; they are identical to the nuclei of helium-4 atoms. Each α-particle has a mass of 4.00261u and carries a positive charge of 2e. [PM.3; QPI.1]
Bernoulli's principle
A principle asserting that; at constant height, the speed of flow of an ideal fluid is greatest where the pressure is smallest, and vice versa. It is quantified by Bernoulli's equation. [CPM.4]
Huygens principle
A principle asserting that; each point on a wavefront can be regarded as a source of secondary waves; in three dimensions these secondary waves are spherical; in two dimensions they are circular. The secondary waves from each point spread out equally in all directions with the wave speed v, just as ripples spread out across the surface of water when a stone is dropped into it. During an interval ∆t, the individual secondary waves travel a distance v1∆t from each point on the wavefront. The new position of the wavefront at 30the end of the interval is the envelope of these individual waves — a curve drawn tangentially through the individual secondary wavefronts. This new wavefront acts in turn as a further source of secondary waves, thus accounting for the continued propagation of the wave. [DFW.2]
Pauli's exclusion principle
A principle asserting that; no two electrons can occupy the same quantum state. Thus, for example, if two electrons in a particular atom have the same values of the quantum numbers n, l and ml, they must also have opposite spins, i.e. 21ms= + for one, while for the other .21ms= − 4[QPI.3; QPM.3]
principle of relativity
A principle asserting that; the laws of physics can be written in the same form in all inertial frames of reference. As originally put forward by Galileo, the principle of relativity covered only the laws of mechanics. The realization that its reach extended to the laws of electromagnetism, was the insight that led Einstein to the development of his special theory of relativity. [RU.1; DFW.4]
principle of complementarity
A principle of quantum mechanics, introduced by Niels Bohr, asserting that it is acceptable to use classically incompatible forms of language (such as those concerning waves and particles) when discussing quantum phenomena, though not simultaneously. Complementarity implies that the properties displayed by a quantum system depend on the apparatus used to examine it, and the properties associated with a system cannot be spoken of in isolation from the means used to determine them. [QPI.4]
nuclear fission
A process in which a heavy nucleussuch as uranium splits into two smaller nuclei of similar size, usually accompanied by the emission of two or three neutrons and approximately 3001MeV of energy. The released energy appears mainly in the form of kinetic energy of the two fragment nuclei, with smaller amounts in the form of γ-ray photons and radioactive decay of the two fragments. Roughly speaking, this release of energy comes about because the process involves a transition from a region of low B/A to a region of higher B/A in the binding energy per nucleoncurve. The energy released in fission reactions is the source of the energy released in atomic bombs and nuclear power stations. [QPM.3]
electrophoresis
A process in which a mixture of molecules or small particles suspended in a fluid is separated into its constituent components by applying a potential difference between two electrodes immersed in the fluid. The process makes use of the fact that the rate of movement of the molecules or particles depends on the charge they carry. [SFP.2]
(b) More generally, a term used either as an abbreviation for electromagnetic radiation or when referring to particles emanating from a source (particularly those resulting from the radioactive decay of nuclei).radiative transition
A process in which a quantum system (such as an atom) undergoes a transition from one energy level to another by the emission or absorption of electromagnetic radiation (i.e. a photon). [QPI.3]
induced fission
A process in which an atomic nucleusis caused to split into two daughter nuclei by some external cause. Some heavy nuclei such as 235U can absorb a thermal neutron and split into two roughly equal fragments with the release of energy and further neutrons. Such nuclei are said to be fissile. [QPM.3]
transition
A process in which the state of a quantum system changes. For confined systems, this generally involves a corresponding change of energy level. [QPI.2]
cyclic process
A process in which the system returns to its initial state. [CPM.3]
isothermal process
A process in which there is no change of temperature. (See also isothermal condition.) [CPM.3]
multiple-scattering process
A process that involves the deflection of a projectile (such as an α-particle), in a large number of individual encounters as it passes through a target (such as a foil of gold atoms). [QPI.1]
nuclear fusion
A processes in which two nuclei 'fuse' together to form a heavier nucleus. If the nucleus produced has mass number A ≤ 56 (e.g. 56Fe) or thereabouts, the process is likely to be exothermic, i.e. it will release energy. Fusion is crucial in stars for both energy release and for the production of the lighter elements, from helium up to iron (Fe), from primordial hydrogen. Fusion reactions are also the basis for the energy released in hydrogen bombs. [QPM.3]
vector product
A product of two vectors a and b, usually written as a × b, and sometimes referred to as the 'cross product' of those vectors. Given two vectors a and b, which are at an angle θ to each other, where 0° ≤ θ ≤ 180°, their vector product a × b is a vector of magnitude ab1sin1θ that points in the direction perpendicular to both a and b, as specified by the righthand rule.Alternatively, if the components of a and b are such that a = (ax, ay, az), and b = (bx, by, bz), then the components of the vector product a × b are given bya × b = (aybz− azby, azbx− axbz, axby− aybx).[PM.4]
scalar product
A product of two vectors a and b, usually written as a1•1b, and sometimes referred to as the 'dot product' of those vectors. Given two vectors a and b, which are at an angle θ to each other, where 0° ≤ θ ≤ 180°, their scalar product a1•1b is defined by the relationa1•1b = ab1cos1θ.Alternatively, if the components of a and b are such that a = (ax, ay, az) and b = (bx, by, bz) then the scalar product of a and b is given bya1•1b = axbx + ayby + azbz. [PM.2]
59strangeness
A property of hadrons that is in some respects similar to electric charge or baryon number. Strangeness is conserved in strong and electromagnetic interactions, but not in weak interactions. 4[QPM.4]
supersymmetry
A proposed symmetry, involving elementary particles and their interactions, that suggests hitherto unconfirmed relationships between fermionsand bosons. Supersymmetry has been used in formulating a number of superunified theories of particle physics. If supersymmetry really is a symmetry of nature, then it implies the existence of several new types of elementary particles. [QPM.4]
compound
A pure substance formed by the chemical combination of different elements. [CPM.1]
electromotive force (EMF)
A quantity measured in volts that describes the ability of a device to drive a current around a circuit. The electromotive force of a device is equal to the potential difference between the terminals of the device when it is part of an open circuit (i.e. when no current is flowing). Sources of EMF include cells, batteries, thermocouples, photovoltaic cells and various devices based on electromagnetic induction, such as generators and transformers. In such devices the EMF may be alternatively defined as the ratio of the power supplied by the device to the current that it produces in a circuit. Note that electromotive force is not a force in the sense defined by Newton's second law. [SFP.3]
decay width
A quantity that arises in the study of hadron resonances, and which is inversely proportional to the mean lifetime of those short-lived particles. Hadron resonances are observed as resonance peaks when certain scattering cross-sections are plotted against energy. The decay width of a given resonance is represented by the full width of the resonance peak at the level where its height is half of its maximum value. The decay width of a resonance has the units of energy. [QPM.4]
x-coordinate
A quantity that describes the position of a point in one dimension, in a specified coordinate system. The x-coordinate of a point (e.g. the instantaneous position of a particle moving along the xaxis) may be positive or negative. It's magnitude indicates distance from a chosen origin, while its sign indicates a direction relative to that origin. [DM.1]
scalar
A quantity that is completely specified by a number, or a number multiplied by an appropriate unit of measurement. Scalar values can be positive, negative or zero. Examples include, distance, speed, mass. Electric charge and temperature. (Contrast with vector.) [DM.2; SFP.1]
vector
A quantity that requires both a magnitude and a direction for its complete specification. Examples include position, displacement, velocity, acceleration, force, torque, angular velocity, momentum, angular momentum, and electric and magnetic fields. A vector can be represented by an arrow whose length is proportional to the magnitude of the vector and whose direction is the same as that of the vector. Vectors can also be specified by giving their components in a chosen coordinate system. In two dimensions, a vector v is written as v = (vx, vy). In three dimensions, three components are required: v = (vx, vy, vz). (Contrast with scalar.) [DM.2; SFP.1]
vector field
A quantity to which a definite magnitudeand direction can be ascribed at every point throughout some region of space. Physical examples include; electric fields, gravitational fields and magnetic fields. [SFP.1]
independent variable
A quantity whose value can be chosen at will within specified limits. (See also dependent variable and function.) [DM.1]
16dependent variable
A quantity whose value is determined by the value of one or more other variables, usually referred to as independent variables. [DM.1]
58standard model
A quantum field theory that incorporates fields representing the twelve fundamental quarks and leptons and the exchange particles of the strong, weak and electromagnetic interactions. It is well supported by current particle physics data. [QPM.4]
orbital angular momentum quantum number
A quantum number, conventionally represented by the symbol l, that characterizes the magnitude L of the orbital angular momentum of an electron in an atom: 4L = l(l +1) ".The quantum number l can take integer values from 0 to n − 1, where n is the principal quantum number. [QPI.3]
orbital magnetic quantum number
A quantum number, conventionally represented by the symbol ml, that determines the z-component, Lz, of the orbitalangular momentum of an electron in an atom:4 Lz = ml".The quantum number ml can take the values ml = 0, ±1, ±2, ..., ±l, where l is the orbital angular momentum quantum number. [QPI.3]
principal quantum number
A quantum number, conventionally represented by the symbol n, that is used (along with other quantum numbers) to label the quantum state of an electron in an atom. It plays a similar role to the Bohr quantum number (also denoted n) in that it is chiefly responsible for determining the energy of an electron in an atom (though in heavy atoms the energy also depends on the orbital angular momentum quantum number, l). The quantum number, n, can take any integer value from 1 upwards. 4[QPI.3]
stationary state
A quantum state in which the probabilities of all the possible outcomes of measurements are independent of time. Although such states may be described by time-dependent wavefunctions Ψ(x, t), they are, for most purposes, adequately described by a time-independent wavefunction ψ(x). In practice, such states are often specified in terms of the values of the quantum numbersthat characterize that state. A typical example would be the state of the hydrogen atom specified by the quantum numbers n = 2, l = 1, ml = −1. [QPI.2]
hybrid state
A quantum state of an atom with a wavefunction that is a linear superposition of the wavefunctions of states of different angular momentum. Important examples include the sp3 hybrid states arising in atoms of carbon, silicon and germanium. Each of these atoms has four valence electrons, a single s electron and three p electrons. When these atoms bond to form molecules or solids, the wavefunctions of their four valence electrons can mix together to form four sp3hybrid states. In these states, all four electrons are unpaired and are available to make four covalent bonds. [QPM.2]
nearly-free electron model
A quantum-mechanical model of the electron gas in solids that goes beyond Pauli's quantum free-electron model by introducing a small (spatially) periodic potential energy change, Vpot, to model the actual periodic crystal structure of the positive lattice ions. This additional potential energy term is included in the Schrödinger equation which is solved to obtain the allowed energies and wavefunctions. The allowed energies are found to be restricted to energy bands separated by energy gaps. The nearly-free electron model thus represents an approach to the band theory of solids. 4[QPM.2]
Heisenberg's uncertainty principle
A quantummechanical principle asserting that there is an inherent limit to the precision with which the values of certain pairs of physical quantities may be simultaneously known. It can be expressed in many forms, two of which are:1 There is a fundamental limit to the precision with which the position x and the momentum component px of a particle can be simultaneously known. For any choice of x-axis, the product of the uncertainties ∆x and∆px obeys the inequality ∆x1∆px≥ "/2.2 There is a fundamental limit to our knowledge of a particle's energy E, when it is measured in a finite time interval ∆t: the uncertainty ∆E in the energy obeys the inequality∆E1∆t ≥ "/2. [QPI.2; QPM.4]
forbidden transition
A radiative transition is said to be forbidden if it corresponds to a change in quantum numbers that does not satisfy the relevant selection rules. Such transitions have a very low probability of occurring in comparison to allowed transitions which do satisfy the selection rules. [QPI.3]
Newtonian telescope
A reflecting telescope that uses a converging mirror (the objective or primary mirror) and a small plane mirror (the secondary mirror). The secondary mirror is positioned at 45° to the optical axis, and directs rays coming from the primary mirror to one side of the telescope tube. An eyepiece lens may be positioned to view the virtual image directly by eye; alternatively a photographic or electronic detector may be used to capture a real image. (See also telescope.) [DFW.3]
Cassegrainian telescope
A reflecting telescope using a converging mirror (the objective or primary mirror) and a small diverging mirror (the secondary mirror). This secondary mirror increases the effective focal 9length of the telescope, and directs the light rays back through a hole in the centre of the primary mirror. An eyepiece lens may be positioned to view the virtual image directly by eye; alternatively a photographic or electronic detector may be used to capture a real image. (See also telescope.) [DFW.3]
Galilean telescope
A refracting telescope that uses a diverging lens as the eyepiece and a converging lens as the objective. (See also telescope.) [DFW.3]
p-n junction
A region (usually a thin layer) within a semiconductor where the doping changes from p-type to n-type. A p-n junction is usually associated with a (similarly narrow) depletion region in which mobile charge carriers are relatively rare due to the recombination of electrons and holes. A p-n junction can act as a rectifier, passing a large current from the pregion to the n-region, but very little current in the reverse direction. Such junctions are found in nearly all semiconductor devices such as transistors and lightemitting-diodes. [QPM.2]
black hole
A region of space from which light is unable to escape due to the action of gravity. When a star has exhausted all its internal sources of energy, it will collapse under its own gravitational attraction. If the mass of the residual stellar core is greater than about three times the mass of the Sun, it will eventually become so concentrated that the escape speed from its surface will exceed the speed of light. In this state, according to classical physics no radiation (or matter) can escape from it, so the collapsing core will inevitably lead to the formation of a black hole. [SFP.2]
secondary mirror
A relatively small mirror used in a reflecting telescope to direct the light after it has been reflected from the objective mirror (or primary mirror). In a Newtonian telescope, the secondary mirror is a plane mirror inclined at 45° to the optical axis. In a Cassegrainian telescope, the secondary mirror is a diverging mirror perpendicular to the optical axis, and 54serves to extend the effective focal length of the telescope. [DFW.3]
right-hand grip rule
A rule for associating one of the two directions along an axis with a given sense ofrotation about that axis. Extend the thumb of your right hand, and curl the fingers of that hand around the thumb. Then, turn your right hand so that its curled fingers twist around the thumb in the same sense that the rotation turns about the given axis. The direction along the axis indicated by your thumb is then the direction associated with the rotation. This rule may be used to associate the direction of an angular velocity with the rotation described by that angular velocity. Also, the rule may be used to associate the direction of current flow in a wire with the sense in which magnetic field lines circle around that wire. [DM.3; SFP.4; DFW.1]
addition rule for probabilities
A rule stating that; if a number of alternative outcomes are mutually exclusive, the probability of getting one or other of these outcomes is found by adding their individual probabilities. [CPM.2]
Bohr model
A semi-classical model of the atom introduced by Niels Bohr in 1913. The model assumes (classically) that a central, positively charged, nucleus is orbited by one or more electrons that are held in place by electrostatic forces. It also assumes (non-classically) that the electrons are confined to Bohr orbits in which the angular momentum is an integer multiple of "(Planck's constant divided by 2π). It further assumes that the electrons do not emit electromagnetic radiationas long as they remain in one of the allowed orbits, but that emission (or absorption) does occur when an electron makes a transition that takes it from one orbit to another. [QPI.1]
Balmer series
A series of lines in the spectrum of atomic hydrogen, the visible members of which have wavelengths 656.2101nm, 486.0741nm, 434.0101nm and 410.121nm. In the context of the Bohr model of the atom, these lines correspond to transitions to the n = 2 Bohrorbit from orbits with n = 3, 4, 5 and 6, respectively. Transitions from orbits with higher values of n correspond to lines that are in the ultraviolet part of the spectrum. [QPI.1]
diffraction grating
A series of uniformly spaced narrow slits of equal width, which act as a coherent source of waves and give rise to interference fringeswhen illuminated with a plane wave. The positions of successive orders of diffraction in the diffraction patternare given by the diffraction equation. [DFW.2]
velocity transformation
A set of equations relating the velocity of a particle in one frame of reference to the velocity of the same particle measured in another frame of reference, which may be moving relative to the first. The velocity transformation is usually expressed in terms of the Cartesian components of the particle's velocity, and may be deduced from the coordinate transformation that relates the two frames of reference. Given a particle that moves with velocity v = (vx, vy, vz) in frame of reference A, and velocity v′ = (vxvyvz′, ′, ′) in frame of reference B, then, if A and B are in standard configuration, with V being the speed of B with respect to A, the Galilean coordinate transformation implies thatxv′ = vx− V, vy′ = vy, zv′ = vz.By contrast, the Lorentz transformation implies that1 ( )2V cVxxxvvv−−′= ,1 ( )1 ( )22 2V cV cxyyvvv−−′= , 1 ( )1 ( )22 2V cV cxzzvvv−−′= . It is the Lorentz transformation that gives the correct result; the Galilean coordinate transformation only provides an approximation at speeds that are small compared with the speed of light. [DFW.4]
coordinate transformation
A set of equations that relates the coordinates of an event in one frame of reference to those of the same event in another frame of reference, which may be moving relative to the first. See, for example, Galilean transformation and Lorentz transformation, and see for comparison velocity transformation. [DFW.4]
equilibrium state
A settled and unchanging state of thermodynamic equilibrium. [CPM.3]
pivot
A short shaft or axle about which a body, such as a lever, can rotate. [PM.4]
object distance
A signed quantity, usually represented by the symbol u, the magnitude of which is equal to the distance from a lens or mirror to an object whose imageis being produced by that lens or mirror. According to the real-is-positive convention, the object distance is positive for real objects and negative for virtual objects.objective$See objective lens and objective mirror. [DFW.3]
image distance
A signed quantity, usually represented by the symbol v, the magnitude of which is equal to the distance from a lens or mirror to the image produced by that lens or mirror. According to the real-is-positive convention, the image distance is positive for real images and negative for virtual images.
cell
A single unit of a battery. It consists of a pair of metal plates immersed in an electrolyte. An electric current is produced by chemical interaction between the plates and the electrolyte. [SFP.3]
comet
A small body (typically 101km or so in diameter) that orbits the Sun in a highly eccentric orbit. When it is sufficiently close to the Sun, dust and gas stream from the surface of the comet and form a characteristic tail that may be more than a million kilometres in length and visible from Earth. [DM.3]
polycrystalline solid
A solid consisting of many tiny crystals joined at their boundaries. The formation of such a solid is the result of the growth and merger of many randomly oriented crystals that originate more-orless simultaneously at different locations. 4[QPM.2]
molecular solid
A solid consisting of molecules that are weakly bound together due to the action of van der Waals forces or because of hydrogen bonding. [QPM.2]
covalent solid
A solid containing neutral atoms joined by covalent bonds, with high bond directionality. Examples include diamond and silicon where the bonds are directed in a tetrahedral arrangement to give an open structure with four neighbours around each atom. [QPM.2]
amorphous solid
A solid in which the atoms exhibit short-range order but not long-range order. Such a solid is distinguished from a liquid by the fact that it is rigid rather than fluid. Materials such as glass can form such solids, even though they do not represent the lowest energy condition for the material. This is possible because the atoms in the material are not sufficiently mobile to allow it to make the transformation to the lower energy crystalline solid. [CPM.1; QPM.2]
wavefunction
A solution of the time-dependent Schrödinger equation, usually represented by Ψ(x, t) for cases involving one spatial dimension, which, according to conventional quantum mechanics, provides the fullest possible description of the state of a quantum system. Knowing the wavefunction that corresponds to any particular state makes it possible to predict the possible outcomes of measurements performed on the system while it is in that state and also allows the prediction of the probability of each of those possible outcomes. For systems that are in stationary states (implying that the probabilities of the possible measurement outcomes do not change with time), the wavefunction may be written as a product of functions that separately depend on space and time. The spatial part of such a product, usually represented by ψ(x) in one dimension, and referred to as the time-independent wavefunction, then satisfies the time-independent Schrödinger equation. (See also Born interpretation.) 4[QPI.2]
time-independent wavefunction
A solution to the time-independent Schrödinger equation. Such solutions may be used to describe the stationary states of a quantum system. [QPI.2]
time-dependent wavefunction
A solution to the timedependent Schrödinger equation. According to conventional quantum mechanics, the time-dependent wavefunction describing a particular state provides the fullest possible description of that state. [QPI.2]
Chandler wobble
A somewhat irregular movement of the Earth relative to its axis of rotation that contributes to the phenomenon of polar motion. The Chandler wobble has an approximate period of 4301days, and causes the North Pole to trace out a roughly circular path on the Earth's surface, with an approximate radius of 61m. A major contribution to the Chandler wobble arises from the misalignment of the Earth's angular momentum with its axis of maximum moment of inertia, since this leads to a torque-free angular acceleration. (This effect is further modified by distortions of the Earth made possible by its lack of perfect rigidity.) [PM.4]
incoherent source
A source in which different regions emit waves with significantly different phases. [DFW.2]
electron gun
A source of electrons (usually of a specific energy). It is an arrangement of anode and cathode maintained at a large potential difference and in a highly evacuated region. Electrons are emitted from the cathode and attracted towards the anode, which is perforated so that the electrons may pass through as a fine beam. [SFP.2]
coherent source
A spatially extended source of wavesis said to be coherent if the emissions contributed by the various regions of the source are always in phase with one another. For example, if plane waves of light impinge normally on a pair of slits in a screen, the slits act as a secondary source of light (by the Huygens principle); this source is coherent because the two slits produce light waves that are in phase at the point of emission. [DFW.2]
static equilibrium
A special case of mechanical equilibrium in which a body is completely at rest. For such a body the net external torque about any point must be zero. [PM.4]
photographic emulsion
A special type of photographic film in which charged particles leave tracks. An important means of detecting particles in high-altitude cosmic ray experiments. 4[QPM.4]
neutrino
A spin 21 uncharged lepton of very small (possibly zero) mass. Three different types of neutrino are known; electron neutrino, muon neutrino and tauon neutrino. [QPM.4]
omega minus
A spin 23baryon (represented by the symbol Ω−) the prediction of which was one of the early successes of the quark model. [QPM.4]
ideal spring
A spring that produces a linear restoring force described by the Hooke's law relation, Fx = −ksx, for all values of the extension x, irrespective of sign. Many real springs behave approximately like ideal springs provided they are not stretched or compressed too much. [PM.1]
generic UPT surface
A surface representing the sets of values of internal energy U, pressure P and temperature T that characterize the equilibrium states of a macroscopic sample of a typical pure substance. The surface is a pictorial representation of the internal energy equation of the substance and shows how different regions correspond to different phases (solid, liquid or gas) or combinations of phases. [CPM.1]
PVT surface for any ideal gas
A surface representing the sets of values of pressure P, volume V and temperature T that characterize the equilibrium states of a given macroscopic system (such as a sample of matter). The surface is a pictorial representation of the system's equation of state. [CPM.1; CPM.3]
generic PVT surface
A surface representing the sets of values of pressure P, volume V and temperature Tthat characterize the equilibrium states of a macroscopic sample of a typical pure substance. The surface is a pictorial representation of the equation of state of the substance and shows how different regions correspond to different phases (solid, liquid or gas) or combinations of phases. [CPM.1]
temperature scale
A system for determining temperatures based on the use of an agreed unit of temperature and a number of fixed points that assign particular temperatures to reproducible physical states. (See, for example, absolute temperature scale.) [CPM.1, CPM.3]
deterministic system
A system for which there are well-defined rules, or equations, governing changes at all times. If these rules are known, they can be used to determine the state of the system at a later time from information about the state of the system at an earlier time. [PM.5]
frame of reference
A system of coordinate axes and synchronized clocks, that makes it possible to specify uniquely the location in space and time of any given event. [PM.1, DFW.4]
Cartesian coordinate system
A system of mutually perpendicular axes, meeting at a single point called the origin, and calibrated in a common way (usually in metres, starting from zero at the origin), that allows the position of any point to be uniquely specified by an ordered set of values. In three-dimensional space, three axes are required; these are conventionally labelled x, yand z; and the coordinates of a point P are represented by the ordered triplet of position coordinates (xP, yP, zP). Three-dimensional Cartesian coordinate systems may be right-handed or left-handed. It is conventional to use right-handed systems for most purposes. [DM.2; DM.3]
closed system
A system that can exchange no matter with its environment. [CPM.3]
linear system
A system that is described by a linear map or a linear equation of motion. [PM.5]
non-linear system
A system that is described by a non-linear map or a non-linear equation of motion. [PM.5]
isolated system
A system which cannot exchange matter or energy with its environment. In the context of mechanics, an isolated system is one that is subject only to internal forces. [PM.3; CPM.3]
stroboscopic (photography)
A technique for recording the motion of an object. As the object moves, a rapid sequence of short-duration flashes enables a camera to record several successive positions of the object on a single photographic image. [DM.2]
refracting telescope
A telescope that uses a lens as its objective. Also called a 'refractor'. (See also Keplerian telescope, Galilean telescope and telescope.) [DFW.3]
reflecting telescope
A telescope that uses a mirror as its objective. Also called a 'reflector'. (See also Cassegrainian telescope, Newtonian telescope, Schmidt telescope and telescope.) [DFW.3]
ideal gas temperature scale
A temperature scale based on the behaviour of ideal gases, and realized in practice by determining the behaviour of real gases in the limit of very low pressures where they obey the ideal gas equation of state. [CPM.1]
thermal energy
A term for the sum of the kinetic energies and mutual potential energy of all the basic particles (e.g. molecules) in a system. Not to be confused with heat. (See typical thermal energy of a particle.) [CPM.1]
sinusoidal
A term indicating a variation that may be described by a sine function. This also applies to a cosine function since cos(θ0) = sin(θ + π/2). [DM.3]
heliocentric
A term meaning 'Sun-centred', that is used to describe the theory propounded by Copernicus and others that the Earth and planets move around the Sun. By contrast, Ptolemy supported the 'Earth-centred' geocentric view that the Sun and planets move around the Earth. [RU.1]
reaction
A term used in Newtonian mechanics to describe one of the paired forces referred to in Newton's third law of motion, the other member of the pair being referred to as the action. [PM.1]
26free electrons
A term used in modelling the behaviourof electrons in metals when the valence electrons that detach themselves from individual atoms are treated as moving freely throughout the volume of the metal without interacting with one another, or with the positive ions, apart from occasional collisions. The free electrons are also called conduction electrons. See Drude's free-electron model and Pauli's quantum freeelectron model. [QPM.1]
diatomic
A term used to describe a moleculeconsisting of two atoms bound together by interatomic forces. [CPM.1]
reversible process
A term used to describe a process where, following the completion of the process, both the system and its environment can be returned to the states they were in prior to the process. Any process that is not reversible is said to be irreversible. [CPM.3]
three-dimensional
A term used to describe a region of space that has three independent directions, or a body that fills such a region. [DM.1]
proportionality
A term used to describe a relationship between two quantities, y and x say, in which altering one of the quantities by a certain factor implies altering the other by the same factor. The existence of such a relationship is indicated by saying that y is proportional to x or by writing y ∝ x. The proportionality of x and yimplies that they are related by an equation of the formy = kxwhere k is a constant, known as the constant of proportionality.proton$A kind of elementary particle found in the nucleus of every atom. Protons carry a positive charge +e (= 1.602 × 10−191C) and have a mass of 1.673 ×10−271kg (= 938.31MeV/c2). The mass of a proton is about 0.1% less than the mass of a neutron and the two particles have similar sizes (about 10−151m). The proton is a stable baryon of spin 21. [CPM.1; QPI.1; QPM.4]
plane polarized
A term used to describe a transverse wave in which the transverse vibrations occurring at all points on the path of the wave are all in the same plane. In such cases the plane defined by the direction of the vibrations and the direction of propagation of the wave is called the plane of polarization of the wave. [DFW.2]
unpaired electron
A term used to describe any electron that occupies a state with quantum numbers n, l, ml and ms in an outer shell of an atom when the state with quantum numbers n, l, ml and −ms is unoccupied. In other words a valence electron that does not have a partner of opposite spin orientation in the same subshell. According to Hund's rule the outer shells contain themaximum number of unpaired electrons permitted by Pauli's exclusion principle. Unpaired electrons from different atoms are shared to form pairs in covalent bonds between atoms. [QPM.2]
inverse square law
A term used to describe any law asserting that the value of a quantity is proportional to the reciprocal of the square of some other quantity, usually the distance from some point. Well-known examples of inverse square laws include; Coulomb's law, Newton's law of universal gravitation and the law relating the intensity due to a spherical wave to the distance from the source of that wave. [DM.3; PM.1; DFW.2]
force law
A term used to describe any law that describes the magnitude and direction of a particular force under specified conditions. Examples include Newton's law of universal gravitation, the law ofterrestrial gravitation, Hooke's law, Coulomb's law and the Lorentz force law. [PM.1]
Higgs boson
A term used to describe any member of a class of hypothetical spin 0 elementary particles that play an important part in the standard model of particle physics. Higgs bosons are required by the standard model in order to account for some of the observed features of the combined electromagnetic and weakinteractions; they also play a crucial role in determining particle masses. Higgs bosons are thought to be very massive (perhaps in excess of 2001GeV/c2). [QPM.4]
quark
A term used to describe any of the charged particles that are currently believed to be fundamental constituents of all hadrons (i.e. baryons and mesons). Quarks are not expected to be observed as isolated particles due to confinement. Six kinds of quark are currently known (implying the existence of six kinds of antiquark). The six types are; up (u), down (d), charm(c), strange (s), top (t) and bottom (b). The quarks all have spin 21, baryon number 31, and a charge that is a multiple of e31. [QPM.4]
meson
A term used to describe any strongly interacting particle that has zero or integer spin (i.e. spin 0, 1, 2, etc.). Each meson is a combination of a quarkand antiquark, and consequently has baryon numberB = 0. Mesons are a sub-class of hadrons. [QPM.4]
monochromatic
A term used to describe electromagnetic radiation of a single frequency. [DFW.2]
diamagnetic
A term used to describe materials which, when placed in a magnetic field, become magnetized in the direction opposite to the applied field. The total magnetic field within the material is therefore less than the applied magnetic field that causes the magnetization. (Contrast with paramagnetic.) [SFP.4]
paramagnetic
A term used to describe materials which, when placed in a magnetic field, become magnetized in the direction parallel to the applied field. The total magnetic field within the material is therefore greater than the applied magnetic field that causes the magnetization. (Contrast with diamagnetic.) 4[SFP.4]
colliding beams
A term used to describe particle physics experiments in which a beam of particles is directed at another beam of particles, moving in more or less the opposite direction. (Contrast with fixed target.) [QPM.4]
fixed target
A term used to describe particle physics experiments in which a particle beam is directed at a stationary target. (Contrast with colliding beams.) [QPM.4]
entangled
A term used to describe states and wavefunctions of systems, consisting of two or more parts, in which it is impossible to associate a particular wavefunction with one part of the system in isolation from the other parts. Such wavefunctions generally predict correlations between the results of measurements performed on different parts of the system, even when those parts are well separated, as in the case of the Einstein-Podolsky-Rosen argument. [QPI.4]
baryon
A term used to describe strongly interactingparticles that have half odd-integer spin (i.e. spin 2321, , etc.). Each baryon is a combination of three quarks, and consequently has baryon number B = 1. Baryons are a sub-class of hadrons. [QPM.4]
parent nucleus
A term used to describe the initial nucleus in any nuclear decay process. The final nucleus that results from the decay is known as the daughter nucleus. [QPM.3]
function
A term used to describe the mathematical relationship that exists between two variable quantities. y and x say, when the value of y depends on the value of x. The dependent variable y is said to be a function of the independent variable x and may be written as y(0x) to emphasize this dependence. The nature of any particular function is usually expressed in terms of an equation, such as y = mx + c, or y = A sin(kx), and may often be conveniently represented by means of a graph of y against x. 4[DM.1]
subtend
A term used to describe the relation between two points (or an arc connecting those points) and the angle between those points as measured at a third point. A circular arc of radius R and arc length sarc is said to subtend an angle (measured in radians) of α = sarc/R at the centre of the circle of which it is part. More generally, any two points A and B may be said to subtend an angle α at a third point C if α is the angular displacement of A from B, as measured at C. [DM.3]
coherent
A term used to describe the relationship between different processes that might allow an event to occur when the contributions of those different processes can be represented by a sum of terms in a wavefunction (as opposed to a sum of probabilities). Coherence is generally regarded as a necessary condition for interference. [QPI.4]
dynamically similar
A term used to describe the relationship between two fluid flows that are geometrically similar, and which have the same Reynolds number. [CPM.4]
fine structure
A term used to describe the small energy splittings in atomic energy levels due to the interaction of the magnetic moments associated with the spin and the orbital behaviour of the electron — the so called spin-orbit interaction. [QPI.3]
macroscopic
A term used to indicate that the relevant size scale is moderately large. For example, a system is said to be macroscopic if it is sufficiently large for its bulk characteristics to be easily measured. Macroscopic systems are normally larger than 0.11mm across and contain more than 1017 atoms. (Contrast with microscopic.) [CPM.1]
39microscopic
A term used to indicate that the relevant size scale is very small. For example, a system is said to be microscopic if it is too small for its bulk characteristics to be easily measured. Microscopic systems are normally smaller than 0.11mm across and contain fewer than 1017 atoms. [CPM.1]
deterministic
A term used to indicate the possibility, in principle, of making exact and complete predictions about the future, given sufficiently exact and complete information about the past. Newtonian mechanics is an example of a deterministic theory, but quantum mechanics is not deterministic. (See also deterministic chaos and deterministic system.) [QPI.2]
hadrons
A term used to refer collectively to mesonsand baryons. Hadrons are composite particles that contain quarks and/or antiquarks, and which participate in strong interactions. Many types of hadron are known, including; protons, neutrons, pions and kaons. (Contrast with leptons.) [QPM.4]
projectile
A term used to refer to any object launched into unpowered flight near the Earth's surface so that it is subject only to air resistance and the effect of terrestrial gravity. If a projectile is modelled as a particle, and the effect of air resistance is ignored, then the trajectory of the projectile will be a parabola. [DM.2]
fundamental forces
A term used when referring to the four known fundamental interactions: the gravitational, weak, electromagnetic and strong interactions. [QPM.4]
Newton's theorem
A theorem stating that; the gravitational effect of any spherically symmetric body, outside its own surface, is identical to that of a single particle, with the same mass as the body, located at the centre of the body. [PM.1]
Einstein's theory of heat capacities
A theory predicting the heat capacities of solids, based on the assumption that each atom in the solid behaves as a three-dimensional quantized oscillator. The theory predicts that the molar heat capacity of any elemental solid at absolute temperature T is given byCm(T) = 3Rx2ex/(ex− 1)2where R is the universal gas constant and x represents the ratio of the solid's Einstein temperature to its absolute temperature. Though rather crude, the theory accounts for some of the observed departures from the classical Dulong-Petit law of heat capacities, according to which Cm = 3R. [QPI.1]
band theory of solids
A theory that accounts for the existence of semiconductors, insulators and metals on the basis of the quantum-mechanical behaviour of electrons confined by spatially periodic potential energyfunctions. The theory implies that the energy levels of electrons in a crystalline solid are distributed in a number of bands that may overlap or be separated by energy gaps of various sizes. The theory provides the foundation for solid state electronics. (See also nearlyfree electron model, and tight-binding model.)4[QPM.2]
Bohm's theory
A theory that replicates all the predictions of quantum mechanics, but does so at the price of introducing a highly non-local 'quantum potential'. It is related to de Broglie's theory, in which the wavefunction was supposed to act as a 'pilot wave', influencing the (classical) motion of particles and guiding them towards the destinations that quantum mechanics predicted. (Bohm's theory may be regarded as a realist interpretation of quantum mechanics, in which case it is known as the ontological interpretation.) [QPI.4]
W particle
A type of elementary particle. A spin 1 exchange particle with a mass about 88 times that of the proton. There are two kinds of W particle, indicated W+and W− according to charge. The existence of the W particles was predicted by the theory of the electroweak interaction. [QPM.4]
scanning tunnelling microscope
A type of microscope, in which a very fine, positively charged, metal tip is brought sufficiently close to the surface of the specimen that electrons can tunnel from the surface to the tip. By moving the tip across the surface of the specimen in such a way that the tunnelling current remains constant, the surface topography is mapped out. Under favourable circumstances, it is possible to deduce the locations of surface atoms. [CPM.1]
β-decay (beta-decay)
A type of radioactive decayprocess. There are three distinct kinds of decay processes that are classed as β-decay. In negative betadecay (β−-decay) the nucleus spontaneously emits an electron and an antineutrino. In positive beta-decay (β+-decay), also called positron decay, the nucleus spontaneously emits a positron and a neutrino. In electron capture the nucleus spontaneously captures an orbiting electron in an s state (quantum number l = 0) and emits a neutrino; an X-ray is also emitted as electrons in outer shells fall into the vacancy left by the capture. [QPM.3]
neutral equilibrium
A type of static equilibrium in which a system displaced slightly from its original position has no tendency to return to that position, nor to move further away from that position. This is the kind of static equilibrium exhibited by a uniform spherical body resting on a horizontal plane. [PM.4]
x-axis
A uniformly-calibrated straight line from which the x-coordinate of a particle can be read. The choice of x-axis incorporates a choice of origin (at which x = 0) and a choice of direction of increasing x. [DM.1]
radian
A unit of angle, common in scientific work. If a circular arc of length r has a radius r measured from a point O, then the angle subtended at O by the endpoints of the arc is 11radian. It follows that 2π 1radians are equivalent to 360°, so 11radian is equivalent to approximately 57.3°. The standard abbreviation of radian is rad. [DM.3]
barn
A unit of cross-section for particle collisions. It is represented by the symbol b and is defined by the relation 11b = 10−281m2. [QPM.4]
electronvolt
A unit of energy, represented by the symbol eV and defined by the relation 11eV = 1.602 ×10−191J. The electronvolt is the change in potential energy of an electron that is displaced through a potential difference of 11volt. [SFP.2; QPM.4]
kilowatt hour
A unit of energy, represented by the symbol kW1h, and defined by the relation 11kW1h = 11kilowatt × 11hour = 3.61MJ.The kilowatt hour is widely used in billing for electrical energy. [PM.2; SFP.3]
atomic mass unit
A unit of mass, denoted u or amu, and defined as one-twelfth of the mass of one atom of carbon-12, the most common isotope of carbon. 11u = 1.6605 × 10−271kg. [CPM.1]
hole
A vacancy in an energy band of a semiconductorthat behaves like a positively charged particle. When electrons are excited from the valence band into the conduction band or to acceptor levels in the semiconductor, there are empty states left in the valenceband. When an electric field is applied to the semiconductor, electrons in the valence band can move into these empty states thereby allowing a current to flow. This movement of electrons in the direction opposite to the field direction is best described as the movement of positively charged holes, in the same direction as the field. In a p-type semiconductor the majority of charge carriers are holes. [QPM.2]
coordinate
A value, determined within a coordinate system, that may be used to specify the position of a point. [DM.1; DM.2]
subject
A variable isolated on one side (usually the left-hand side) of an equation, and therefore expressed in terms of the other variables in the equation. [DM.1]
average velocity
A vector quantity that measures the net rate of change of a particle's position over a given time interval. If the particle undergoes a displacement∆r in a time interval ∆t, then the average velocity over that time interval is defined to be∆t∆〈 〉 =rv . [DM.2]
torque
A vector quantity, usually denoted by G, that measures the turning effect of a force about a specified point. The torque about a point O due to a force F is given by the vector product G = r × Fwhere r is the displacement vector from O to the point of application of F. This implies that G has magnitude rF1sin1θ, and that it points in a direction that is perpendicular to r and F, as specified by the right-hand rule. The SI unit of torque is the N1m. [PM.4]
zero vector
A vector that has zero magnitude, and therefore may be associated with any direction. It is represented in printed text by the symbol 0. [DM.2]
strong nuclear force
A very short-range attractiveforce (also called the strong force or the strong interaction), that acts between nucleons. It does not act on electrons or other leptons and is almost independent of electric charge. The strong nuclear force is responsible for holding the nucleus together, despite the mutual electrostatic repulsion of its constituent protons. The strong nuclear force is the strongest of the four fundamental forces. 4[RU.1; QPM.3; QPM.4]
aqueous humour
A watery fluid in the human eye that fills the chamber between the cornea and the crystalline lens. It contributes substantially to the focusing power of the eyelens system: the cornea + aqueous humour combination acts as a fixed focal lengthconverging lens with a power of about 401dioptres. [DFW.3]
probability wave
A wave (also known as a de Broglie wave) that is associated with a particle in quantum physics. The wavelength of the wave is related to the particle's momentum magnitude p by means of the de Broglie formula (λdB = h/p), while the square of the wave's amplitude at any given point is proportional to the probability of detecting the particle in the vicinity of that point. The concept of a probability wave is a crude precursor to the more precise notion of a time-dependent wavefunction. [QPI.2]
longitudinal wave
A wave composed of oscillationsthat take place in a direction parallel to the direction of propagation of the wave. (Contrast with transverse wave.) [DFW.2]
transverse wave
A wave composed of oscillationsthat take place in a direction perpendicular to the direction of propagation of the wave. (Contrast with longitudinal wave.) [DFW.2]
seismic wave
A wave in the Earth, generated by an earthquake. P-(primary) waves are longitudinal waves, whereas S-(secondary) waves are transverse waves. [DFW.2]
standing wave
A wave that does not travel, although it can be regarded as being the superposition of two travelling waves, travelling in opposite directions. Along the path of the wave there are regularly spaced points, called nodes, at which the wave causes no disturbance; these nodes are separated by half a wavelength. At all points between the nodes oscillations occur at a common frequency but with differing amplitudes. A common example of a standing wave arises in the case of a string stretched between fixed endpoints (as in a musical instrument); the standing waves that can be excited on such a string are restricted by the requirement that an integer number of half-wavelengths must fit between the endpoints, where the disturbance is zero. [DFW.2]
travelling wave
A wave that propagates from one place to another. One example of such a wave is represented by the function y(x, t) = A1sin1(kx − ω0t + φ). Here A is the amplitude of the wave, and the phase of the wave is (kx − ω0t + φ), where k is the angular wavenumber, ω is the angular frequency, and φ is the phase constant. [DFW.2]
spherical wave
A wave that spreads out isotropically from a fixed source, with spherical wavefronts. The intensity of a spherical wave obeys an inverse square law. [DFW.2]
spherical wavefront
A wavefront produced by a spherical wave. Such a wavefront takes the form of a spherical surface and connects points in the (spherical) wave that have the same phase. [DFW.2]
van der Waals force
A weak, short range, attractive force that arises between closely separated atoms or molecules as a result of interactions between the fluctuating electric dipoles each of those atoms or molecules induces in the other. The van der Waals force is also known as the London force, and can be the main cause of bonding when stronger forces are absent, as in the cases of solid neon and solid argon, and for a range of molecular solids. [QPM.2]
order of diffraction
A whole number n, associated with each of the intensity maxima seen in a diffraction pattern. When a beam of light passes through a double slit or a diffraction grating, the beam transmitted in the same direction as the incident beam is said to be the 'zeroth order' diffracted beam (n = 0). The next peaks on either side are called 'first-order peaks' and are associated with n = 1 or 'first-order' diffracted beams, the next are 'second-order' (n = 2), and so on. The order of diffraction appears in the diffraction equation:nλ = d sin θn44[DFW.2]
Carnot engine
An 'ideal' heat engine, the operation of which is based on a Carnot cycle. A Carnot engine converts heat to work with the greatest efficiency possible for any heat engine. [CPM.3]
SI submultiple
An SI submultiple is one of a number of standard factors of the form 10−3, 10−6, 10−9, etc. Each is represented by a standard prefix such as milli, micro, nano, etc. [DM.1]
state space
An abstract 'space' in which the state of a (classical) system may be represented by a point. If mquantities are required to completely specify the state of a system, then the corresponding state space is mdimensional and the point in state space that represents any given state of the system will have m coordinates. The changing state of a system as it evolves with time can be represented by a trajectory in state space. [PM.5]
SQUID
An acronym for Superconducting Quantum Interference Device. Such a device typically consists of two Josephson junctions connected in parallel, and may take the form of a loop of superconductor interrupted by two 'weak link' point contacts. The electric current that flows in the loop is extremely sensitive to changes in the magnetic flux through the loop, so a SQUID can be used to detect tiny changes of magnetic field. [QPM.2]
asymmetry effect
An effect that influences the properties of nuclei, including their masses, and which arises from the fact that the strong nuclear force is slightly stronger between pairs of unlike nucleons than between pairs of like nucleons. (In other words, it is slightly stronger between a neutron and a proton than it is between two neutrons or between two protons.) [QPM.3]
alternating current
An electric current that periodically reverses direction as well as varying in magnitude. Such currents are frequently sinusoidal functions of time. (Contrast with direct current.) [DFW.1]
LC circuit
An electrical circuit consisting of an inductor and a capacitor. Such circuits support charge oscillations at a natural frequency ƒ = 1/2π LC , where L is the inductance and C the capacitance. When an LCcircuit is driven by an externally supplied signal, its response will be greatest when the frequency of the driving signal is close to the natural frequency of the LCcircuit. This provides the basis for the tuned circuitsused in radio and television receivers. (See also inductive circuit and capacitive circuit.) [DFW.1]
relative permittivity
An electrical property of an insulator, represented by the symbol εr. The relative permittivity of an insulator may be determined by dividing the capacitance of a capacitor when the insulator fills the region between the plates, by the capacitance of the same capacitor when its plates are separated by a vacuum. Relative permittivity is a dimensionless quantity. [SFP.2]
resistor
An element in an electrical circuit whose main function is to provide electrical resistance. [SFP.3]
tauon neutrino
An elementary particle that has no known substructure and is therefore regarded as a truly fundamental particle. It is the partner to the tauon in the third generation of leptons. It has no charge, spin 21 and a mass of less than 181MeV/c2. [QPM.4]
Dulong-Petit law
An empirical law stating that; all solid elements have molar heat capacities of about 3R (= 251J1K−11mol−1) where R is the universal gas constant. This law is valid for most elements at room temperature, but is not true for diamond at room temperature, nor for other substances at temperatures well below room temperature. The law applies to elemental solids well above their Einstein temperatures. [CPM.2; CPM.3; QPI.1]
Hooke's law
An empirical law stating that; when a body is stretched, the magnitude of the restoring forcewhich opposes the stretching is directly proportional to the increase in the body's length. Hooke's law is not a fundamental law that must be obeyed by all bodies. Rather it describes the behaviour of some bodies, such as springs or elastic strings, provided they are not stretched too far. If a body is stretched along the x-axis, with x measuring the extension of the body, i.e. the displacement of the free end from its equilibrium position, then Hooke's law may be written in the form Fx = −kx where k is the force constant of the restoring force. A spring that exactly obeys Hooke's law is said to be an ideal spring, and the force constant of such a spring is called the spring constant ks. [PM.1]
Ohm's law
An empirical law, applying only to certain materials and only under certain circumstances, stating that; the potential difference V across a sample is directly proportional to the current i that flows through it. The proportionality is usually expressed as V = iR, where V drops in the direction of the current flow, and the constant of proportionality R represents the resistance of the sample. As long as Ohm's law is applicable, the resistance of a sample will be independent of potential difference and current. [SFP.3]
phase cell
An entity that corresponds to specified ranges of position and velocity and which may, therefore. be used to describe the position and velocity of a particle to within a given precision. [CPM.2]
differential equation
An equation involving derivatives, such as the simple harmonic motion equation( )dd ( )222x ttx t= −ω .The solution of a differential equation is generally a function, and involves a number of arbitrary constantsin addition to the parameters (such as ω) that appear in the equation itself. In the case of the s.h.m. equation, for example, the general solution is x(t) = A1sin(ω0t + φ), where A and φ are arbitrary constants. [DM.3; PM.1]
equation of a straight line
An equation of the form y = mx + c, where m and c are constants that respectively represent the gradient and the intercept of the line. [DM.1]
equation of motion
An equation that expresses (explicitly or implicitly) the position of a moving object as a function of time. Such equations often take the form of differential equations and are obtained by combining Newton's second law of motion with the force laws that are appropriate to the system under consideration. [PM.1]
internal energy equation
An equation that relates the internal energy to other macroscopic variables, such as volume and temperature, for a macroscopic system in an equilibrium state. (See also internal energy and Joule's law of ideal gases.) [CPM.1]
equation of state
An equation that relates the variables of pressure, volume and temperature for a macroscopic system in an equilibrium state. For an ideal gas, the equation of state is PV = nRT. [CPM.1; CPM.3]
Einstein's photoelectric equation
An equation that sets the maximum kinetic energy of an electron liberated in the photoelectric effect equal to the quantum energy of the incident radiation minus the work function of the target material:.2max 21mv = hf −φ 4[QPI.1]
temperature
An equilibrium property of macroscopic systems, with many overlapping shades of meaning. In macroscopic terms, temperature determines the direction of heat flow. When two bodies at different temperatures are brought into thermal contact, heat will flow from the body with the higher temperature to that with the lower temperature until the two bodies reach the same temperature. In microscopic terms, temperature can be related to the mean translational kinetic energy of the microscopic constituents of a system. More specifically, in the case of a gas, the temperature determines the distribution of molecules amongst their allowed phase cells (in classical physics) or translational quantum states (in quantum physics). (See Maxwell-Boltzmann distribution for further detail.) Assigning a value to a temperature generally involves the use of a specific temperature scale, such as the absolute temperature scale. Such scales relate temperature to some measurable property of systems such as the pressure of a fixed quantity of ideal gas (obtained by considering the behaviour of real gases in the limit of low pressure), or the efficiency of a heat engine. The SI unit of temperature is the kelvin (K). [CPM.1; CPM.2; CPM.3, QPM.1]
Michelson-Morley experiment
An experiment carried out in 1887, which used an interferometer in an attempt to measure the speed of the Earth through the ether. The null result effectively proved that the ether did not exist and paved the way for Einstein's special theory of relativity. [DFW.2; DFW.4]
Young's two-slit experiment
An experiment first carried out by Thomas Young in 1801, in which light from a source is diffracted by two closely separated narrow parallel slits and, as a result, produces a doubleslit diffraction pattern. The experiment gives convincing evidence of the wave-like propagation of light. [DFW.2]
thought experiment
An experiment that we can imagine taking place, although carrying it out may be rather difficult in practice, and for which the outcomes can be predicted based on underlying physical principles. Often used in relation to the special theory of relativity, where everyday manifestations of the phenomena predicted by the theory are rare. [DFW.4]
supernova
An extremely violent stellar explosion that causes a star to suddenly flare up in brightness and then gradually fade again over a period of (typically) a year or so. The explosion occurs when a massive red giant star runs short of fuel and collapses under its own gravity. During the collapse, nuclear reactions convert electrons and protons into neutrons and neutrinos. As a result, apart from leaving behind an expanding cloud of gas known as a 'supernova remnant', a supernova can also lead to the formation of a neutron star. [SFP.2]
6blackbody
An ideal absorber of electromagnetic radiation that would absorb all the radiation that was incident upon it. Such a body would also be an ideal emitter, and would emit electromagnetic radiation with a spectrum that depended only on the temperature of the body. (See blackbody radiation.)blackbody radiation$Electromagnetic radiation that is in thermal equilibrium with matter at a fixed temperature. Its name derives from the fact that its spectrum is identical to that which would be emitted by a blackbody at the same temperature. Blackbody radiation is also called thermal radiation or cavity radiation. It consists of a gas of photons with a range of energies described by Planck's radiation law. [QPI.1; QPM.1]
inertial frame of reference
An inertial frame of reference is a frame of reference in which any particle that is not acted on by an unbalanced force, moves with constant speed along a straight line. In other words, an inertial frame is a frame of reference in which Newton's first law is applicable. Any frame of reference that moves with constant velocity relative to an inertial frame of reference is also an inertial frame of reference. [PM.1; DFW.4]
Copenhagen interpretation
An interpretation of quantum mechanics developed by Bohr, Heisenberg and others in the mid 1920s, and long regarded as the 'conventional' interpretation. It views the standard formalism as providing the most complete possibleaccount of an individual system. Accepting the indeterminacy and indeterminism of quantum mechanics and Bohr's principle of complementarity, it presents probabilities as an inherent and unavoidable part of the theory, and treats measurement as an unanalysable interaction between a (logically) classical measuring apparatus and a quantum system. [RU.1; QPI.4]
many worlds interpretation
An interpretation of quantum mechanics which, in one version at least, asserts the existence of a large number of parallel universes, each of which realizes one of the possibilities encompassed by the branching wavefunction describing the state of a system and the relative state of the rest of the Universe. [QPI.4]
extended object
An object that subtends a non-zero visual angle at the eye (or other optical system). It can be thought of as a connected collection of point objectslocated at progressively increasing distances from the optical axis. [DFW.3]
telescope
An optical device for enlarging the visualangle subtended by a very distant object, and/or increasing the apparent brightness of such objects. It uses an objective lens (or objective mirror) to gather light and produce a real image of the distant object in the focal plane of the objective. This image is viewed through an eyepiece lens which forms an enlarged virtual image of the real image at some point between the eye's near point (near-point adjustment) and far point (far-point adjustment). Telescopes that use an objective mirror are called reflecting telescopes (or just 'reflectors'), whereas those that use an objective lens are called refracting telescopes (or just 'refractors'). [DFW.3]
driven damped harmonic oscillator
An oscillator, typically a particle of mass m on a spring, that is subject to a linear restoring force −kx, a linear damping force −bvx, and an externally imposed periodic driving force, usually of the form cos( )0drive F F tx= Ω . The instantaneous displacement x(t) of such an oscillator can be written as the sum of two terms xdec + xdri where xdecrepresents a decaying transient motion, similar to that of a damped harmonic oscillator, and xdri represents a steady motion, due to the driving force, that will persist after the decaying motion has died away. After a sufficiently long time, only the steady motion will remain and it may be described byx(t) = A1sin(Ω0t + φ0)where Ω is the driving (angular) frequency of the applied force and A and φ are (non-arbitrary) constants. The value of the steady-state amplitude A is given by2 2 200( ) ( b m)F mAω −Ω + Ω=2where ω0= k m . This implies that the oscillator will enter a state of resonance, characterized by relatively large values of A, when ω00 is close to Ω. The energy of a driven damped oscillator that has entered its steady state is constant, the driving force supplies energy to the oscillator at the same rate that it is dissipated by the damping force. This rate is a maximum when the oscillator is driven at its natural frequency. [PM.2]
normalization factor
An overall factor (appearing in a function), the value of which may be chosen to ensure that the function satisfies some specified normalization rule. An example is the factor A in Boltzmann's distribution law: p = Ae−E/kT. [CPM.2]
heat bath
Any enclosure at a controlled temperature, which can supply heat to a system, or absorb heat from it, without undergoing any appreciable change of temperature itself. [CPM.3]
Bohr orbit
Any of the circular paths that an electron is allowed to follow as it orbits a nucleus, according to the Bohr model of the atom. In the case of the hydrogen atom, each value of the Bohr quantum number ncorresponds to an orbit in which the magnitude of the angular momentum is L = n". The radius of such an orbit is rn = n2a0, and the speed of the electron is vn = e2/2"ε0n. Here, " is Planck's constant divided by 2π and a0 is the Bohr radius. [QPI.1]
SI multiple
Any one of a number of standard factors of the form 103, 106, 109, etc. Each is represented by a standard prefix such as kilo, mega, giga, etc. [DM.1]
conservation principle
Any principle that expresses the constancy in time of a physical quantity (such as energy or momentum) under specified circumstances.Examples include the principles of conservation of charge, conservation of energy, conservation of linear momentum and conservation of angularmomentum. [PM.1]
heat
Any quantity of energy that is transferred as a direct result of a difference in temperature. According to one widely used convention, the symbol Q is used to represent heat that is transferred to a system from its environment. This convention implies that positive values of Q tend to increase the internal energy of the system. [RU.1; CPM.1; CPM.3]
work
Any quantity of energy that is transferred by non-thermal means. According to one widely used convention, the symbol W is used to represent work that 67is transferred to a system from its environment. This convention implies that positive values of W tend to increase the internal energy of the system.The work done by a constant force F on a body that undergoes a displacement s is defined by the scalar productW = F1•1s = Fs1cos1θ.If the force is not constant, then this product is replaced by the limit of an appropriate sum, which may be expressed as a definite integral. In the case of a force that varies in strength but always acts along the x-axis this integral takes the form∫=BAxW F dxwhich may be interpreted as the area under the graph of Fx against x between x = A and x = B. In three dimensions the work done depends on the particular path (e.g. between A and B) that the body moves along and can be represented by the line integral∫=BAW F •ds .The work done on any body by a force is the energy transferred to that body by the force. When a non-zero resultant force acts on a body, the work done by that force is related to the change in the body's translational kinetic energy by the work-energy theorem, according to which222 121W = ∆Εtrans = mv − mu[RU.1; PM.2; CPM.1; CPM.3]
electric dipole
Any system that produces an electric field similar to that of two electric charges of the same magnitude q, but with opposite signs, separated from one another by a fixed distance d. Such a system is characterized by an electric dipole moment of magnitude qd. 4[QPM.2]
unified field theory
Any theory that attempts to unify gravitation and electromagnetism in a single classical field theory. The term is sometimes used to refer specifically to the unsatisfactory unified field theories formulated by Albert Einstein and various co-workers. [RU.1]
solution (of an equation)
Any value which, when substituted into a given equation, turns that equation into a true identity. For example, x = 2 is a solution of the equation 3x = 4 + x because 3 × 2 is identical to 4 + 2. The idea of a solution may be extended to other types of equation, including differential equations, where the solution takes the form of a function. (See also quadratic equation formula, and, in the context of differential equations, general solution.) [DM.2]
arbitrary constants
Constants that arise in the general solution of a differential equation that are not present in the equation itself. The number of arbitrary constants in the general solution is equal to the order of the differential equation, and the values of the arbitrary constants are determined by the initial conditions that determine the details of the solution. [PM.1]
microwaves
Electromagnetic radiation with a wavelength between about 1 × 10−31m and 1 × 10−11m, or a frequency between about 3 × 10111Hz and 3 × 1091Hz. [DFW.2]
infrared radiation
Electromagnetic radiation with a wavelength between about 7 × 10−71m and 1 × 10−31m, or a frequency between about 4 × 10141Hz and 3 × 10111Hz. [DFW.2]
radio waves
Electromagnetic radiation with a wavelength greater than around 10−11m or a frequency less than about 3 × 1091Hz. [DFW.2]
γ-rays
Electromagnetic radiation with a wavelengthshorter than around 10−111m or a frequency greater than about 3 × 10191Hz.$A common source of such radiation is decaying radioactive nuclei. 4[QPM.3, DFW.2]
ultraviolet radiation
Electromagnetic radiation with wavelength between about 1 × 10−81m and 4 × 10−71m or frequency between about 3 × 10161Hz and 8 × 10141Hz. [DFW.2]
X-rays
Electromagnetic radiation with wavelengthbetween around 1 × 10−81m and 1 × 10−111m or frequency between about 3 × 10161Hz and 3 × 10191Hz. [DFW.2]
leptons
Fundamental particles of spin 21 that do not participate directly in strong interactions, though they may interact via the weak or, if charged, the electromagnetic interaction. Only six types of lepton are known; electrons, electron neutrinos, muons, muon neutrinos, tauons and tauon neutrinos (or, in terms of symbols, e−, νe, µ−, νµ, τ0−, ντ). [QPM.4]
energy histogram
Generally taken to be the same thing as the translational energy histogram. [CPM.2]
logarithm to the base e
Given a positive number x, its logarithm to the base e is the power to which e must be raised to obtain the given number. So if x = ey then we say that y is the log to the base e of x, and we write y = loge1x. In the case where x is a positive variable, it is possible to define a logarithmic function using the relationship, ƒ(x) = loge1x. The logarithmic function is the inverse of the exponential function, since loge1ey = y. The idea of a logarithm and of a logarithmic function may be extended to bases other than e, though logarithms to the base e are known as natural logarithms. [PM.2]
magnitude (of a scalar)
Given any scalar quantity, positive or negative, its magnitude is a positive quantity, equal to the value of the given scalar apart from any overall minus sign. For example, both 5 and −5 have magnitude 5. The modulus symbol | | is used as an instruction to take the magnitude of the enclosed scalar. Thus, for example, |1−51| = 5. The magnitude of a scalar is often referred to as its 'modulus' or its 'absolute value'. 4[DM.1]
magnitude (of a vector)
Given any vector quantity v, its magnitude is a positive scalar quantity v that indicates the 'length' or 'size' of the given vector. The modulus symbol | | is sometimes used as an instruction to take the magnitude of the enclosed vector. Thus, for example, the magnitude of v may be denoted by |1v1| or v. If v is expressed in terms of its Cartesian components v = (vx, vy, vz), then the magnitude of v is given by|1v1| = 2 2 2v = vx+vy+vz. [DM.2]
linear superposition
Given n functions Ψ1, Ψ2, Ψ3, ... Ψn, their linear superposition is any expression of the form4Ψ = c1Ψ1 + c2Ψ2 + c3Ψ3 + ... + cnΨnwhere c1, c2, c3, etc. are numbers, which may generally be complex numbers. (See also principle of superposition.) [QPI.4]
general solution
In the context of a differential equation, the general solution is a function that satisfies the equation and which contains a number of arbitraryconstants equal to the order of the differential equation. An example is the general solution to the (second-order) simple harmonic motion equation; in this case the required function may be written as x(t) = A1sin(ω0t + φ), where A and φ are arbitrary constants that are determined by the initial conditions of the motion (ω is not an arbitrary constant since it appears in the simple harmonic motion equation). Subject to certain common conditions, any solution to a differential equation may be obtained from the general solution by making appropriate choices of the arbitrary constants. [DM.3, PM.1]
initial conditions
In the context of a differential equation, the initial conditions provide the information required to evaluate the arbitrary constants that arise in the general solution to the differential equation. For example, given a particle that moves in accordance with the simple harmonic motion equation, the general solution to that equation implies that x = A1sin(ω0t + φ), but in order to know exactly where the particle is at any given time it is necessary to determine the arbitrary constants A and φ. This can be done if the position and velocity of the particle are known at time t = 0; these are the initial conditions in this case. [PM.1]
internal force
In the context of a given system, an internal force is a force that acts within the system and which has a reaction that also acts within the system. [PM.3]
eigenstate
In the context of quantum mechanics, an eigenstate of a given observable is a state that allows only one possible outcome for a measurement of that observable. That predicted outcome is said to be the eigenvalue that corresponds to the eigenstate. (Note: this is not the most general definition of eigenstate. The term also arises in mathematical contexts without any reference to quantum mechanics or measurements.) [QPI.4]
equilibrium position
In the context of simple harmonic motion, the equilibrium position is the midpoint of that motion. [DM.3]
force
Informally, this is the amount of 'push' or 'pull' exerted on a particle, which, if unopposed, causes it to depart from the uniform motion predicted by Newton'sfirst law of motion. It is, therefore, that which causes (or tends to cause) acceleration. It is a vector quantity, and so has both magnitude and direction. It is quantified by means of Newton's second law of motion, which says that the acceleration a of a particle is proportional to the resultant force F that acts on it, and inversely proportional to its mass m. Thus, in terms of vectors:F = maor in terms of (scalar) componentsFx = max,4Fy = may,4Fz = mazThe SI unit of force is the newton (N). [PM.1]
field lines
Lines used in pictorial representations of vector fields. They are directed along the field direction at every point and their spacing in any region indicates the magnitude of the field in that region: the closer together the lines, the stronger the field. Electric fieldlines emerge from positive charges and disappear into negative charges. Closed electric field lines can surround regions of changing magnetic flux. According to Maxwell's equations, magnetic field lines are continuous and have no beginning or end. However, outside a permanent magnet, magnetic field lines emerge from north poles and disappear into south poles. (To maintain continuity, the opposite is true inside the magnet, although this is not observed directly.) Closed magnetic field lines can surround electric currents and regions of changing electric flux. Gravitational fieldlines begin at infinity and terminate at masses. [SFP.1; DFW.1]
antimatter
Matter composed of antiparticles. The term may be applied to any quantity of matter from a single antiparticle to a collection of antiparticles, possibly even to antiatoms. [QPM.4]
quantum field theory
One of the major subdivisions of quantum physics, comparable to quantum mechanics. Quantum field theory is centrally concerned with fields, but allows them to be viewed as assemblies of field quanta, usually referred to as 'particles' (e.g. photons). The techniques of quantum field theory can be used to describe individual elementary particles, but are especially useful in situations that involve varying particle numbers, such as the emission and absorption of photons or the creation and annihilation of particle-antiparticle pairs. Quantum field theory provides a natural context for the formulation of quantum physical theories that accord with the principles of the special theory of relativity. Particular examples of such theories include quantum electrodynamics, quantum chromodynamics and the unified theory of the electroweak interaction. In practice, processes described by such theories are usually regarded as involving a number of intermediate states, the effects of which are calculated using Feynman diagrams which are constructed and evaluated according to a set of Feynman rules appropriate to the particular theory under consideration. [RU.1, QPM.4]
quantum mechanics
One of the major subdivisions of quantum physics. Quantum mechanics is typically concerned with systems such as nuclei, atoms, molecules and electrons in solids, all of which have the feature that they may be treated as a finite number of interacting particles. Quantum-mechanical problems are often discussed in terms of a wave mechanical formalism which emphasizes the concept of a wave function, satisfying an appropriately formulated Schrödinger equation. 4[RU.1; QPI.2]
bottom quark
One of the six types of quark. It is the only quark to have non-zero bottom (or bottomness). [QPM.4]
charm quark
One of the six types of quark. It is the only quark to have non-zero charm. [QPM.4]
up quark
One of the six types of quark. [QPM.4]
box notation
One of the two common ways of writing down the electronic configuration of an atom (the other being standard notation). In box notation, a small box is shown for each combination of the quantum numbers n, l and ml. The spin magnetic quantum number ms of any occupying electron is indicated by an upward or downward pointing arrow depending on whether ms = 21+ or 21− . If a box contains both upward and downward arrows, both spin states for that combination of n, l and ml are occupied. For example, the ground state of carbon is written in the box notation as [QPI.3]
standard notation
One of the two common ways of writing down the electronic structure of an atom (the other being box notation). In standard notation, the structure is given using spectroscopic notation and the number of electrons occupying each subshell is indicated by a superscript. For example, in standard notation the ground state of carbon is written as4C41s212s212p244[QPI.3]
Feynman rules
Procedures arising in quantum field theories that enable Feynman diagrams to be interpreted as mathematical expressions that can be used to predict physical quantities such as cross-sections. [QPM.4]
Van Allen belts
Regions surrounding the Earth where charged particles (mostly protons and electrons) are trapped by the Earth's magnetic field. They were discovered in 1958 by James Van Allen using data from the Explorer satellite mission. [SFP.4]
reversible adiabat
See adiabat, which has the same meaning. 4[CPM.3]
reversible adiabatic condition
See adiabatic condition, which has the same meaning. [CPM.3]
electric motor
See alternating current motor and direct current motor. [DFW.1]
magnifying power
See angular magnification. [DFW.3]
stop
See aperture stop. [DFW.3]
β-
See beta.back EMF$The EMF that arises in an electric motor or similar device as the motor starts to turn, and which opposes the externally supplied EMF that is responsible for that turning. Since an electric motor is constructed like an electric generator, any movement of its coil will produce an induced EMF which opposes the change that caused it (by Lenz's law). This is the back EMF, which must act in the opposite direction to the applied EMF 5from the battery or power supply that caused the coil to move. [DFW.1]
thermal radiation
See blackbody radiation. [QPM.1]
coefficient of viscosity
See coefficient of dynamic viscosity. [PM.1]
mutual inductance
See coefficient of mutual inductance. [DFW.1]
microstate
See configuration. [CPM.2; CPM.3]
principle of conservation of energy
See conservation of energy. [PM.2]
convex lens
See converging lens. [DFW.3]
positive lens
See converging lens. [DFW.3]
concave mirror
See converging mirror. [DFW.3]
positive mirror
See converging mirror. [DFW.3]
position coordinate
See coordinate. [DM.1]
damped
See damped harmonic oscillator.damped harmonic oscillator$An oscillator, typically a particle of mass m on a spring, that is subject to a linear restoring force −kx, and to a linear damping force −bvx, where x is the instantaneous displacement of the particle from its equilibrium position, vx is the instantaneous velocity of the particle, and both k and bare positive constants. In the case of light damping, when b/m is small, the damped harmonic oscillator's displacement from equilibrium at time t is given byx(t) = (A01e−t0/τ0)1sin(ω0t + φ)where A0 and φ are arbitrary constants, τ = 2m/b, and the angular frequency ω has a value close to the natural frequency, ω0= k m , of the corresponding undamped harmonic oscillator. As a result of the damping, the energy of a damped harmonic oscillator decreases with time. [PM.2]
derived function
See derivative. [DM.1]
chaotic
See deterministic chaos. [PM.5]
concave lens
See diverging lens. [DFW.3]
equivalent focal length
See effective focal length. [DFW.3]
eigenvalue
See eigenstate. [QPI.4]
charge
See electric charge. 4[SFP.1]
current
See electric current. 4[SFP.3]
conventional current
See electric current. [SFP.3]
potential
See electric potential or gravitational potential as appropriate.potential difference$The difference in potentialbetween two specified points. In electrostatics, potential difference is usually given the symbol ∆V. However, when discussing capacitors and electric circuits, the symbol V is conventionally used. 4[SFP.2]
EMF
See electromotive force.22emission (of radiation)$See absorption.empirical$Based on experimental observation.emulsion (photographic)$The photosensitive surface of photographic film; it consists of a layer of microscopic crystals of a silver halide suspended in a transparent gelatinous material. [DFW.3]
electronic configuration
See electronic structure.electronic structure$The arrangement of electrons amongst the quantum states of an atom as indicated by listing which of the atom's quantum states are occupied by its constituent electrons. The electronic structure can be written down using either the standard notation or the box notation. [QPI.3]
line
See equation of a straight line.linear accelerator$A type of particle accelerator in which charged particles are accelerated in a straight line. It is also known as a linac. [QPM.4]
decay constant
See exponential decay law. [QPM.3]
exponential decay
See exponential process. [PM.2]
exponential growth
See exponential process.exponential process$A process of growth or decay that can be described by an exponential functionv(t) = v0eα1t. Exponential growth corresponds to a positive value of α, exponential decay to a negative value of α. In either case the process is characterized by the fact that the quantity v changes its value by equal factors in equal intervals of time, irrespective of when those intervals begin or end. A particularly well-known example is the decay of radioactive nuclei described by,N(t) = N01exp(−λt)where N0 is the number of parent nuclei at t = 0, and the decay constant λ, the reciprocal of the mean lifetime τ,is related to the half-life T1/2 by T1/2 = loge(2)/λ. [PM.2; SFP.3; QPM.3]
fluoresce
See fluorescence.fluorescence$A process by which atoms or molecules absorb energy, often in the form of radiation of a short wavelength (e.g. in the ultraviolet region of the spectrum) and re-emit it, usually, as radiation of longer wavelengths (e.g. in the visible region of the spectrum). Atoms undergoing this process are said to fluoresce. [SFP.3]
conduction electrons
See free electrons. [QPM.1]
γ-
See gamma.Galilean coordinate transformation$The coordinatetransformation of classical physics or Newtonian physics. If an event has coordinates (x, y, z, t) in frame of reference A, then the coordinates of the same event in frame of reference B, which is in standard configurationwith A, are x′ = x − Vt, y = y′, z = z′ and t = t′,where V is the relative speed of B with respect to A. Note that these equations are NOT CORRECT, and provide only an approximation to the Lorentz transformation at low speeds. (See also velocity transformation.) [DFW.4]
thermal reservoir
See heat bath. [CPM.3]
fissile
See induced fission. [QPM.3]
dielectric
See insulator. [SFP.2]
Snell's law
See law of refraction. [DFW.2]
Newton's law of universal gravitation
See law of universal gravitation. [PM.1]
gravitational constant
See law of universal gravitation. [SFP.1]
linac
See linear accelerator. [QPM.4]
map
See linear map and non-linear map.mass energy$The energy that a body possesses by virtue of its mass, as given by Emass = mc2, where c is the speed of light in a vacuum. The existence of mass energy is one of the many implications of the special theory of relativity. The mass energy of a free particle is the difference between its (total) relativistic energy and its relativistic translational kinetic energy. Mass energy is also known as rest energy. [PM.3; DFW.4]
logarithmic function
See logarithm to the base e. [PM.2]
natural logarithm
See logarithm to the base e. [PM.2]
hypermetropia
See long-sightedness. [DFW.3]
magnetic moment
See magnetic dipole.magnetic monopole$A hypothetical 'particle' which, if it existed, would produce a purely radial magnetic field similar to the electric field of an isolated electric charge. Maxwell's equations imply that magnetic monopoles do not exist; so that magnetic field lines must either form closed loops (like those associated with a current-carrying wire), or they must always begin at a north pole and end at a south pole (like those associated with a magnetic dipole). Consequently, the magnetic flux, due to a magnetic field, through a closed surface is zero, since that closed surface cannot enclose any magnetic monopoles. [SFP.4; DFW.1]
electric flux
See magnetic flux.electric generator$See alternating current generatorand direct current generator. [DFW.1]
monopole
See magnetic monopole. 4[SFP.4]
metal
See metallic solid.metallic solid$A solid in which the valence electronsare freed from their parent atoms and are bound only by the surface of the metal itself. The bonding in a metallic solid can be thought of as arising from the attraction between the lattice of positive ions and the electron gas occupying the same space. The bonding is nondirectional and usually results in a close packed structure. [QPM.2]
compound microscope
See microscope. [DFW.3]
daughter nucleus
See parent nucleus. [QPM.3]
initial phase
See phase constant. [DM.3]
polar coordinate system
See plane polar coordinate system and spherical polar coordinate system.polarization$The property of a transverse wave that implies the existence of a restriction on the direction of the transverse vibrations. (See plane polarized for an example of such a restriction.) [DFW.2]
complementarity
See principle of complementarity. [QPI.4]
simultaneity
See relativity of simultaneity. [DFW.4]
irreversible process
See reversible process. [CPM.3]
rotational energy
See rotational kinetic energy. 4[CPM.2]
dot product
See scalar product. [PM.2]
theory of special relativity
See special theory of relativity. [DFW.4]
spin
See spin angular momentum quantum number. [QPI.3; QPM.4]
strong force
See strong nuclear force.strong interaction$See strong nuclear force. [QPM.4]
thermal isolation
See thermal contact. [CPM.3]
thermodynamic equilibrium
See thermal equilibrium. [CPM.3]
translational energy
See translational kinetic energy. [CPM.2]
cosine function
See trigonometric functions. [DM.3]
sine function
See trigonometric functions. [DM.3]
quantum-mechanical tunnelling
See tunnelling. [QPM.3]
cross product
See vector product. [PM.4]
Galilean velocity transformation
See velocity transformation. [DFW.4]
light
See visible light. [DFW.2]
weak interaction
See weak nuclear force. 4[QPM.4]
work done
See work. [PM.2]
law of conservation of mechanical energy
Seeconservation of mechanical energy. [PM.2]
principle of conservation of mechanical energy
Seeconservation of mechanical energy. [PM.2]
aperture diameter
The 'effective' diameter of a lens(or mirror); it may be the actual diameter of the lens (or mirror) or, if the lens or mirror aperture is limited in some way (by an adjacent aperture stop, for instance), it would be the lesser diameter of the limited aperture. It is common (and convenient) to express the aperture diameter of a lens or mirror as a fraction of the focal length of that lens or mirror (e.g. D = ƒ0/8). The denominator of this fraction is known as the F-numberof the lens (or mirror). Hence D = ƒ0/F (which in the example above means that F = 8). 4[DFW.3]
mole
The SI unit for the quantity of a pure substance, represented by the symbol mol. The mole is one of the seven SI base units, and is defined as the amount of substance that contains as many elementary units (atoms, molecules. ions etc.) as there are atoms in 0.0121kg of carbon-12. One mole of any pure substance therefore contains Avogadro's number of the basic particles (molecules or atoms) of that substance. For a pure substance made up of atoms (or molecules) of relative atomic (or molecular) mass Mr, one mole is a sample of mass Mr × 10−31kg. 4[CPM.1]
ampere
The SI unit of electric current, represented by the symbol A. The ampere is one of the seven SI base units and is defined by the following statement: When a steady current of one ampere flows in each of two straight, parallel, infinitely long, wires, set one metre apart in a vacuum, the magnetic force acting on each wire is of magnitude 2 × 10−71N per metre of its length. [SFP.3; SFP.4]
volt
The SI unit of electric potential and electric potential difference, represented by the symbol V¸ where 11V = 11J1C−1. [SFP.2]
joule
The SI unit of energy and of work, represented by the symbol J, and defined by the relation 11J = 11kg1m21s−2 = 11N1m. [PM.2]
newton
The SI unit of force, represented by the symbol N, and defined by the relation 11N = 11kg1m1s−2. An unbalanced force of magnitude 11N will cause a 41particle of mass 11kg to accelerate at 11m1s−2 in the direction of the force. [PM.1]
hertz
The SI unit of frequency, represented by the symbol Hz, where 11Hz = 11s−1. A frequency of 11Hz is equivalent to one cycle per second. [DM.3; DFW.2]
henry
The SI unit of inductance (both the coefficient of self-inductance and the coefficient of mutual inductance), represented by the symbol H, where 11H = 11V1s1A−1. [DFW.1]
metre
The SI unit of length, represented by the symbol m. The metre is one of the seven SI base units, and is defined as the distance that light travels in a vacuum in 1/299179214581second. [DM.1]
weber
The SI unit of magnetic flux, represented by the symbol Wb, where 11Wb = 11T1m2. [DFW.1]
kilogram
The SI unit of mass, represented by the symbol kg. The kilogram is one of the seven SI base units, and is defined by a manufactured standard kilogram kept in France. [PM.1]
watt
The SI unit of power, represented by the symbol W, and defined by the relation 11W = 11J1s−1. [PM.2]
ohm
The SI unit of resistance, represented by the symbol Ω, and defined by the relation 11Ω = 11V1A−1. [SFP.3]
kelvin
The SI unit of temperature and temperature difference, represented by the symbol K. The kelvin is one of the seven SI base units, and is defined as 1/273.16 of the absolute temperature of the triple point of H2O. A temperature difference of one kelvin (11K) is equivalent to a temperature difference of one degree Celsius (11°C), but the absolute and Celsius scales have different origins. [CPM.1]
centripetal acceleration
The acceleration of a particle moving in a circle. The acceleration is directed towards the centre of the circle and has magnitude ω02r, where ω is the angular speed of the particle about the centre of the circle, and r is the radius of the circle. [DM.3]
instantaneous acceleration
The acceleration of an object at a particular instant. See acceleration. [DM.1]
acceleration due to gravity
The acceleration of an object moving under the influence of gravity lone, close to the Earth's surface. It is directed vertically downwards and has an approximate magnitude of 9.811m1s−2, which is conventionally given the symbol g. [DM.1; PM.1]
angle of reflection
The acute angle (usually denoted R) between the normal to a reflecting surface and the direction of a specified ray that has been reflected from the surface. 4[DFW.2]
angle of incidence
The acute angle (usually denoted i) between the normal to a surface and the direction of a specified ray that is incident upon the surface.4[DFW.2]
angle of refraction
The acute angle (usually denoted r) between the normal to a refracting interface and the direction of a specified ray that has been refracted at the interface. [DFW.2]
binding energy per nucleon
The amount of energy, obtained by dividing the binding energy B of a specified nucleus by the mass number A of that nucleus. The binding energy per nucleon provides a measure of the stability of a nucleus relative to other nuclei. A larger value of B/A indicates a more stable nucleus. 4[QPM.3]
angular velocity
The angular velocity of a particle or body about a point O, is a vector quantity w, with magnitude equal to the angular speed about O and directed along the (instantaneous) axis of rotation through O in the sense indicated by the right-hand grip rule.If the displacement of a particle from O is r, and if the velocity of that particle relative to O is v, then the angular velocity w of that particle about the point O is related to r and v by the vector productv = w× r(Note that this result is not restricted to circular motion.)In the case of a rotating rigid body, the angular velocity about every point fixed within the body has the same value at any given time. [DM.3; PM.4]
thin lens approximation
The approximation of treating a lens as though it were a thin lens. This is a useful approximation for many lens systems: the lens equationimplicitly assumes the thin lens approximation, and the assumption that all rays pass undeviated through the optical centre of a lens is also only valid within the limits of this approximation. [DFW.3]
classical continuum approximation
The approximation of treating the numerous, narrowly separated, quantized translational energy levels associated with a gas of particles in a macroscopic container, as a continuous distribution of possible energies. Treating the energy levels in this way justifies the introduction of a density of states function. The approximation is valid when the de Broglie wavelength of a typical particle in the gas is much less than the length that characterizes its container. [QPM.1]
signed area under a graph
The area bounded by the curve of a graph, the horizontal axis and two vertical lines drawn from specified values on the horizontal axis. A positive sign is given to an area above the horizontal axis and a negative sign to an area below the horizontal axis. Note that the area is expressed in terms of the units used on the axes, not in terms of the physical area of paper. [DM.1]
equipartition of energy theorem
The assertion in classical statistical mechanics, that, in a system in equilibrium at absolute temperature T, each independent molecular degree of freedom contributes kT/2 to the average energy per molecule, where k is Boltzmann'sconstant. So, if a molecule has ƒ degrees of freedom, its average energy will be f0kT/2, as long as the equipartition theorem applies. [QPI.1; CPM.2]
mean free path
The average distance that particles in a gas travel between collisions. [QPM.2]
occupation factor
The average number of particles occupying a given quantum state in thermal equilibrium. The occupation factor for distinguishable particles is the Boltzmann occupation factor. For indistinguishablebosons it is the Bose occupation factor, and for indistinguishable fermions it is the Fermi occupation factors. [QPM.1]
Fermi speed
The average speed of electrons near the Fermi level. The Fermi speed vF is given, to a very good approximation, by F2Fmv /2 = E where EF is the Fermi energy. [QPM.2]
optical centre (of a lens)
The axial point at the centre of a thin lens through which rays will pass without being deviated. [DFW.3]
optical axis
The axis about which a lens or mirror is rotationally symmetrical. If the lens does not have circular symmetry (as with a cylindrical lens), the optical axis can alternatively be defined as the axis passing through the optical centre of the lens that is perpendicular to the 'plane' of the lens. [DFW.3]
soft magnetic behaviour
The behaviour of magnetic materials that lose much of their magnetization when the applied magnetic field responsible for that magnetization is removed. Such materials are generally easy to magnetize, but their magnetization does not persist. [SFP.4]
hard magnetic behaviour
The behaviour of magnetic materials that retain much of their magnetization when the applied magnetic field responsible for that magnetization is removed. Such materials are generally difficult to magnetize, but the magnetization persists. [SFP.4]
chromatic aberration
The blurring caused by the separation of the colours in the image produced by a lens. Because the refractive index of a material varies with optical frequency, blue light is focused more strongly by a glass (or similar) lens than is red light. Hence, the focal point of the lens is not uniquely defined for general illumination, with the result that images of objects illuminated with white light will be subjected to a rainbow-like blurring. Mirrors do not suffer from chromatic aberration. [DFW.3]
57spherical aberration
The blurring of the image produced by a spherical lens or spherical mirror and caused by the fact that rays further away from the optical axis are focused more strongly than rays close to the axis. Parabolic mirrors, in which the mirror surface has a parabolic rather than spherical shape, are frequently used to eliminate spherical aberration in large telescope mirrors. Alternatively, a Schmidt plate may be used to introduce a predistortion in the incident wavefront in order to counteract spherical aberration. [DFW.3]
fluid mechanics
The branch of classical physics that investigates and predicts the behaviour of fluids, whether at rest or in motion. [CPM.4]
fluid dynamics
The branch of fluid mechanics that concentrates on fluids that are moving, and the forces they exert on immersed solid objects. Fluid dynamics is also called hydrodynamics, even if the fluid involved is not water. [CPM.4]
thermodynamics
The branch of macroscopicclassical physics concerned with the study of heat and its relationship to energy in general. [RU.1; CPM.3]
trigonometry
The branch of mathematics concerned with the study of right-angled triangles, the associated trigonometric ratios and their generalizations. [DM.2]
mechanics
The branch of physics concerned with force and motion. [RU.1]
statistical mechanics
The branch of physics that explains and predicts the behaviour of (large-scale) macroscopic systems in terms of the statistical behaviour of their microscopic constituent particles. Statistical mechanics uses the methods of probabilitytheory and statistical analysis to predict the likely behaviour of the constituent particles, and relies on the fact that, in a system containing a vast number of particles, such 'likely' behaviour is practically certain to happen. [RU.1; CPM.2]
irreversibility
The characteristic of physical processes that prevents their time-reversed versions from occurring spontaneously. [RU.1]
double-slit diffraction pattern
The characteristic pattern of illumination (featuring well-defined maxima and minima of intensity) observed on a screen that is far from an illuminated pair of narrow parallel slits. The slits act as a secondary coherent source of waves. The maxima in the pattern occur at angles θnto the incident beam, where θnsatisfies the diffraction equation. [DFW.2]
single-slit diffraction pattern
The characteristic pattern of illumination (featuring well-defined maxima and minima of intensity) obtained when a single slit of width w is illuminated normally with plane waves of wavelength λ. The first minimum in the pattern occurs at an angle θ to the incident beam, where sin1θ = λ/w. [DFW.2]
21electron charge
The charge carried by the electron is −e = −1.602 × 10−191C. [SFP.1]
charge number
The charge number of a particle is its charge divided by e (the magnitude of the charge of an electron). [QPM.4]
cyclotron motion
The circular motion of a charged particle in the plane perpendicular to a magnetic field. [SFP.4]
near point
The closest point on which the eye can focus. It is conventional to assume a standard near-point distance of 2501mm for a 'normal' eye (this point is then often called the normal near point). [DFW.3]
adiabatic condition
The condition PVγ = A that may be used to specify a particular reversible adiabatic process in a given quantity of ideal gas where the ratio of heat capacities is γ. The parameter A will have a constant value for any particular reversible adiabatic process, but will have different values for different reversible adiabatic processes that correspond to different values of the entropy. [CPM.3]
light damping
The condition in which a damped harmonic oscillator is less than critically damped and 35consequently only returns to its equilibrium positionafter completing several oscillations. [PM.2]
29heavy damping
The condition in which a damped harmonic oscillator is more than critically damped and consequently does not oscillate, but returns slowly to its equilibrium position. [PM.2]
critical damping
The condition in which a damped harmonic oscillator just fails to oscillate and comes to rest especially rapidly. For an oscillating body of mass m, subject to a linear restoring force −kx, and to a linear damping force −bvx, the motion will be critically damped when b = 2 km . [PM.2]
near-point adjustment
The condition in which a magnifying glass, microscope or telescope positions the final virtual image (to be observed by the eye) at the normal eye's near point. The angular magnification is slightly greater in near-point adjustment than in farpoint adjustment, but the eye is more relaxed in the latter adjustment. [DFW.3]
normalized
The condition in which a specified function or a set of related values (such as the wavefunction of a particle, or a set of probabilities for the possible outcomes of some process) satisfies some specified normalization rule (such as the requirement that the probability of finding the particle somewhere should be 1).normal near point$The location of the near point for a 'normal' eye. It is conventionally assumed to be at a distance of 2501mm from the eyelens. [DFW.3]
translational equilibrium
The condition in which a system is free from any net external force, so that∑ = 0iFi.The linear momentum of such a system will be constant. [PM.4]
forward bias
The condition in which an external voltage is applied across a p-n junction so as to reduce the electric field in the depletion layer and increase the diffusion current flowing across it. In forward bias the positive terminal of the external voltage source is connected to the p-type material and the negative terminal to the n-type. [QPM.2]
state
The condition of a system, described in sufficient detail to distinguish it from other conditions that would behave differently. In classical physics the state of a system may be specified by listing the values of various observable quantities (e.g. the pressure and temperature of a given quantity of ideal gas). In quantum mechanics, the state of a system is specified by its wavefunction, and the meaning of 'behave differently' must encompass the indeterminacy and indeterminism of quantum mechanics. [CPM.3; QPI.4]
thermal equilibrium
The condition of an isolated system in which there is no net flow of heat between any two parts of the system. Such a system may be characterized by a uniform temperature. A system is said to be in thermal equilibrium with a heat bath if it is 61at the same temperature as the heat bath, since there is then no heat flow between the system and the heat bath. Thermal equilibrium represents a settled and unchanging state in which macroscopic properties are independent of time. It is also referred to as thermodynamic equilibrium. 4[CPM.1; CPM.3; QPM.1]
adiabatic inaccessibility
The condition that exists between two equilibrium states of a system when it is impossible to go from one state to the other by any adiabatic process. [CPM.3]
coefficient of self-inductance
The constant of proportionality L in the relation.dd ( )( ) indti t|V t | = L×between the magnitude of the self-induced EMF in a coil and the magnitude of the rate of change of current in the coil. The value of L depends on the construction of a coil. For a long cylindrical solenoid, L = µAN2/l, where µ is the permeability of the core of the solenoid, A is its cross-sectional area, l is its length and N is the number of turns. The coefficient of self-inductance is sometimes simply referred to as the self-inductance, or just the inductance of the coil. The SI unit of self-inductance is the henry, represented by the symbol H, where 11H = 11V1s1A−1. (See also coefficient of mutual inductance.) [DFW.1]
coefficient of mutual inductance
The constant of proportionality M in the relationti tV t Mdd ( )( )1|2| = ×between the magnitude of the mutually induced EMF in a secondary coil of wire and the magnitude of the rate of change of current in the primary coil of wire, where the two coils have a common magnetic flux linkage, as in a transformer. The value of M depends on the construction of the two coils. For two long cylindrical solenoids, with complete magnetic flux linkage between them, M = µAN1N2/l, where µ is the permeability of the core of each solenoid, A is their cross-sectional area, l is their length, and N1 and N2 are the number of turns on the primary and secondary coils, respectively. The coefficient of mutual inductance is sometimes simply referred to as the mutual inductance. The SI unit of mutual inductance is the henry, represented by the symbol H, where 11H = 11V1s1A−1. (See also coefficient of self-inductance.) [DFW.1]
coefficient of sliding friction
The constant of proportionality µslide in the relationF = µslideNbetween the magnitude F of the frictional force on a body as it slides over a solid surface, and the magnitude N of the normal reaction force that the surface exerts on the body.The value of µslide depends on the surfaces involved and their state of lubrication, but is largely independent of other factors, including the area of contact and the speed of the object. In any given situation, the coefficient of sliding friction is usually slightly smaller than the coefficient of static friction. [PM.1]
phase constant
The constant part of the phase of an oscillation or a wave, usually represented by the symbol φ. The phase constant is sometimes called the 'initial phase', since it determines the phase of the oscillation (or wave) at t = 0 (and x = 0). [DM.3; DFW.2]
coefficient of static friction
The constant µstatic in the relationF = µslideNbetween the magnitude F of the maximum frictional force that can oppose the sliding motion of a body over a solid surface, and the magnitude N of the normal reaction force that the surface exerts on the body.The value of µstatic depends on the surfaces involved and their state of lubrication, but is largely independent of other factors, including the area of contact. In any given situation, the coefficient of static friction is usually slightly higher than the coefficient of slidingfriction. [PM.1]
universal gas constant
The constantR = 8.3141J1K−11mol−1that appears in the equation of state of an ideal gas: PV = nRT. The universal gas constant has the same value for all ideal gases, irrespective of their molecular composition. It is related to Boltzmann's constant, k, and Avogadro's constant, Nm, by R = Nmk. [CPM.1]
radial coordinate
The coordinate that measures distance from the origin in a polar coordinate system. [DM.3]
Lorentz transformation
The coordinate transformation of special relativity. If an event has coordinates(x, y, z, t) in frame of reference A, then the coordinates of the same event in frame of reference B, which is in standard configuration with A, are2 222 21 /( / )1 /V ct Vx ctz zy yV cx Vtx−−′=′=′=−−′=where V is the relative speed of B with respect to A. An approximation to the Lorentz transformation at low speeds is provided by the Galilean coordinate transformation. (See also velocity transformation.) [DFW.4]
total cross-section
The cross-section due to both elastic and inelastic scattering. [QPM.4]
cube
The cube of a quantity is the result of multiplying the quantity by itself and then multiplying the result by the original quantity again:x3 = x × x × x. [DM.1]
derivative
The derivative of a function ƒ(0y) with respect to y is another function of y, sometimes called the derived function, that is equal to the rate of change of ƒ(0y) with respect to y at each value of y. Its value at any given value of y is equal to the ratio ∆ƒ/∆y in the limit as ∆y becomes very small and is usually written as dydƒ. The value of dydƒ at any given value of y is also equal to the gradient of the graph of ƒ plotted against yat the given value of y. [DM.1]
second derivative
The derivative of the derivative of a function. Given a function ƒ(0y), its second derivative with respect to y is also a function of y, and may be written as 22dd ƒ( )yy. [DM.1]
modes of oscillation
The different kinds of oscillation that a system can exhibit simultaneously. [DM.3]
focal length
The distance between a lens's optical centre and its focal point or, in the case of a mirror, the distance between its focal point and the point where the optical axis intersects the mirror's surface. For a converging lens or converging mirror, it is the distance over which parallel rays are brought to a focus. [DFW.3]
range
The distance from the initial position of a projectile to the point at which the projectile ends its flight. [DM.2]
radius of curvature (of a spherical mirror)
The distance from the mirror's centre of curvature to its surface. It is equal to the radius of that sphere, part of whose surface constitutes the mirror. A spherical mirror's focal length ƒ is equal to half its radius of curvature, ρ, i.e. ƒ = ρ0/2. [DFW.3]
radius of a nucleus
The distance r from the centre of a nucleus at which the electric charge density ρc(r) falls to one-half the value it has at the nuclear centre. For example, the radius of the 208Pb nucleus is about 6.81fm. [QPM.3]
wavelength
The distance, measured along the direction of propagation of a wave, between successive points that are oscillating in phase. For convenience, wavelength is frequently thought of as the distance between two successive wave crests. [DFW.2]
density of states function for photons
The distribution with respect to energy of the quantum states available to photons inside a cavity of volume V is described, in the classical continuum approximation, by the density of states functionDp(E) = CE2where C = 8πV/h3c3 = (3.206 × 10751J−31m−3)V. [QPM.1]
density of states function for electrons
The distribution with respect to energy of the states available to an electron in Pauli's quantum free-electron model of a metal of volume V, is described, in the classical continuum approximation by the density of states functionDe(E) = B′Ewhere (2 ) (1.06 10 J m ) .4 3 2 56 3 2 33m VhVB− −= ×π′=(There is a factor of 2 in B′ to account for the two electron spin states corresponding to each translational quantum state.) [QPM.1]
free will
The doctrine that human beings are free to determine their own actions. [RU.1]
drift speed
The drift speed of a collection of particles is the magnitude of the average velocity of those particles. For example, when an electric field Ex is applied to a metal wire, the conduction electronsundergo periods of acceleration in the direction opposite to Ex between collisions. This results in a drift of the electron gas at a constant average speed characterized by the drift speedvd = (eEx0/m)(λ0/〈1v1〉)where λ is the mean free path and 〈1v1〉 is the average thermal electron speed. [SFP.3; QPM.2]
Doppler effect
The effect that causes the observed frequency of the waves from a source to depend on the relative motion of the source and the observer. If the relative motion is such that the source and the observer approach each other, the observed frequency is higher than the emitted frequency (the observed wavelength is shorter). If the relative motion is such that the source and observer recede from each other, the observed frequency is lower than the emitted frequency (the observed wavelength is longer). The Doppler effect is widely used to measure the speed of approach or recession of a source of radiation, particularly in astronomy. [DFW.2]
Meissner effect
The effect whereby all magnetic flux is expelled from the interior of a type I superconductorin the transition to the superconducting state upon being cooled below the superconducting transition temperature TC. The effect is due to the magnetic properties of the superconductor and is not a direct consequence of the infinite conductivity. [QPM.2]
photoelectric effect
The effect whereby electrons are emitted from matter (usually from a metallic electrode) when electromagnetic radiation of sufficiently high frequency is incident on it. [QPI.1]
reversibility of light path
The effect whereby reversing the direction of all the rays that indicate a particular light path results in another possible light path. That is to say, if a ray describes the path taken by light in propagating from A to B then the same ray, with its direction reversed, will also describe the path taken by light in propagating from B to A. [DFW.3]
Hall effect
The effect whereby the application of a magnetic field perpendicular to a wafer of conducting material carrying a current along its length, causes a potential difference across the width of the wafer. Hall probes use this effect to measure the strength of magnetic fields. [SFP.4]
electric field due to a point charge
The electric fielddue to a point charge is spherically symmetric around the charge. If a charge Q is placed at the origin, theelectric field at a point specified by the position vector risr rˆ4( )20rQπεe =where rˆ is a unit vector in the direction of r and ε0 is the permittivity of free space. Thus, the magnitude of the electric field depends only on the distance r from the charge and it is directed away from a positive charge or towards a negative charge. [SFP.1]
electric potential
The electric potential V(r) at a point specified by the vector r is the electrostatic potentialenergy per unit charge at that point. So, if Eel is the electrostatic potential energy of charge q at a point r, the electric potential at that point isel1( ) EqV r = .Electric potential has a scalar value at every point in space, so it is an example of a scalar field. The SI unit of electric potential is the volt, represented by the symbol V, where 11V = 11J1C−1. [SFP.2]
Balmer's formula
The empirical formulanm4364.5622⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧−=nnλngiving the wavelengths of the spectral lines of the Balmer series which includes the visible lines in the spectrum of atomic hydrogen. [QPI.1]
internal energy
The energy arising from the kinetic energy of the system's constituents and the potential energy of their mutual interaction. It does not include any contribution from the motion or position of the system as a whole. It is an equilibrium property of a macroscopic system that changes by an amount equal to the sum of the heat transferred to the system and the work performed on the system. In thermodynamics, it is represented by a function of state, U, that is conserved in any isolated system. In the case of a monatomic ideal gas, U = 3nRT/2, where n is the quantity of gas (in moles), R is the molar gas constant, and T is the absolute temperature of the gas. (See also first law of thermodynamics.) 4[CPM.1; CPM.3]
magnetic energy
The energy associated with a given distribution of electric currents. This energy is often regarded as being 'stored' in the magnetic field created by the currents. In the case of a current carrying inductor, the magnetic energy is Emag = 221Li , where iis the current in the inductor, and L is the coefficient of self-inductance. (Contrast with the electrical energy of a capacitor.) [DFW.1]
vibrational energy
The energy associated with oscillatory motion of the parts of a system relative to the centre of mass. In the case of a diatomic molecule, the vibrational energy is associated with oscillations in the distance between the atoms. It does not include translational or rotational contributions to the energy. [CPM.2]
Pauli's distribution
The energy distribution function, Ge(E), for free electrons in a metal at (absolute) temperature T. According to Pauli's quantum freeelectron model, the function Ge(E) is the product of the density of states function for electrons and the Fermi occupation factor: Ge(E) = De(E)FF(E). The quantityGe(E)1∆E represents the number of free electrons in the metal with energy between E and E + ∆E. 4[QPM.1]
energy density (at a surface)
The energy falling perpendicularly on unit area of the surface. It is equal to the intensity of the radiation multiplied by the time of exposure. In the case of photographic film, the energy density at some point on the film is known as the exposure of the film at that point. [DFW.3]
molar latent heat of melting
The energy per molerequired to melt a solid into a liquid, whilst the temperature remains fixed at the melting temperature.The SI unit of molar latent heat of melting is the J11mol−1. [CPM.1]
potential energy
The energy that a body possesses by virtue of position, shape or internal structure. Typical examples are gravitational potential energy, strain potential energy and electrostatic potential energy. A potential energy may be associated with each conservative force that acts on a body or between a system of bodies. The potential energy, Epot, associated with any particular configuration of a system is the workthat would be done by the relevant conservative force in going from that configuration to an agreed reference configuration that has been arbitrarily assigned zero potential energy. Because of the arbitrary nature of this reference configuration, only changes in potential energy are physically significant. The change in potential energy, when a system goes from some initial configuration to some final configuration, is minus the work done by the relevant conservative force during that change. (Note that this is not generally equal to the work done by any external forces that bring about the change, since those forces may be non-conservative.)Epot(final) − Epot(initial) = ∆Epot = −Wcons(initial → final)(See also gravitational potential energy and strain potential energy.) [RU.1; PM.2]
Boltzmann's equation
The equation S = k logeW, that relates the entropy S of a given equilibrium state of a macroscopic system to the number W of configurationsthat correspond to that equilibrium state. The constant kis Boltzmann's constant. [CPM.3]
de Broglie formula
The equation λdB = h/p for the de Broglie wavelength of a material particle in terms of Planck's constant, h, and the magnitude of its (relativistic) momentum, p. The result is also valid for photons, which are massless. 4[QPI.1]
Bernoulli's equation
The equationP + ρv2/2 + ρgh = constantthat describes the law of conservation of energy in an ideal fluid of density ρ. It relates pressure P, speed vand height h, at different points along a streamline. [CPM.4]
ideal gas equation of state
The equationPV = nRTwhich applies to a sample of ideal gas in thermal equilibrium, where P is the pressure, V the volume, n the quantity of gas (expressed in moles), T the (absolute) temperature and R (= 8.3141J1K−11mol−1) the molar gas constant. [CPM.1]
diffraction equation
The equationnλ = d sin θn that relates the wavelength λ of plane waves normally incident on a diffraction grating of grating spacing d, to the angle θn between the direction of the incident beam and the direction of the diffracted beam of order of diffraction n. 4[DFW.2]
Euler's equations
The equations of motion of a rotating rigid body. They are usually written as differential equations relating the rates of change of the various components of the body's angular velocity, to the components of the net external torque that acts upon the body. [PM.4]
uniform motion equations
The equations that describe the uniform motion of a particle. For a particle moving in one dimension, with initial position x0, the equations may be writtenvx = constant,44sx = vxt.In terms of vectors, the equations may be writtenv = u,44444s = u0twhere s represents the displacement from the initial position and u is the initial velocity. [DM.1; DM.2]
lens equation
The equationu f1 1 1+ =vthat relates the object distance u, the image distance vand the focal length ƒ of a thin lens. (The equation also holds true for curved mirrors.) In the real-is-positive convention, the focal length of a converging lens or mirror is positive, that of a diverging lens or mirror is negative; real images and real objects are positive, and virtual images and virtual objects are negative. [DFW.3]
Lorentz factor
The factor 2211cV−which occurs often in equations relating to the special theory of relativity. It is represented by the symbol γ (gamma) and is dimensionless. (See also Lorentz transformation, time dilation, Lorentz contraction, velocity transformation, relativistic energy and relativistic momentum.)[DFW.4]
Boltzmann occupation factor
The factor NAe−E/kTthat determines the average number of particles occupying a quantum state of energy E in a system of Ndistinguishable particles in thermal equilibrium at absolute temperature T. The parameter A is a normalization factor, and k is Boltzmann's constant. [QPM.1]
angular magnification
The factor by which the apparent angular size of an object is increased when viewed through an optical system or instrument. It is defined by the equation M = αIM0/0αOB, where αIM is the visual angle subtended at the eye by the image and αOBis the maximum visual angle that can be subtended at the eye by the object (i.e. when the object is at the eye's near point). Also called the magnifying power. [DFW.3]
Bose occupation factor
The factore 11( )( )B−=E− kT F E µ.that determines the average number of particles occupying a quantum state of energy E in a system of indistinguishable bosons in thermal equilibrium at absolute temperature T. For photons, the characteristic energy µ is 0. [QPM.1]
Fermi occupation factor
The factore 11( )( )F+=E−EFkTF Ethat determines the average number of particles in a single quantum state of energy E for a system of identical fermions in thermal equilibrium at absolute temperature T. The energy EF that is a characteristic of the system is called the Fermi energy. [QPM.1]
non-locality
The feature of quantum mechanics that allows it to account for the predicted and observed correlations between the results of measurements carried out simultaneously at well-separated locations. [QPI.4]
indeterminacy
The feature of quantum mechanics that implies the impossibility of having totally precise knowledge of all of the observables of a system at the same time. [QPI.4]
indeterminism
The feature of quantum mechanicswhich implies that it is not generally possible to use knowledge of the precise value of an observable at some particular time to predict the precise value of that same observable at an arbitrary later time. [QPI.4]
relativistic force
The force acting on a body as determined by the rate of change of the relativistic momentum of the body. (See also Newton's second law of motion.) [DFW.4]
tension force
The force that a stretched elastic body will exert on an attached object, or which one part of such a body exerts on a neighbouring part. [PM.1]
gravitational force
The force that acts on a body due to its interaction with a gravitational field. In the case of a point particle of mass m, it is given by Fgrav(on m at r) = mg(r), where g(r) is the gravitational field at the position r of the particle. The gravitational force between two point masses is described by the law of universal gravitation. [SFP.1]
magnetic force
The force that acts on a body due to its interaction with a magnetic field. In the case of a point particle of charge q moving with velocity v, the magnetic force is given by Fm = q(v × B(r)), where B(r) is the magnetic field at the position r of the particle. (This is part of the Lorentz force law.) Note that a magnetic force cannot change the speed of a charged particle, since it always acts at right angles to the direction of motion of the particle, but it can still cause the particle to accelerate by changing the direction of the particle's motion. [SFP.4]
electrostatic force
The force that acts on a body due to its interaction with an electric field. In the case of a point particle of charge q, it is given by Fel (on q at r) = qe(r), where e(r) is the electric field at the position r of the particle. The electrostatic force between two charges is described by Coulomb's law. [SFP.1]
frictional force
The force that arises when relative motion occurs or is tending to occur between two solid bodies that are in contact. Slightly different laws apply, depending on whether the object is moving or not. (Seecoefficient of static friction and coefficient of sliding friction.) [PM.1]
Bohr's equation
The formula derived by Bohr, using his model of the hydrogen atom, which gives the wavelength of any spectral line in the hydrogen atom, due to the electron making a transition from an orbit characterized by the quantum number n to a lower orbit characterized by the quantum number q, namely91.127 nm.2 22 2⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧−→ =n qq nλn qWhen q is put equal to 2, Bohr's equation reduces to Balmer's formula. [QPI.1]
Planck-Einstein formula
The formulaE = hfthat relates the energy E of a photon of monochromaticelectromagnetic radiation to the frequency ƒ of that radiation where h = 6.626 × 10−341J1s. is Planck's constant. [QPI.1]
barometric formula
The formulaP(z) = P(0) exp(−z/λ)that relates pressure P to altitude z in a thin isothermal atmosphere, where the scale height is λ. [CPM.4]
Einstein's postulates (of special relativity)
The foundations on which the special theory of relativity are built. The postulates are:1$The principle of relativity: the laws of physics can be written in the same form in all inertial frames of reference.2$The principle of the constancy of the speed of light: the speed of light (in a vacuum) has the same constant value in all inertial frames of reference.[DFW.4]
expansivity
The fractional increase in volume of a substance per unit increase in its temperature, under specified conditions (e.g. at constant pressure). [CPM.1]
time-dependent Schrödinger equation
The fundamental equation of quantum mechanics (at least in Schrödinger's wave-mechanical approach to the subject). The time-dependent Schrödinger equation is a differential equation. Its solution is the time-dependent wavefunction that provides the fullest possible description of the state of a quantum-mechanical system — including its time-evolution, in the absence of a measurement. (Measurements cause the wavefunction to change abruptly and unpredictably, in a way that is not described by the time-dependent Schrödinger equation.) [QPI.2]
gravitational interaction
The fundamental interaction between all particles that possess mass. (Note that, according to the general theory of relativity, gravitational interactions also involve massless particles.) (See also strong, weak and electromagnetic interaction.) [QPM.4]
electromagnetic interaction
The fundamental interaction between particles that possess electric charge. (See also strong, weak and gravitational interaction.) [QPM.4]
unification
The fusing together (in a mathematical sense) of two or more theories (usually quantum theories of fundamental forces) in order to produce a more comprehensive theory that incorporates all important aspects of the original theories and usually more besides. Particular examples include the electroweak theory and the various proposals for grand unified and/or superunified theories. [RU.1]
specific heat capacity
The heat capacity per unit mass of a specified substance. In other words, the energy per unit mass and per unit temperature rise needed to raise the temperature of a sample of a specified substance under specified conditions (such as constant pressure or constant volume). Specific heat capacity is measured in units of J1K−11kg−1, and is often referred to simply as 'specific heat'. [CPM.3]
heat capacity at constant pressure
The heat capacityof a body when its pressure is kept constant. [CPM.3]
valence band
The highest occupied energy band in a solid. In metals this band is only partially full and this allows the conduction of electricity. The valence band in an insulator or a semiconductor is completely full at very low temperatures, but holes are formed at higher temperatures by electrons being thermally excited into the conduction band. [QPM.2]
periods
The horizontal rows in the Periodic Table of the elements. Elements in a given period all have the same principal quantum number n in the outer shell and the subshells are filled up as one progresses from the left to the right across the period. [QPI.3]
pairing energy
The increase in binding energy per nucleon for nuclei that have even numbers of protonsand/or neutrons, rather than odd numbers. [QPM.3]
argument
The independent variable that actually determines the value of a function, e.g. θ is the argument of sin1θ, and 2θ is the argument of sin1(2θ). [DM.3]
spin-orbit interaction
The interaction between the magnetic moments associated with the spin and orbitalangular momentum of each electron in an atom. The spin-orbit interaction gives rise to splittings in the atomic energy levels due to the fact that the potential energy of the interaction is positive when the two magnetic moments are aligned parallel to each other and negative when they are antiparallel. 44[QPI.3]
thin-film interference
The interference that occurs between waves that are reflected from the front and back surfaces of a thin film. The interference can lead to interference fringes or bright coloration. [DFW.2]
rotational kinetic energy
The kinetic energy associated with the rotational motion of a body. For a body rotating with angular speed ω about a fixed axis, the rotational kinetic energy is221Erot = Iωwhere I is the body's moment of inertia about the axis of rotation. In the case of a diatomic molecule the rotational energy is associated with rotations of the molecule about axes perpendicular to the line joining the atoms. It does not include translational or vibrational contributions to the energy. 4[PM.4; CPM.2]
boundary layer
The layer of fluid next to a solid surface that remains dominated by viscous effects, no matter how large the Reynolds number, Re, may be. For Reynolds numbers much greater than 1, the thickness of this layer is proportional to 1/ Re . The boundary layer is the region in which the fluid velocity makes an abrupt transition from the value found in the external flow to the value of zero (relative to the solid surface) required by the no-slip condition. Eddies and whirlpools tend to form within the boundary layer. [CPM.4]
depletion region (or depletion layer)
The layer of material extending along the boundary in a p-n junction. In this depletion region the electrons and holes have recombined to leave bare donor and acceptor ions that create an electric field directed across the junction from the n-side to the p-side. [QPM.2]
binding energy
The least amount of energy needed to separate a system into its (appropriately specified) components. For example, in the case of a nucleus, the binding energy is the energy required to separate the individual protons and neutrons that comprise the nucleus. (The binding energy is therefore equal to the energy that would be released if the nucleus were to be assembled from its separated constituents.) [CPM.1; QPM.3]
eyepiece lens
The lens in a microscope or telescopewhich is positioned next to the eye, often called just the eyepiece. [DFW.3]
critical angle
The limiting angle of incidence beyond which total internal reflection occurs. It is given by: sin1icrit = n2/n1 for a ray of light travelling from a medium of refractive index n1 into a medium of refractive index n2. [DFW.2]
conduction band
The lowest unfilled energy band in a solid, containing the conduction electrons for a semiconductor. This band is completely empty in an insulator or semiconductor at very low temperatures but becomes partly populated due to thermal excitation of electrons from the valence band as the temperature rises. [QPM.2]
magnitude of the acceleration due to gravity
The magnitude of the downward acceleration due to gravity at the Earth's surface. Represented by the symbol g, this quantity has a value close to 9.811m1s−2 across much of the Earth's surface. [DM.1]
magnetic field strength
The magnitude of the magnetic field. A particle of charge q moving with speed v at an angle θ to a magnetic field of strength Bexperiences a force of magnitude Fm = |1q1|1vB sin1θ. This equation can be used to interpret the SI unit of magnetic field, the tesla (T), where 11T = 11N1s1m−11C−1. A magnetic field of strength 11T exerts a force of 11N on a particle of charge 11C moving perpendicularly to it at a speed of 11m1s-1. The magnetic field strength near a typical bar magnet is of order of 10−11T; large superconducting magnets produce magnetic field strengths of several hundred tesla. The magnitude of the Earth's magnetic field, measured at the surface, is of the order of 10−51T. [SFP.4]
rest mass
The mass of a particle as measured by an observer relative to whom the particle is at rest. Associated with a given rest mass is a particular mass energy. [DFW.4]
molar mass
The mass per mole of a pure substance.The SI unit of molar mass is the kg1mol−1. [CPM.1]
formalism
The mathematical aspects of a subject including equations, protocols and procedures for carrying out calculations and making predictions. [QPI.4]
factorization
The mathematical process of writing an expression of the form a0 + a1x + a2x2 + ... anxn as a product of factors of the form an(x −α)(x − β0)...(x − ω). For example, ax2 + bx + c can be written as a(x − α)(x − β0), where the quantities α and β can be expressed in terms of a, b and c. [DM.2]
integration
The mathematical process used in the evaluation of (definite) integrals. [PM.2]
modulus sign
The mathematical symbol | | used to denote the magnitude of the enclosed quantity. For example, |1−3.411| = 3.41. The terms 'modulus' and 'magnitude' are often used to mean the same thing. [DM.3]
critical current density
The maximum electric current per unit area that can flow in a superconductorwithout that superconductor reverting to its normal conducting state. When current flows in a superconducting material, in the usual way, a magnetic field is created with a maximum magnitude at the surface of the material. The field magnitude is proportional to the magnitude of the current, so if the 14current flow is sufficiently great, the critical magnetic field strength BC is reached at the surface and the material reverts to the normal state. [QPM.2]
critical magnetic field strength
The maximum magnitude, BC, of applied magnetic field for which the Meissner effect can occur in a superconductor. At larger applied fields the flux penetrates the material destroying the superconductivity. The value of BC is strongly temperature dependent, increasing from zero at the superconducting transition temperature TC to a maximum at 01K. [QPM.2]
superconducting transition temperature
The maximum temperature TC at which a material can display superconductivity. For temperatures below TC the electrons form Cooper pairs, becoming fully paired at 01K. The pairing is gradually destroyed by thermal agitation as the temperature rises towards TC. [QPM.2]
confinement
The mechanism arising from the interaction of quarks and gluons that prevents them from being observed as free particles. It is generally supposed that this is a consequence of quantum chromodynamics, but despite a good deal of supporting evidence, this has still not been rigorously proved. [QPM.4]
fundamental mode
The mode of oscillation of a standing wave with the lowest possible frequency. In the case of a wave on a string, the fundamental mode has a wavelength equal to twice the length of the string. [DFW.2]
angular speed
The modulus of the rate of change of angular position of a particle or body:dtdθω = .The angular speed of a body, about a point O represents the magnitude of its angular velocity about O. Angular speed is a positive scalar quantity with the SI unit rad1s−1. [DM.3; PM.4]
angular momentum
The momentum associated with the rotational motion of a body. For a particle, the angular momentum l, about a point O, is defined by the vector productl = r ×pwhere r is the displacement of the particle from the point O, and p is the linear momentum of the particle. This implies that if the angle between r and p is θ, then l has magnitude rp1sin1θ, and points in a direction that is perpendicular to r and p, as specified by the right-hand rule. The SI unit of angular momentum is the kg1m21s−1.For an extended body, the angular momentum L about a given point depends on the way the body's mass is distributed, and on the components of its angular velocity w. There are a number of important special cases in which the body is in uni-axial rotation about an axis of symmetry and L = I0w, where I is the moment of inertia about that axis. However, L = I0w is not a general relation that will be true in all circumstances. (See conservation of angular momentum.) [PM.4]
linear momentum
The momentum associated with the translational motion of a body. For a particle of mass mtravelling with velocity v, the linear momentum isp = mv.For a rigid body of mass M,p = mvCM.where vCM is the velocity of the body's centre of mass. (See also conservation of linear momentum, and relativistic momentum.) [PM.3]
far point
The most distant point on which the eye can clearly focus. For a 'normal' eye, it is at infinity (i.e. rays from this point are parallel as they enter the eye). [DFW.3]
ciliary muscle
The muscle tissue within the eye which is used to change the shape of the eyelens (either squashing or stretching it), thereby changing its focal length and so enabling it to bring objects at different distances to a sharp focus on the retina. [DFW.3]
normal
The normal to any surface at a point is the line perpendicular to the surface at that point. In more general usage, normal is another word for perpendicular. [DFW.2]
action at a distance
The notion that one body may influence another with which it is not in contact, without the aid of any intermediate agency such as an ether or a field. [RU.1]
Avogadro's number
The number of basic particles (atoms, molecules, ions, etc.) in one mole of any substance. Avogadro's number is equal to the number of atoms in 12 × 10−31kg of the carbon isotope carbon-12 (6.022 × 1023). [CPM.1]
neutron number
The number of neutrons in a specified nucleus. The neutron number is usually represented by the symbol N and is equal to the difference between the mass number A and the atomic number Z, so N = A − Z. 4[QPM.3]
valency
The number of valence electrons in an isolated atom of a specified element. In the context of Drude's free-electron model and Pauli's quantum freeelectron model, the valency of a metal is equal to the number of electrons released per atom into the freeelectron gas. [QPM.1]
quantum numbers
The numerical quantities that identify the possible stationary state wavefunctions of a quantum system. In the case of an electron in an atom, examples include the principal quantum number n, the orbital angular momentum quantum number l, and the orbital magnetic quantum number ml. They are usually integers (apart from spin, s, which, for the electron, is equal to 21). The possible values of the quantum numbers (apart from spin) are determined by finding the allowed solutions of Schrödinger's equation. [QPI.2]
superconductivity
The phenomenon exhibited by a number of materials, whereby, at a sufficiently low temperature, the resistivity becomes zero (i.e. the electrical conductivity becomes infinitely large) and magnetic flux is expelled. 4[QPM.2]
long-range order
The phenomenon exhibited by some forms of matter, particularly crystalline solids, in which the neighbours of a typical atom show signs of regularity and order in their spatial arrangement, andthat order extends even to quite distant neighbours. A line of atoms, for instance, in which the interatomic spacing remains constant over many atoms, clearly displays long range order. (Contrast with short-range order, and see also radial density function.) [CPM.1]
population inversion
The phenomenon occurring in a material medium that is required for laser action on a suitable optical transition between two energy levels of the atoms of that medium. Population inversion implies the maintenance of a higher population of atoms in the upper level of the transition than the lower, so that incident resonant radiation will, on average, stimulate emission and be amplified rather than being absorbed. [QPI.3]
viscosity
The phenomenon of internal friction in a fluid, that tends to reduce the relative velocity of two neighbouring layers of the fluid and leads to energy dissipation. It also gives rise to a viscous force when an object moves through a fluid. (See Stokes' law.) Viscosity is also sometimes used as shorthand for coefficient of viscosity. [PM.1; CPM.4]
inertia
The phenomenon that causes a body to continue in its state of uniform motion (including the possibility of remaining at rest) unless acted upon by an unbalanced force. The mass of a body provides a measure of its inertia. (See inertial mass.) [PM.1]
electron pairing
The phenomenon that occurs in the covalent bonding of two atoms, whereby electrons that are unpaired in the separated atoms are shared to form a pair with opposite spin states in the bonded molecule. This electron pairing of valence electrons generally allows each atom to be surrounded by a closed shell, or closed subshell, of electrons. [QPM.2]
friction
The phenomenon whereby a force (called a frictional force) acts on a body when it is in contact with another body (or with a viscous medium) and when there is relative motion, or a tendency for relative motion, between those bodies (or between the body and the medium.) [PM.1]
radioactivity
The phenomenon whereby an unstable nucleus spontaneously decays and, as a consequence, emits ionizing particles or electromagnetic radiation. There are three main modes of radioactive decay: α-decay, β-decay and γ-decay; see those entries for further details. [QPM.3]
7bonding
The phenomenon whereby atoms are bound together to form molecules or solids. There are several different kinds of bonding though all are essentially manifestations of the electrical interaction between charged particles. For further details see covalent bond, ionic bond, mixed bonding, hydrogen bonding, metallic solid and van der Waals forces.
self-induction
The phenomenon whereby changes to the electric current flowing in a coil (or any other circuit element) are hampered by the self-inductance of the coil. Changing the current in a coil creates a changing magnetic field in the space in and around that coil. This changing magnetic field will give rise to a changing magnetic flux through the coil; and this, by Faraday's law, will create an EMF in the coil. By Lenz's law, the direction of this induced EMF will be such that it opposes the original current change that caused it. Changes in current are therefore 'opposed' and the extent of the opposition will depend on the coil's self inductance, which determines the magnitude of the induced EMF produced by a given rate of change of current in the coil. [DFW.1]
dispersion
The phenomenon whereby different colours of light (or different frequencies of electromagnetic radiation) are spread out when they cross an interface between two media of different refractive index. It occurs because the refractive index, and hence the angle of refraction, varies slightly with frequency. [DFW.2]
degeneracy
The phenomenon whereby more than one quantum state is associated with a particular energylevel in a given system. Any energy level that corresponds to more than one quantum state is said to be degenerate. [QPI.2]
wave-particle duality
The phenomenon whereby quantum systems (including elementary particles and electromagnetic radiation) can exhibit properties or modes of behaviour that classical physics would associate with the mutually exclusive categories of waveand particle (e.g. the diffraction of electrons). [QPI.1]
relativity of simultaneity
The phenomenon whereby two spatially separated events that are simultaneous according to one observer (i.e. happening at the same time in his/her frame of reference), may occur at two different times according to another observer, provided the second observer is moving relative to the first. (See also causality and space-time conjunction.) [DFW.4]
constructive interference
The phenomenon whereby two superposed oscillations or waves produce a resultant with a larger amplitude than either of the original oscillations or waves. The extreme case occurs when the oscillations or waves are exactly in phase, so that their phase difference is 0 or an integer multiple of 2π. [DFW.2]
destructive interference
The phenomenon whereby two superposed oscillations or waves produce a resultant with a smaller amplitude than either of the original oscillations or waves. The extreme case occurs when the oscillations or waves are exactly out of phase, so that their phase difference is an odd integer multiple of π. [DFW.2]
diffraction
The phenomenon whereby waves are able to bend round obstacles or spread from apertures. According to the Huygens principle, each point on a wavefront can be regarded as a small source of secondary waves. When a wavefront meets a partial obstacle, secondary waves spread out from the unimpeded parts of the wavefront and it is this that gives waves their ability to 'bend round corners'. 4[DFW.2]
brittle fracture
The phenomenon, exhibited by some materials, where the application of a stress leads to a sudden failure of the material with little or no plastic deformation. Many real materials contain tiny cracks, either within the bulk or on the surface, which can act as a source of weakness. Stress is concentrated at the ends of these cracks, stretching them open. If a crack is large enough, even a small additional stress can cause the crack to suddenly and catastrophically extend right across the sample, creating brittle failure. Brittle fracture typically occurs in materials that are not ductile and which have a large covalent component to their bonding. [QPM.2]
permeability of free space
The physical constant µ0 = 4π × 10−71T1m1A−1 = 4π × 10−71kg1m1C−2, that plays a role in determining the magnitude of magnetic forcebetween two current-carrying wires separated by a vacuum. [SFP.4]
permittivity of free space
The physical constant ε0 = 8.854 × 10−121C21N−11m−2, that plays a role in determining the magnitude of the electrostatic forcebetween charged particles separated by a vacuum. [SFP.1]
focal plane
The plane that passes through a lens's or mirror's focal point and is perpendicular to its optical axis. [DFW.3]
fulcrum
The point at which a lever is supported; often coincident with a pivot. [PM.4]
critical point
The point on the PVT surface of a substance that corresponds to the highest temperatureequilibrium state in which the liquid and gas phases coexist. At the critical point, the distinction between liquid and gas phases is meaningless. [CPM.1]
centre of curvature (of a spherical mirror)4
The point that lies at the centre of the sphere of which the surface of the spherical mirror forms a part. [DFW.3]
focal point
The point to which parallel rays striking a converging lens or mirror converge, or from which parallel rays striking a diverging lens or mirror appear to diverge. Also called the principal focus. [DFW.3]
initial position
The position of a particle at some chosen starting time, usually at t = 0. [DM.1]
nucleus
The positively charged core of an atom, which accounts for nearly all of its mass. A nucleus consists of one or more protons and a number of neutrons. (See also atomic number, mass number, andneutron number.) [CPM.1; QPI.1; QPM.4]
harmonics
The possible standing waves that can occur in a given system. For a string with fixed endpoints, the first harmonic is the same as the fundamental mode. The second harmonic occurs when there are two half-wavelengths in the length of the string; the third occurs when there are three half-wavelengths in the length of the string, and so on. [DFW.2]
electrical energy
The potential energy associated with a given distribution of electric charges. This energy is often regarded as being 'stored' in the electric field created by the charges. In the case of a charged capacitor, the electrical energy is Eel = 221CV , where Vis the potential difference across the capacitor, and C is its capacitance. (Contrast with the magnetic energy of an inductor.) 4[SFP.2]
electrostatic potential energy
The potential energy of a particle or body that arises from its interaction with other particles or bodies via the (conservative) electrostatic force. The electrostatic potential energy of a charge q, placed at a point where the electric potentialis V, is given by Eel = qV. [SFP.2]
strain potential energy
The potential energy of a stretched body subject to conservative restoring forces; i.e. the work done by those forces in returning the body to its unstretched configuration. In the case of an ideal spring extended by an amount x from its unextended state, the strain potential energy is given byEstr = 21ksx2. [PM.2]
gravitational potential energy
The potential energyof a particle or body that arises from its interaction with other particles or bodies via the (conservative) gravitational force. A particular example is the potential energy associated with terrestrial gravitation, in which case Egrav = mgh, where m is the mass of the body, g is the magnitude of the acceleration due to gravity, and his the height of the body above an arbitrarily agreed position of zero gravitational potential energy. Another important example is the potential energy of a body of mass m at a distance r from the centre of the Earth: Egrav = −GMEm/r, where G is the universal gravitational constant and MEis the mass of the Earth. More generally, the gravitational potential energy of a body of mass m, placed at a point where the gravitational potential is Vgrav, is given by Egrav = mVgrav. [PM.2, SFP.2]
gauge pressure
The pressure excess over atmospheric pressure, that would, for example, be registered by a suitably calibrated gauge carried by a diver. [CPM.4]
44Pauli pressure
The pressure exerted by a gas of fermions as a direct consequence of Pauli's exclusion principle. When a system of fermions (such as electronsor neutrons) is at a relatively low temperature, the energy levels of the system fill from the ground state upwards. Because of the exclusion principle many particles are forced into quite high energy levels, in spite of the relatively low thermal energy. These particles have a high average translational energy and, by the usual kinetic theory argument, give rise to a large pressure. It is this that constitutes the Pauli pressure. The electrons in a white dwarf star provide an example of this phenomenon: the star is supported against gravitational collapse by the Pauli pressure exerted byits electrons. [SFP.2]
conservation of energy
The principle that the total energy of any isolated system is constant. A more informal statement of this principle is that energy may neither be created nor destroyed. [RU.1; PM.2]
conservation of mass
The principle, in classical Newtonian mechanics, that the mass of any system remains constant, provided no matter enters or leaves the system. A more informal statement of this principle is that mass cannot be created or destroyed. (The development of special relativity has shown that this principle is not generally true, though it is still of considerable value and is widely used within Newtonian mechanics.). [RU.1, PM.1]
additivity of mass
The principle, in classical Newtonian physics, that the mass of a system is the sum of the masses of its constituent parts. (The development of special relativity has shown that this principle is not generally true, though it is still of considerable value and is widely used within Newtonian mechanics.) [PM.1]
radial probability density
The probability per unit length of finding a particle at a radial distance r from some specified point. When the (three-dimensional) probability density for finding the particle in the neighbourhood of the point is spherically symmetric about the point (as in the case of an s-state electron in an atom) the radial probability density is related to the probability density byradial probability density = 4πr2× (probability density) 50= 4πr21|1ψ0(r, θ, φ)1|2.The probability of finding such a particle in the narrow region between r and r + ∆r is 4πr21|1y0(r, θ, φ)1|21∆r.[QPI.3]
probability density
The probability per unit volume (in three dimensions) of detecting a particle in the vicinity of a given point. If the wavefunction describing the particle is normalized, the probability density is equal to |1Ψ1|2, the square of the magnitude of the wavefunction. For an electron in an atom, described by the time-independent wavefunction 48 ψ0(r, θ, φ) =ψ1(r) ×ψ2(θ0) ×ψ3(φ0)the probability density for detection at the point with spherical polar coordinates(r, θ, φ) is|1 ψ0(r, θ, φ)1|2 = |1 ψ1(r)1|2× | ψ2(θ0)1|2× |1 ψ3(φ0)1|2.The SI unit of (three-dimensional) probability density is m−3. For a particle confined to one dimension, the probability density is defined as the probability per unit length of detecting the particle in the vicinity of a given point, and the SI unit of (one-dimensional) probability density is m−1. 4[QPI.3]
collapse of the wavefunction
The process whereby a wavefunction is supposed to undergo an abrupt and unpredictable change due to a measurement. The result of the collapse is conventionally supposed to be an eigenstate of the measured observable, corresponding to the eigenvalue that was the result of the measurement. Wavefunction collapse is not a feature of the time evolution described by the time-dependent Schrödinger equation. [QPI.4]
reflection
The process whereby the direction of propagation of a wave travelling in a single medium, is changed as a result of its interaction with a boundary. When waves are reflected at a boundary they obey thelaw of reflection. [DFW.2]
stimulated emission
The process whereby the emission of radiation from an atom in an excited stateoccurs as a result of its interaction with incident electromagnetic radiation. If the excited state of the atom is such that an electron can make a radiative transition, of energy E, to a state of lower energy, then, incident photons of energy E, can stimulate the excited atom to emit a photon of energy E. This process occurs with a much greater probability than the process of spontaneous emission which can take place in the absence of incident photons. The emitted photon is in the same quantum state as the incident photon. In terms of waves, the emitted radiation has the same frequencyand phase as the incident radiation and it travels in the same direction. The process of stimulated emission allows the construction of lasers. [QPI.3]
spontaneous emission
The process whereby the emission of radiation from an atom in an excited stateoccurs spontaneously, without interaction with other atoms or with incident photons. Spontaneous emission from atoms in a specified excited state occurs randomly and in such a way that a population of those atoms will decay exponentially with a characteristic time constant.44[QPI.3]
interpolation
The process whereby the known values of a function, at certain points or in certain regions, are used to determine the approximate form of the function in other regions where its value may not be accurately known. The procedure is based on the assumption that the function varies smoothly between its known values — an assumption that may be seriously flawed in particular cases. Interpolation is often used (often intuitively) in graphical work. [QPI.3]
exposure (of photographic film)
The product of the intensity I of the light falling on a given part of the film and the exposure time ∆t; that is, exposure = I11∆t. The exposure is a measure of the energy density of the light (i.e. the light energy per unit area) falling on that part of the film. [DFW.3]
commutative
The property of a product of factors whereby the result is independent of the order in which the factors are multiplied together. An ordinary algebraic product of scalar quantities x and y is commutative since xy = yx for all possible choices of xand y. The scalar product of two arbitrary vectors is similarly commutative since a1•1b = b1•1a. However, the vector product a × b is not commutative because a × b = −b ×a. [PM.4]
direction
The property of a vector that determines its orientation. A common way of expressing the direction of a vector is to specify the angle between a particular axis or reference line and the vector. For example, in two dimensions, it is customary to specify the direction of a vector in terms of the angle (measured anticlockwise) between the positive x-axis and the vector. An alternative method is to specify the components of the vector relative to a particular coordinate system. [DM.2]
electronegativity
The property of an atom that measures its affinity for electrons. A strongly electronegative atom in a covalent bond with a less electronegative atom will take more than an equal share of the bonding electron pairs. This gives it a net negative electric charge leaving its partner with a net positive charge. In extreme cases, a complete transfer of one or more electrons to the more electronegative atom takes place and an ionic bond is formed by the electrostatic attraction between positive and negative ions. [QPM.2]
indistinguishable
The property of identical particles in quantum physics (two hydrogen atoms, for example) that prevents them from being labelled for the purposes of specifying and counting configurations. In quantum physics, identical particles are exactly alike and have no individual identity. [QPM.1]
Joule's classification
The proposal by James Joule that, for the purpose of calculating the pressure of a gas, it would make no difference if we imagined dividing the molecules into three classes: one-third moving to and fro along the x-axis, one-third moving to and fro along the y-axis and one-third moving to and fro along the zaxis. [CPM.2]
reductionism
The proposal that observed phenomena can be explained in terms of more basic phenomena, until some level of fundamental entities and interactions is reached. (Contrast with emergence.) [RU.1]
emergence
The proposal that some physical systems may display properties that could not be predicted on the basis of a complete knowledge of the underlying phenomena to which they might otherwise be reduced. (Most physicists would deny the truth of this in principle, but they would also accept it as effective in practice.) [RU.1]
heat capacity
The quantity of energy per unit temperature rise needed to raise the temperature of a given body under specified conditions (such as constant pressure or constant volume). The SI unit of heat capacity is the J1K−1. [CPM.3]
velocity
The quantity that describes the (instantaneous) rate of change of the position of a body. For a particle moving in one dimension along the x-axis, the velocity vx at any time is the rate of change of the particle's position x and is given by the gradient of the particle's position-time graph at the relevant time. This gradient is equal to the derivative of the position with respect to time, so the velocity at time t may be writtentxtxddv ( ) = .Velocity is a vector quantity, characterized by a direction as well as a magnitude. In one dimension the sign of vx suffices to indicate the direction, but in two or three dimensions, some other method must be used to indicate direction. This is often achieved by expressing the velocity vector in terms of its Cartesian components, as in v = (vx, vy, vz), wherettdd( )rv =and r(t) is the position vector. [DM.1; DM.2]
acceleration
The quantity that describes the (instantaneous) rate of change of velocity of a body. For a particle moving in one dimension along the x-axis, the acceleration ax at any time is the instantaneous rate of change of the particle's velocity vx, and is given by the gradient of the particle's velocity-time graph at the relevant time. This gradient is equal to the derivative of the velocity with respect to time at the relevant time, so the acceleration at time t may be written tta txxdd ( )( )v= . [DM.1]Acceleration is a vector quantity, characterized by a direction as well as a magnitude. In one dimension the sign of ax suffices to indicate the direction, but in two or three dimensions some other method must be used to indicate direction. This is often achieved by expressing the acceleration vector in terms of its (Cartesian) components, as in a = (ax, ay, az), wheretttdd ( )( )va =and v(t) is the velocity vector. [DM.2]
displacement (vector)
The quantity that describes the difference between the position of a point and the position of a specified reference point. In the case of a particle moving in one dimension, along the x-axis, if the particle starts at position x1 and moves to position x2, then the displacement of the particle from its initial position issx = x2− x1.The magnitude of this displacement is the distance sbetween the two points, so s = |1sx1|.Displacement is a vector quantity characterized by a direction as well as a magnitude. In one dimension the sign of sx suffices to indicate the direction, but in two or three dimensions some other method must be used toindicate direction. This is often achieved by expressing the displacement vector in terms of its (Cartesian) components. Thus, if point P1 has the position vector r1 = (x1, y1, z1) and point P2 has the position vectorr2 = (x2, y2, z2), then the displacement s = (sx, sy, sz) from P1 to P2 is defined bys = r2− r1 = (x2− x1, y2− y1, z2− z1).In this case the distance between the two points is given by22 122 122 1s =|s|= (x − x ) + (y − y ) + (z − z ) .Note that a displacement is entirely specified by its magnitude and direction; it is not tied to any particular starting point or finishing point, even though such points may be used to specify it. [DM.1; DM.2]
position (vector)
The quantity that determines the location of a point relative to the origin of a specified coordinate system.In one dimension the position of a point can be specified by means of a single coordinate value, x say. The motion of a particle that moves along the x-axis can then be described by expressing its x-coordinate (its instantaneous position) as a function of time.Position is a vector quantity characterized by a directionas well as a magnitude. In one dimension the sign of a single coordinate value (such as x) suffices to determine the direction relative to the origin, but in two or three dimensions more information is required. This is often provided by expressing the position vector of a point in terms of its Cartesian components. Thus, a point with position coordinates (x, y, z), has the position vector r = (x, y, z). The magnitude of this position vector is the distance between the origin and the specified point, and is given by| | .2 2 2r = r = x + y + z 4[DM.1; DM.2]
quantum electrodynamics
The quantum field theoryof the electromagnetic interaction. It is often abbreviated to QED. [RU.1; QPM.4]
tunnelling
The quantum-mechanical phenomenon whereby a particle confined in a potential well with walls of a finite height, has a wavefunction that penetrates some distance into the classically forbidden region (where the particle's potential energy is more than its total energy). If this region is of a finite width, it is possible for the particle to tunnel through the classically forbidden region and be detected in some other classically allowed region where its potential energy is again less than its total energy. [QPI.2;QPM.3]
Bohr radius
The radius of the lowest orbit in the Bohr model of the hydrogen atom:2e2004m eaπε "= = 0.53 × 10−101mwhere me and e are the mass of the electron and the magnitude of the charge on the electron, respectively, and " is Planck's constant divided by 2π. [QPI.1]
depth of focus
The range over which the lens-toimage distance can be adjusted without the image of a fixed object becoming unacceptably blurred. [DFW.3]
frequency
The rate at which cycles of a periodic oscillation are completed. For an oscillation of period T, the frequency is given by the reciprocal of the period; ƒ = 1/T. The SI unit of frequency is the hertz (Hz), where 11Hz = 11s−1. The concept of frequency may also be extended to the case of waves, where a wave of period T is said to have a frequency ƒ = 1/T. In this case the frequency represents the rate at which complete cycles of the wave pass a fixed point. [DM.3, DFW.2]
electric current
The rate at which electric chargeflows in a given direction across a fixed plane (Often the current flows in a wire and the plane is perpendicular to the wire.) If the total charge q in some region is changing with time due to the flow of an electric current into that region, then the instantaneous value of the electric current is given by i = dq/dt. In metal wires, the flow of electric current is actually caused by negatively 20charged electrons moving in the opposite direction to that of the current. For this reason, the current is sometimes called the conventional current. The SI unit of electric current is the ampere (A). [SFP.3]
resistance
The ratio R of the magnitude of the potential difference between the ends of a sample to the magnitude of the current flowing through that sample; R = |1VR1|1/1|1i1|. In materials that obey Ohm's law, the resistance is constant, independent of the values of VR or i. The SI unit of resistance is the ohm (Ω), where 11Ω = 11V1A−1. [SFP.3]
F-number
The ratio of a lens's (or mirror's) focal length ƒ to its aperture diameter D. [DFW.3]
density
The ratio of mass to volume for a homogeneous system. It is possible to define the density at a given point in any system by taking a small volume element around that point and evaluating the ratio of mass to volume for that volume element. [CPM.1]
charge to mass ratio of the electron
The ratio of the charge, −e, to the mass, me, of an electron. It is more easily measured than either the charge or the mass separately and has the value−e/me = −1.759 × 10111C1kg−1. [SFP.1]
51refractive index
The ratio of the speed of light in a vacuum to the speed of light in a particular medium; hence, refractive index n = c/v. The refractive index of a medium is always greater than one. (See also law of refraction (Snell's law)). [DFW.2]
ratio of heat capacities
The ratio γ = CP0/CV of the molar heat capacities at constant pressure and constantvolume for a given quantity of a specified substance. For an ideal gas with ƒ effective degrees of freedom, γ = (1ƒ + 2)/ƒ, implying that γ is 1.67 for a monatomicideal gas, 1.40 for a diatomic ideal gas and 1.33 for a triatomic ideal gas under moderate conditions. [CPM.3]
normal reaction force
The reaction to any contact force. When an object rests on (or is pressed into) a solid surface, the solid is compressed slightly. The solid resists compression by exerting a force on the object. This reactive force acts at right angles to the surface at 42the point of contact, and is therefore called a normal reaction force. [PM.1]
virtual object
The real image that would have been formed by rays converged by a lens or mirror if those rays had not been intercepted by some other lens or 66mirror (for which the unformed real image acts as a virtual object). [DFW.3]
rest energy
The relativistic energy of a particle that is not moving. For a particle of (rest) mass m, the rest energy E0 is given by E0 = mc2. Rest energy is also known as mass energy. [QPM.4]
no-slip condition
The requirement that the fluidimmediately next to a solid surface should always be stationary relative to the surface. [CPM.4]
cycle
The set of successive values that a periodic function passes through as its argument is increased by one period. For example, in the case of the periodic function Asin(ω0t + φ), a cycle would consist of the succession of values between A and −A that the function passes through as ω0t + φ increases by 2π. [DM.3]
standard configuration
The simplest possible arrangement of two inertial frames of reference with constant velocity relative to each other. The axes of the first frame of reference are all parallel to the corresponding axes of the second frame of reference. The origins of the two frames of reference coincide at t = t′ = 0, and the origin of the second frame of reference moves along the x-axis of the first in the positive direction. The two frames of reference maintain the same relative orientation while moving. [DFW.4]
blind spot
The small region at the back of the eye, within the area of the retina, where the optic nerveenters. Any light falling on this spot will be undetected. [DFW.3]
atom
The smallest electrically neutral sample of an element that retains the fundamental chemical and physical identity of that element. 4[CPM.1]
molecule
The smallest part of a given pure substance that retains the chemical identity of that substance. From a microscopic point of view, a molecule is a particular group of atoms bound together in a given way. [CPM.1]
speed of light
The speed at which all electromagnetic radiation propagates. In a vacuum it is represented by the symbol c and has a value 3.00 × 1081m1s−1 (to three significant figures). In other media, the speed of light is less than c, and is often different for different frequencies of radiation, so giving rise to the phenomenon of dispersion. Einstein's special theory of relativity is based on the postulate that the speed of light (in a vacuum) has the same constant value in all inertial frames of reference; that is, it is not the speed relative to a fictitious ether, nor is it the speed with respect to the source of radiation. Causality in Einstein's theory relies on the fact that the speed of light in a vacuum is the maximum speed at which a signal can travel. [DFW.2;DFW.4]
terminal speed
The speed at which an object moving through a medium under the influence of an applied force, encounters a resistive force that is equal in magnitude to the applied force and therefore ceases to accelerate. The term is often used to refer specifically to the maximum speed that can be attained by an object falling freely through air, under the influence of gravityand aerodynamic drag alone. [PM.1]
rad
The standard abbreviation for radian. [DM.3]
quantum state
The state of a quantum system defined with sufficient precision that it may be associated with a unique wavefunction. In the case of a stationary state, described by a time-independent wavefunction, it may be possible to specify the state in terms a unique set of quantum numbers. (If the system is a particle with spin, such as an electron in an atom, the relevant spin magnetic quantum number must be included.) Note that a quantum state is distinct from an energy level, which may correspond to several quantum states, all of which have the same energy, but different wavefunctions. (Such an energy level is said to be degenerate.) [QPI.2]
ground state
The state that corresponds to the lowest discrete energy level of a quantum system. An example is the 1s state of the hydrogen atom. [QPI.1]
Carathéodory's statement of the second law of thermodynamics
The statement that; in the neighbourhood of any equilibrium state of a macroscopic system, there are states that are adiabatically inaccessible. [CPM.3]
Kelvin's statement of the second law of thermodynamics
The statement that; no cyclic process is possible which has, as its sole result, the complete conversion of a positive quantity of heat into work. [CPM.3]
Clausius's statement of the second law of thermodynamics
The statement that; no cyclic process is possible which has, as its sole result, the transfer of heat from a cooler body to a hotter one. [CPM.3]
Boltzmann's statement of the second law of thermodynamics
The statement that; the entropy of the Universe tends to a maximum. [CPM.3]
excited states
The states of a quantum system which have more energy than the ground state. In the context of an atom, the excited states correspond to energy levels of higher energy than the ground state energy level. [QPI.1]
Born interpretation
The suggestion, first explicitly advanced by Max Born, that in quantum mechanics the wavefunction of a particle determines the probability of finding the particle in a given region. For example, if the particle is confined to the x-axis and is described by the normalized time-independent wavefunction y0(x), then the probability of finding it in the small region between x and x + ∆x isP = |1y0(x)1|21∆x.Similarly, in three dimensions, the probability of finding the particle in a given small region of volume ∆V, centred on the point r, isP = |1y0(r)1|21∆V.In the context of de Broglie waves, Born's interpretation may be taken to imply that the probability of finding a particle in a given small region is proportional to the square of the amplitude of the particle's de Broglie wave in that region. This justifies the interpretation of de Broglie waves as probability waves. 4[QPI.4]
BCS theory
The theory by Bardeen, Cooper and Schrieffer which, in 1957, gave a quantum-mechanical explanation of superconductivity by considering the formation of Cooper pairs and the development of the superconducting energy gap at low temperature. [QPM.2]
special theory of relativity
The theory, proposed by Albert Einstein in 1905, that relates the observations made by different inertial observers who are in uniform relative motion. (This restriction to uniform relative motion is what accounts for the use of the term 'special' in the name of the theory.) The theory is based on Einstein's postulates, the first of which, the principle of relativity, asserts that the laws of physics can be written in the same form in all inertial frames of reference, while the second, the principle of the constancy of the speed of light, asserts that the speed of light (in a vacuum) has the same constant value in all inertial frames of reference. At the heart of the special theory of relativity are the Lorentz transformations, that relate the coordinates (x, y, z, t) of an event in a specified inertial frame, to the coordinates (x′, y′, z′, t′) of the same event in some other inertial frame. The consequences of this relationship include the effects referred to as Lorentz contraction and time dilation, as well as modified expressions for translational kinetic energy and linear momentum. It also gives rise to the idea of mass energy embodied in the most famous equation in all of physics, E = mc2. Maxwell's equations already obey Einstein's theory without the need for modification; electromagnetic induction by motion arises directly from the application of the Lorentz transformation to Maxwell's equations. The predictions of the special theory of relativity have been extensively supported by experiments performed to test their validity. [RU1; DFW.4]
general theory of relativity
The theory, published by Albert Einstein in 1916, that generalizes the ideas of his earlier special theory of relativity by extending them to non-inertial frames of reference. An important principle of the theory asserts that an accelerating frame of reference is locally equivalent to one that is located in a gravitational field. Consequently, the general theory of relativity is also a theory of gravitation, and as such supersedes Newton's theory of gravity. (The predictions 27of Newton's theory approximate those of general relativity in situations where the gravitational fields are weak.) According to general relativity, gravity manifests itself in the geometric structure (curvature) of spacetime. Mass and other sources of gravity determine that curvature, and moving bodies respond to that curvature, giving rise to the appearance of a 'gravitational force'. [RU.1, DFW.4]
penetration depth
The thickness of the surface layer of a superconductor within which the magnetic flux exclusion observed in the Meissner effect is incomplete. It is a persistent supercurrent flowing in this layer that creates the cancellation of the applied magnetic field.[QPM.2]
time constant
The time constant τ of an exponential decay process is the time taken for the decaying quantity to fall to 1/e of its value at any time. Such a process is described by a function of the form v = v0e−t0/τ. For a damped harmonic oscillator, of mass m, subject to a damping force that is proportional to velocity (Fx = −bvx), the time constant is τ = 2m/b. For an electrical circuit constructed from a capacitor of capacitance Cand a resistor of resistance R the time constant is τ = RC. [PM.2; SFP.3]
lifetime (against spontaneous emission)
The time constant τ that characterizes the spontaneous decay of an atom in a specified excited state. Decay to a lower energy level occurs in a random fashion and in such a way that that if there are N0 atoms in a given excited state at time t then the number remaining in that state at time t + τ will be, on average, N0/e. [QPI.3]
mean lifetime
The time constant τ that characterizes the spontaneous decay of particles that decay in a random fashion and in such a way that if there are N0particles in a given sample at time t then the number remaining in that sample at time t + τ will be, on average, N0/e. The mean lifetime is sometimes referred to as the lifetime, and is related to the half-life T1/2 of the particles by T1/2 = τ loge(2). [QPM.4]
exposure time (for photographic film)
The time for which photographic film is exposed to the incident light. It can be adjusted by setting the shutter-speed on the camera. The total exposure at some point in the film plane is then given by the product of the intensity at that point and the exposure time. [DFW.3]
half-life
The time required for half of a given sample to decay when the relevant decay is an exponential process. (See exponential process and mean lifetime for further details.) [QPM.3]
average value
The typical or representative value of a quantity that may, in principle, have any one of a range of values. The term average value may be taken to mean the predicted average value or the measured average value, depending on context. 4[CPM.2]
typical thermal energy of a particle
The typical translational kinetic energy of a molecule in a gas in thermal equilibrium at temperature T. It is approximately equal to kT, where k is Boltzmann's constant. [QPM.1]
predicted average value
The typical value of some quantity as predicted by multiplying each possible value of the quantity by its probability and then adding together the results. [CPM.2]
centripetal force
The unbalanced force (whatever its origin) required to keep a body in uniform circular motion about a fixed point. When a particle of mass mmoves around a circle of radius r with uniform angular speed ω (and therefore uniform speed v = rω), its acceleration is always directed towards the centre of the circle and has magnitude a = rω2 = v2/r. It follows from Newton's second law of motion that such a particle must be subject to an unbalanced force, directed towards the centre of the circle, with magnitude F = mrω2 = mv2/r; this is the centripetal force. 4[PM.1]
resonant frequency
The value of the driving (angular) frequency of a driven damped harmonic oscillator that creates the condition of resonance in which the amplitude is a maximum for a given level of damping. [PM.2]
stopping potential
The value of the retarding potential which just stops the flow of photoelectrons in an experiment to verify Einstein's theory of the photoelectric effect. [QPI.1]
intercept
The value on the vertical axis of a graph at which a plotted straight line crosses that axis, provided the vertical axis passes through the zero point on the horizontal axis. [DM.1]
resultant
The vector obtained by combining two or more other vectors using the operation of vector addition. For example, if s = s1 + s2 then s is the resultant of s1and s2. (See also triangle rule.) [DM.2]
magnetic field
The vector quantity B(r) that determines the magnetic force that would act on any charged particle as it moves through the point specified by the position vector r. It is defined by the requirement that the magnetic force Fm on a particle of charge q moving with velocity v as it passes through the point r is given by Fm = q[v × B(r)]
electric field
The vector quantity e(r) that determines the electrostatic force that would act on any chargedparticle placed at the point specified by the position vector r. It is defined as the electrostatic force per unit test charge, so if Fel is the electrostatic force on a particle of charge q at point r, then e(r) = Fel/q. The electric field has both magnitude and direction at each point in space, so it is an example of a vector field, and electric fields due to different sources add vectorially at every point. For an important example of an electric field see electric field due to a point charge. At any point, the electric field component in a given direction is equal to minus the gradient of the electric potential, V, in that direction. For example, the x-component and the radial component are given respectively by Ex = −dV/dx and Er = −dV/dr.The SI unit of electric field is N1C−1 or (equivalently) V1m−1. [SFP.1, SFP.2]
Kepler's laws
Three empirical laws, deduced by Johannes Kepler, that approximately describe the motion of the planets around the Sun. The laws state that;1 The orbit of each planet is an ellipse with the Sun at one focus.2 A radial line from the Sun to a planet sweeps out equal areas in equal intervals of time.3 The square of the orbital period of each planet is proportional to the cube of its semimajor axis.4Kepler's laws will hold for other planetary systems as well as the Sun's, but the constant of proportionality in the third law will differ from one system to another. [DM.3]
Kirchhoff's laws
Two laws, introduced by Gustav Kirchhoff, that describe the flow of steady direct currents in electrical circuits. The laws state that:1 The sum of the potential changes in a given sense around a circuit is zero. (In this sum, a potential drop is taken as negative and a potential rise as positive.)2 At a junction of two or more wires, the current flowing into the junction is equal to the current leaving the junction. [SFP.3]
