A level Physics Paper 3
Determining g: Errors
- Air resistance acting on the card will cause acceleration to be less than g - Reaction time will affect t
Why are fusion conditions hard to maintain?
- Any contact with the container results in a decrease of temperature
Investigating Momentum: Errors
- Assuming string is inextensible so acceleration of mass hanger is the same as that of the trolley
Investigating Standing Waves: Method
- Attach one end of the string to a vibration generator - Place the other end over a pulley and attach a mass hanger - Change the masses on the mass hanger (and therefore the tension in the string) - Then change the frequency until a standing wave is formed -Measure the wavelengths at these frequencies
Determining wavelength of light: Safety
- Avoid shining lasers in people's eyes
What does the Maxwell-Boltzmann distributuion curve look like?
- Goes through the origin as no molecules have zero energy - Only a few molecules have high energy - There is no maximum energy that a molecule can have
Determining wavelength of light: Errors
- If slit width is big then pattern won't spread out as much
Wavefront
*A line joining points at the same position along a wave*
What is a radioactive atom?
*A radioactive atom has an unstable nucleus which emits aloha, beta or gamma radiation.*
What are electric fields?
*A region where a charged particle experiences a force*
Real Image
*An image that: -Can be projected onto a screen -Is on the other side of the lens as the object*
Virtual Image
*An image that: -Can't be projected onto a screen -Is on the same side of the lens as the object*
Yield Point
*Beyond this point the material suddenly undergoes a large increase in extension (it 'gives') as the atomic substructure is rearranged*
What does it mean for a material to be ductile?
*Can be drawn out into wires as it undergoes a lot of plastic deformation*
Longitudinal Waves
*Direction of oscillation is parallel to the direction of propagation of the wave* A longitudinal wave is composed of areas of compression (high pressure) and rarefaction (low pressure) caused by particles oscillating backwards and forwards
Transverse Waves
*Direction of oscillation is perpendicular to the direction of propagation of the wave* Transverse waves are composed of particles that make up the wave oscilating up and down
What is the binding energy?
*Energy released when the nucleus is formed from individual nucleons. It is the energy associated with the strong force.*
What does it mean for a material to have a high tensile stress?
*It can withstand a large force under tension before breaking*
What does it mean for a material to be stiff?
*It has a large young modulus and so can withstand a large load with just a small extension*
What does it mean for a material to be hard?
*It is resistant to indentation or scratching*
What is meant by nuclear decay being spontaneous?
*It means that the decay cannot be influenced by any external factors*
What is meant by nuclear decay being random?
*It means that we can't know which nucleus will decay next as each nucleus has a fixed probability of decay*
Plastic Deformation
*Permanent deformation caused by strain when stress exceeds a certain value. The material won't return to it's original shape.*
Elastic Deformation
*Region where the material will return to its original shape when the stress is removed*
What does it mean for a material to be brittle?
*Shatters under a sudden force as it cracks with little or no plastic deformation just beyond the elastic limit due to the propagation of the cracks*
Critical Angle
*The angle for which the angle of refraction is 90* If the angle of incidence is larger than the critical angle, total internal reflection occurs sinC = 1/n
Refraction
*The change in direction of a wave when it passes from one medium into another with a different optical density* This is caused by a change in the speed of the wave
Diffraction
*The change in direction of a wave when it passes through a gap of similar size to it's wavelength*
What is the mass deficit?
*The difference in mass between a nucleus and the total mass of the nucleons. The total mass of the nucleons is greater than the mass of the nucleus.*
Wavelength
*The displacement between a point on a wave and the identical point on the next wave*
Amplitude
*The maximum displacement from the mean position*
Threshold frequency
*The minimum frequency required for a photon to have enough energy to free an electron on the surface of a metal*
Frequency
*The number of complete oscillations in one second* f = 1/T v = fλ
Elastic Limit
*The point beyond which the material is permanently deformed, it won't return to it's original shape*
Limit of Proportionality
*The point until which force and extension (or stress and strain) are directly proportional. After this point it may behave elastically, but they will no longer be proportional*
Momentum & Newton's 2nd Law
*The rate of change of momentum of a body is directly proportional to the resultant force applied to the body, and is in the same direction as the force* This is because: F=ma and a=(v-u)/t F=m(v-u)/t F=dp/dt -> this is the rate of change of momentum. This is the mathematical way of writing a rate of change but we can write the average change of small timescales as Δp/Δt
Period
*The time taken for one complete oscillation*
Breaking stress
*The value of stress in a material when it breaks*
Coherance
*Waves which have are of the same frequency, wavelength, polarisation and in a constant phase relationship*
Plane Polarisation
*When the oscillations of a transverse wave all occur in one plane* Light is partially plane polarised when it reflects off a flat surface
Path Difference
*the difference in distance from each source to a particular point* If wave source is coherent can be used with the phase of the waves to see how the waves will interfere. Path difference of a whole number of wavelengths gives complete constructive interference, path difference with an extra half a wavelength gives complete destructive interference
Superposition
*when two or more waves of the same type meet at a point the resultant displacement of will be the sum of the individual displacements*
How can we produce electron beams?
- The photoelectric effect - Thermionic emission
Determining Young Modulus: Errors
- There may be significant creep (plastic deformation) at higher masses as the metal stops behaving elastically -
How do linear accelerators use electric fields?
- There's a maximum potential difference that can be achieved. - To get around this tubes of increasing lengths are used with an AC supply that alternates when the particle is half way through to accelerate the particle. - The frequency of the AC supply remains constant, so as the particle accelerates the tubes keep getting longer because they need to spend the same amount of time in each tube
How can we reduce the amount of oscillations in a system?
- We can put systems in place that dampen the oscillations - ductile materials can undergo plastic deformation which provides critical damping.
Determining Young Modulus: Safety
- Wear safety spectacles because the wire is under tension and so could snap - Take care when adding masses as if they fall on someone's feet that would hurt
Determining viscosity: Method
- Weigh 3 balls of different sizes and measure their diameters in 3 different places - Zero a scale with the 250 cm³ measuring cylinder on it, then fill it with washing up liquid to the 200 cm³ mark and measure the mass in order to calculate density - Place 3 rubber bands along the cylinder so that the balls will be moving at terminal velocity by the time that it reaches the band - The other two rubber bands should be far apart enough that a reasonable time interval can be measured - Measure the distances between the rubber bands - Using a stopwatch measure the time taken for each ball to pass the rubber bands - Use this to calculate the terminal velocities - Repeat 3 times
Hydrometer
A hydrometer is an instrument for measuring the density of liquids. The inner (solid) part of the hydrometer has a constant mass and so in different liquids it will float to different extents
Validity Definition
A measurement is valid if it measures what it is supposed to be measuring
Accuracy Definition
A measurement result is considered accurate if it is judged to be close to the true value. It is a quality denoting the closeness of agreement between measurements and true value.
What is a moderator in a nuclear reactor?
A moderator (usually water or graphite) is in the reactor to slow down the neutrons before they reach the next fuel rod so that they are slow enough to be absorbed.
What is a perfect black body radiator?
A perfect black body radiator will give off energy across the entire electromagnetic spectrum, as is shown in the previous graph. We assume that stars act as perfect black body radiators.
What is a magnetic field?
A region of space where a magnetic pole feels a force
What is a gravitational field?
A region where a mass experiences a force
Resolving vectors
A single diagonal vector can also be broken down into it's horizontal and vertical components. The principle is the same as when finding resultant vectors.
Interference
A special kind of superposition where the waves are coherant
Standing Wave
A standing wave is formed when a wave and it's reflection superpose to form areas of complete destructive interference (nodes) and complete constructive interference (anti nodes) One standing wave was 2 ovals in it. The fundamental frequency has oval in it
What is the Equation for discharging a capacitor
Again, you can replace with Q with V or I and the equation still holds.
Newton's First Law
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
What is a black body radiator?
An object that is considered to be a perfect absorber an therefore emitter of EM radiation. As such it emits EM radiation of all wavelengths.
Viscosity: Fluids
As temperature increases, viscosity decreases (as intermolecular forces decrease)
Viscosity: Gas
As temperature increases, viscosity increases (as greater kinetic energy means more collisions between particles thus more friction)
de Broglie equation
Based on the fact that if a wave has a particle nature, particles have a wave nature. This is linked to their momentum by λ=h/p This is why when a beam of electrons are passed through graphene (very thin gaps in it) you can see diffraction patterns.
What is Capacitance?
C=Q/V it is the amount of charge a capacitor ca store per one volt. it is measured in Farrads (F)
How can we calculate the energy needed to remove one nucleon from the nucleus?
Calculate the binding energy per nucleon. This can be used as a measure of how strongly different nuclei are held together.
What are Capacitors and how do they work?
Capacitors have two metal plates in them (these tend to be large thin sheets than are rolled to make it more compact) with an insulator called a dielectric between them. The dielectric can also be found between layers where the metal is rolled. This is to avoid charge from jumping across. When the circuit is on, electrons move from one half of the capacitor through the circuit to the other half. As such, a potential difference is created across the capacitor. At this point the capacitor is said to be fully charged.
Compressive stress/strain
Causes the length of the material to decrease, the forces act towards the center
Tensile stress/strain
Causes the length of the material to increase, the forces act away from the center
What is centripetal force?
Centripetal force is the resultant force required to produce and maintain circular motion.
What are cepheid variables?
Cepheid variables are stars whose luminosity changes with a fixed period.
Why are cepheid variables useful?
Cepheid variables close enough to use trigonometric parallax to calculate their distance and therefore their intrinsic luminosity can be observed for data about their period. This lead to a period luminosity relationship being established. Therefore, by observing the period of a cepheid variable that is too far away to use trig parallax, we can calculate its luminosity and therefore its distance.
Photoelectric effect
Certain kind of lights can charge the gold leaf as they give the metal on the top enough energy for it's outer electrons to escape. Later a photoelectric cell (with a vacuum) was created to show the same effect. This depends on the frequency of the light though, not the amplitude (intensity) which cannot be explained with the wave theory of light.
How was the neutron discovered?
Chadwick performed a series of experiments in which alpha particles hitting beryllium caused it to give off an unknown radiation. Chadwick discovered that it was a new particle called a neutron.
What are control rods?
Control rods are rods made of cadmium or boron and absorb excess neutrons, thus slowing down the reaction. If there is a failure in the control rods system gravity pulls them completely down and the reaction stops.
Convex lense
Converge parallel rays of light at the focal length away from the lens
What was Dalton's Model?
Dalton found that atoms can be distinguished by their masses and can be combined to produce compound molecules.
What is damping?
Damping is the material or system causing energy loss during damped oscillations.
What is dark energy and why do we think it exists?
Data shows that the expansion of the universe is actually accelerating rather than slowing down. The reason for this expansion is unknown but has been called dark energy.
Density
Density = Mass/volume
Kinetic energy of a photoelectron
Depending on the metal, each electron needs a specific amount of energy to escape, this is called it's work function. The rest of the photons energy is converted to kinetic energy. hf =φ+ mv(max)²
How to particle detectors work?
Detectors can detect charged particles as they ionise
What does a black body radiation curve look like?
Different stars will have different peak wavelengths, depending on their temperature.
Diffraction grating and equation
Diffraction gratings have lot's of slits through which the light diffracts and then forms diffraction patterns. It follows the equation: n λ = d sin θ you have to be able to derive this equation where: n = the order of the maxima (central one is 0 then 1 etc) λ = wavelength d = spacing between slits (found by 1/(number of slits per m) θ = angle between normal and direction of the bright spot
Focal length
Distance between the lens and focal point
Concave lense
Diverge parallel rays appear to have come from a virtual focus, a focal length behind the lens
Adding vectors
Draw both vectors next to each other head to tail and then use Pythagoras and/or trig to calculate the missing side of the triangle and the angle. Remember, in order to draw these correctly, you'll probably have to move one of the vectors.
Upthrust
Due to Archemides' principle, upthrust is equal to the the weight of the fluid displaced. This can be found if you know the density of the fluid and the volume of the object
Current in circuits
Due to the CONSERVATION OF CHARGE current is the same in series but splits in parallel.
Potential Difference in circuits
Due to the CONSERVATION OF ENERGY potential difference is split in series but the same in parallel
How do you calculate radial electric field strength?
E=Q/4πεr² where ε is the permittivity of free space (therefore this only works in a vacuum, but air is considered to be close enough) This can be derrived from E=F/Q and coulombs law
How can you calculate the strength of a uniform electric field?
E=V/d
How can we combine the equations for kinetic energy and momentum?
Ek=½mv² and v=p/m so when we combine both of these we get: Ek=p²/2m
How do electron probes work?
Electron beams are fired at the material being researched and the resulting diffraction pattern can be used to explore the molecular structure.
Atomic absorption spectra
Electrons of an atom can absorb photons from a light source and momentarily be exited. However, they can only absorb certain frequencies due to the discrete energy levels. This means that light coming from the stars for example have black lines in the spectra where elements have absorbed the photons of those frequencies. this is how scientists know what stars are made of.
How can we calculate the force due to gravity
F = (Gm₁m₂)/r² Where G is the gravitational constant 6.67 x 10⁻¹¹
How can you calculate force in an electric field?
F= Eq
Stokes Law
F = 6πηrv Only works for -Small cylindrical objects -Travelling at small velocities -Where there is laminar flow
How can we derrive the equation for a charged particle in a magnetic field?
F=Bqv The force is at a right angle to the motion so F=mv²/r Bqv=mv²/r r=mv/Bq or r = p/Bq
Newton's Second Law
F=ma
How can we measure the strength of the force from the motor effect?
F = BIL sinθ Where F is the force, B is the magnetic flux density, I is the current moving through the wire and θ is the angle that the current makes with the magnetic field lines.
How can we calculate the force acting on a charged particle in a magnetic field?
F = Bev sinθ Where F is the force, B is the magnetic flux density, e is the charge of the particle, v is the velocity of the particle and θ is the angle between the velocity and the magnetic field lines.
What is Coulomb's Law?
F = kQ₁Q₂/r² where k is a constant k=1/4πε
How can we derive the equation for the gravitational field strength of a mass?
F = m₁g F = (Gm₁m₂)/r² so m₁g = (Gm₁m₂)/r² g=Gm/r²
Principle of moments
For an object that is in equilibrium: - the sum of the clockwise moments = the sum of the anticlockwise moments - There is no resultant force.
Newton's Third Law
For every action there is an equal and opposite reaction
How does gamma ray emission work?
Gamma radiation doesn't alter the structure of the nucleus but as it carries away energy so the energy of the nucleus must drop. Therefore it often occurs after alpha or beta decay because they leave the nucleus in an exited state. Gamma rays are emitted by the de-excitation of the nucleus in the same way as light is emitted when electrons return to their ground state.
What are hadrons?
Hadrons are heavy particles that are affected by the strong force and aren't fundamental.
What are hadrons made of?
Hadrons consist of quarks, which are fundamental particles. The six quarks exist in symmetrical pairs, up and down, top and bottom and charm and strange. The symmetry of the model predicted the top quark, which was later discovered.
What is Hubble's Law?
Hubble found out that a galaxies red shift is proportional to it's distance - further away galaxies move away faster. This means that the universe is expanding. v = H₀d where H₀ is Hubble's constant
What is the life cycle of a low mass star?
Hydrogen gas in space is gathered by gravity to form a protostar. The force of gravity becomes so strong that the star starts to fuse hydrogen. The star becomes a main sequence star and the inward force of gravity is balanced by the outward force of vibrating particles and EM radiation trying to escape. A star of similar mass to our sun will eventually run out of hydrogen to fuse, so it will start to contract due to gravity. This enables the star to fuse helium and so it expands into a red giant and outer layers drift off to form a planetary nebula. A low mass star will run out of helium to fuse and so will contract again, but it cannot get hot enough to fuse anything above helium. The core is left as a white dwarf, which will eventually cool to create a black dwarf.
Floating
If an object is floating, then the weight of the fluid displaced = the weight of the object
What is the open option?
If matter is sparse in the universe, then it will keep expanding until everything is so far apart that it freezes.
How can the creation of particles occur?
If there is enough energy, such as a gamma ray photon, then that energy can be converted into mass using E=mc². The matter produced will always be a matter antimatter pair and the energy of the photon has to be equal to at least the resting energies of both particles.
Work done at angles
In order to find out work done, you need to resolve the forces to find the component of a force that is acting in the direction of motion.
Semiconductors
In solids the outer energy levels form energy bands. There is a valency band where the electrons normally reside and a conduction band where they can move and carry charge. In metals the valency and conduction band overlap. In semi conductors, if enough energy is applied (such as temperature in thermistors or light in an LDR) the electrons can jump the energy gap from the valency band to the conduction band, and thus carry charge. In an insulator the energy gap is too big, the material is destroyed before there is enough energy for the electrons to move to the conduction band.
Velocity
Is a vector and therefore has both direction and magnitude. =displacement / time
What are leptons?
Leptons are light particles that aren't affected by the strong force, and are fundamental.
Measuring the refractive index of a solid
Measure the corresponding angle of refraction for 5 separate angle of incidences then plot a graph of sin i (on the y axis) vs sin r. The gradient will give you the refractive index of the medium
Determining EMF and r: Errors
Measurements from electric circuits like this don't usually need to be repeated as there are few random errors and judgments to make. Therefore more than 6 values should be measured so that anomalies can be spotted better.
What can hadrons be split into?
Mesons and Baryons
Current-potential difference graphs
Need to be able to sketch them for: -Filament bulbs -Thermistors -Resistors -Diodes
Terminal velocity
Need to know how to explain this as well
What does accuracy depend on?
It cannot be quantified and is influenced by by random and systematic errors
What does precision depend on?
It is influenced only by random effects and can be expressed numerically by measures such as standard deviation.
Investigating Standing Waves: Safety
Keep feet away from under the mass hanger and slotted masses in case they fall
What does this graph tell us?
Nuclei smaller than iron can be combined to have larger binding energies per nulceon (fusion). Larger nuclei can break apart to have greater binding energy per nucleon (fission).
What is the Stefan-Boltzmann law?
L=σAT⁴ L = luminosity σ = Stefan-Boltzmann constant A = Area T = Temperature The distribution of a black body radiator is given by the Stefan-Boltzmann law. For a sphere this is L=4πr²σT⁴
Photoelectric effect: particle theory
One photon collides with one electron on the SURFACE and gives the electron its energy. If the photon has enough energy (this depends on the frequency) then a photoelectron is emitted, therefore this is instantaneous. Einstein proposed the particle theory of light in 1905.
Uses of optical fibres
Optical fibres are used to transmit information (e.g. cables for telephones or the internet) It can carry a lot more information across a longer distance for a smaller cost than previously used copper cables
What is a free oscillation?
Oscillation that happens when a system performs oscillations free from the influence of any outside forces
Investigating stress
See through plastic structures can be investigated for stress by placing a polarising filter on either side. The first one provides polarised light. As light travels slower through areas with stress, it then interferes with other light of the same wavelength at the next polarising filter. The resulting colours can be used to analyse the stress
How do we calculate a root mean square value?
Square the values, find the mean of the squares and then root the mean. This gives an average speed that is a bit larger than the actual mean value.
What are the 5 stages of fusion?
Stage 1 - Two protons fuse Stage 2 - One proton turns into a neutron (deuterium nucleus) Stage 3 - Another proton joins (He-3 nucleus) Stage 4 - Two He-3 nuclei fuse Stage 5 - Two protons break off leaving an He-4 nucleus
What data can we receive from stars?
Stars are so far away from us that the only data that we have about them is the radiation we receive from them and we can measure this wavelength and intensity.
Stress Strain Graphs for Different Materials
Stiffer materials have a steeper gradient. Stronger materials have a large breaking stress Brittle materials have a very small plastic regions
Young Modulus
Stress/Strain
What is Bohr's Model?
The GCSE model, positive nucleus orbited by negative electrons in different quantum shells.
What is the Hertzsprung-Russel diagram?
The Hertzprung-Russel diagram is the result of the luminosity of stars compared to the sun plotted against temperature. The y-axis is a log scale going from 10-⁶ to 10⁶. The x-axis is a reverse log scale, halving in even increments (Look at the graph).
What is the Hubble constant?
The Hubble constant is difficult to determine as astronomical distances are hard to measure accurately. The currently accepted value is 70.9
How can we determine the age of the universe?
The Hubble constant tells us how fast the universe is expanding, so if we calculate backwards we can find the time that the universe was all one point just before the big bang. The uncertainty in this age (between 10 bn and 20 bn years) comes from our uncertainty in H₀.
What does the graph of binding energy per nucleon against mass number look like? Where is the peak?
The Peak is at Iron-56
What is specific latent heat?
The amount of energy required to change the state of a substance when it is at a constant temperature depends on the specific latent heat constant L. ∆E=mL
What is specific heat capacity?
The amount of energy required to heat 1 kg of a substance by 1 K
Potential difference
The amount of work done per unit of charge
What is a parallax angle?
The angle subtended at the star by the radius of the earths orbit.
Charge of an electron
The charge of an electron is 1.6 x 10-¹⁹ This can also be used to calculate the charge of an ion
What is the decay constant?
The decay constant is the fixed probability that a radioactive nucleus will decay in any given second. Its symbol is λ
Error Definition
The difference between the measurement result and the true value if a true value is thought to exist. This is not a mistake in the measurement.
What does Lenz's Law state?
The direction of an induced e.m.f. is such that it opposes the change creating it. This is due to the conservation of energy, as if the e.m.f. would be in the same direction as the change, you would have created energy. Lenz's Law is where the negative sign in Farraday's equation comes from.
What do the charging and discharging graphs of capacitors look like?
The discharging graphs look the same when you replace charge with voltage or current.
How does thermionic emission work?
The electrons gain enough thermal energy to leave the surface of the metal. This means that it needs to be heated up to very high temperatures.
What is gravitational potential energy?
The energy possessed by an object by virtue of where it is in a gravitational field
gravitational potential energy
The energy that an object has by virtue of it's position in a gravitational field. = mgh
What is a molecules potential energy?
The energy that it has by virtue of its position in a structure or relation to other molecules.
What is the nuclear decay equation and from what is it derived?
The equation dN/dt = -λN can be integrated to give us N=N₀e^(-λt) This can also be written as A=A₀e^(-λt)
How can you draw radial electric fields?
The equipotentials are circles that are closer together at the centre than the outside. If you put two opposite point charges next to each other, the lines will join and flow from positive to negative. If you put two same point charges next to each other, the lines will bend away from each other.
Where do errors come from?
The error can be due to both systematic and random effects and an error of unknown size is a source of uncertainty.
What is the flat option?
The expansion force and gravity could potentially form an equilibrium and the universe could stop expanding and stay constant.
What is magnetic flux?
The field lines of a magnetic field. They always act from north to south. The quantity of flux φ is measured in webers (Wb)
What is a driving frequency?
The frequency of an external force applied to a system undergoing forced oscillations
What is natural frequency?
The frequency of oscillation that a system will take if it undergoes free oscillations
How does the Kelvin scale of temperature work?
The gaps in the scale are identical to those in the Celsius scale, but the scale starts at absolute zero. Therefore converting degrees Celsius to Kelvin requires adding 273
What is a half life and what is its formula?
The half-life of a substance is the time taken for the activity of a sample to halve. If you substitute t1/2 into the nuclear radiation equation you can derive the equation t1/2 = (ln2)/λ which proves that the half-life is constant.
Uncertainty Definition
The interval within which the true value can be considered to lie with a given level of confidence or probability.
What happened as a result of the alpha particle scattering experiment?
The model of the nucleus was revised to have a positive nucleus and a lot of empty space.
What is simple harmonic motion?
The motion of an oscillating object. it has a restoring force that tries to return the object to an equilibrium position, that is proportional to the distance from the equilibrium position. F=-kx The negative sign is there as acceleration is always to the centre of the oscillation
What is the motor effect and which hand rule do we use for it?
The motor effect is when a wire with a current going through it is placed in a magnetic field it experiences a force. We use flemming's left hand rule: Thumb = Motion First Finger = Field Second Finger = Current
Significant figures
The number of SF used in recording the measurements depends on the resolution of the measuring instruments and should usually be the same as is given in the instrument with the fewest SF in its reading.
What is activity?
The number of radioactive nuclei that decay per second in a given sample. A = dN/dt = -λN
Focal Point
The point where rays incident on the lens and parallel to the principal axis will be made to meet by the refraction of the lens
How can uncertainty be found?
This can be estimated by considering the instruments and the methods and will be expressed as a range. The confidence will be qualitative and based on the goodness of the line of best fit and the size of the percentage uncertainty.
What does validity depend on?
This depends on both the method and the instruments
What do we use this equation for?
This equation is often used in particle physics, where an elastic collision between a known particle and an unknown particle can help us to identify what the unknown particle is.
What was Thompson's Model?
Thompson discovered electrons to be smaller particles that are in atoms. He came up with the plum pudding model that electrons are small negative charges embedded in a positive "dough".
Polarisation
Transverse waves can be polarised as they can all travel in different planes but still perpendicular to the propagation of the wave. Longitudinal waves can't be polarised as they only travel in one plane already
What are the dangers of nuclear radiation?
When nuclear radiation ionises molecules in your DNA, it can lead to mutations, which can make the cell cancerous. Alpha particles aren't dangerous outside of your body because they are stopped by a layer of dead skin cells, however, it is very dangerous if ingested as alpha particles are so ionising. Gamma radiation pose minimal danger both inside and outside of your body, but constant long term exposure does result in the danger of cancer. Beta particles are moderately ionising and therefore moderately dangerous and as such exposure should be limited.
What is Charles' law?
Volume of a gas is proportional to its absolute temperature Constants: -Mass -Pressure V₁/T₁ = V₂/T₂
Photoelectric effect: wave theory
Wave theory would state that the intensity of the light would have more energy and so be able to free electrons, but this is not the case. Wave theory also says that energy can build up, but the release of electrons is immediate as soon as the right frequency is met
Photon model of a wave
Waves are made of discrete packets of energy called photons. The energy of the photons depends on their frequency through the equation E=hf where h is plack's constant
Why do we want to accelerate particles?
We accelerate particle to high speeds to collide them so that we can discover new information about them.
How can we measure the distance to a standard candle?
We can measure the intensity of a star above our atmosphere, and so using the intensity equation I = P/A we can create the equation: I = L/4πd² As the luminosity of the star is known, we can calculate the distance to it.
How can we measure the temperature of a star?
We can measure the wavelength of peak intensity that comes from the star. As this wavelength is directly related to the temperature we can calculate the temperature using Wien's Law.
How can we measure radiation and what are the units?
We can use a Geiger-Mueller counter to measure radiation. This is reported as counts per second with the unit becquerel (Bq)
How else can we calculate the luminosity of a star?
We can use the peak wavelength and Wien's law to calculate the temperature of a star. We can also use spectral lines to determine whether it is a main sequence star. If it is, we can use it's temperature and the H-R diagram to find its luminosity.
How can we create a cathode ray?
We can use thermionic emission to release electrons and then accelerate them in an electric field.
How can we draw a straight line graph for the discharge of a capacitor?
We can write the equation for discharge as: lnV=lnV₀-t/RC Therefore, if you plot lnV against time, you get a gradient that is -1/RC and a y intercept of lnV₀
How do we classify stars?
We classified stars based on their temperature, as stars that have a similar temperature tend to share a lot of other properties as well. These categories are O B A F G K M O h B e A F ine G uy K iss M e
How can we calculate binding energy?
When E is in Joules and m is in kg: ∆E=∆mc² When E is in MeV and m is in u E = 931.5m
What is electron positron pair production?
When a pair of electrons and positrons are created from energy. They will always travel in directions that conserve momentum.
Ohm's law
When a resistor follows ohms law current is directly proportional to the potential difference.
What is forced oscillations?
When a system oscillates under the influence of an external (usually repeatedly applied) force
Why does electromagnetic induction work?
When a wire is moved through a magnetic field, the electrons in it experience a force making them move through the wire. This creates an e.m.f..
Transfer of energy
When an object falls, gravitational potential energy is converted into kinetic energy. This happens as energy must be conserved. For this specific conversion, you don't even need to know the mass of the object as mgh=½mv² and therefore the Ms cancel out, leaving you with gh=½v² In this conversion you assume that air resistance can be ignored
How can we detect electron rays?
When electron rays hit a screen that is covered with a specific chemical, it will flouresce (emit light)
Atomic emission spectra
When electrons in an atom gain energy (through heating or a current being passed through them) they are momentarily exited and move to a higher energy level. When they almost instantaneously return to their ground state, they emit this excess energy as a photon. Depending on the amount of energy the electron has this photon will have a different frequency which can correspond to a point in the visible light spectrum. As energy levels are discrete, individual elements will only produce certain frequencies of protons.
projectile motion
When objects are thrown up into the air or kicked off a cliff or something similar, they move in a curved line. By separating the horizontal and vertical components of this motion we can calculate distances, times and velocities etc. The vertical component just goes straight up and down and has acceleration due to gravity.
Polarising filters
When polarising filters are places in the same orientation, there is no difference (because the second one let's through all of the light that the first one let through) but when they are at 90 degrees to each other, no light is let through.
Why is the time constant RC important?
When the a time equal to the time constant (RC) elapses, the charge decreases by a factor of 1/e (therefore to roughly 37%)
When does an object have a maximum amplitude?
When the driving frequency matches the frequency of the natural frequency
What is flux linkage?
When we are dealing with a coil of wire rather than with a single wire, so we measure the amount of flux interacting with a coil of wire and call it flux linkage. Flux linkage is Nφ and Nφ = BAN
Why does fusion work?
When we combine smaller nuclei the mass of the new nucleus is less than the mass of the constituent parts. This excess mass is converted into energy. The excess energy can be used as power.
Centre of gravity
The point where the entire weight of an object appears to act. This is essentially the same thing as the centre of mass This always lies along the line of symmetry. for a flat irregular object hang it from different points and draw a line straight down. Where the lines connect that's the centre of mass, because it will always hang directly under a point of suspension. For other irregular objects it can be found using moments.
Phase
The position of a point on a wave at a specific moment in time
Electromotive force
The potential difference of the entire circuit (therefore the cell)
Repeatability Definition
The precision obtained when measurement results are obtained by a single operator using a single method over a short timescale. A measurement is repeatable when similar results are obtained by students from the same group using the same method. Students can use the precision of their data to judge this.
Reproducibility Definition
The precision obtained when measurement results are obtained by different operators using different pieces of apparatus. A measurement is reproducible when similar results are obtained by students from different groups using a different method and different apparatus
What happens to nuclear radiation once it has been emitted?
The radiation particle will leave the nucleus with a set amount of kinetic energy. As it travels through the air it ionises particles in its path and loses KE in that process until it has no KE left and is absorbed by the substance where it stopped.
What is luminosity?
The rate at which energy of all types is radiated by an object in all directions.
Current
The rate of flow of charged particles. found by I=Q/t
Viscosity
The resistance of a fluid to flowing
Resolution Definition
The smallest measuring interval and the source of uncertainty in a single reading.
What is internal energy?
The sum of the kinetic and potential energies of molecules in a substance.
How does the synchatron work?
The synchatron has an AC supply that has a constantly changing frequency and a changing magnetic field. This means that the particle can accelerate in a single circle rather than in a spiral.
Structure of optical fibres
There is also a cladding surrounding it with a lower refractive index, to decrease the critical angle and protect the optical fibre from damage
What was the problem with the mass of nuclei and a model with no neutrons?
There was a difference between nuclear mass and the number of protons known to be in an atom. Rutherford proposed that proton electron pairs in the nucleus made up the remaining mass.
What are electric field lines?
These are lines drawn to visualise the forces caused by this field. The arrows show conventional charge movement from positive to negative. The closer the field lines are together the stronger the field is.
How do linear accelerators accelerate particles?
They accelerate particles in a straight line using electric fields. They are built in one straight line.
What happens when a particle and its anti-particle meet?
They annihilate and produce the equivalent amount of energy (as photons). These also conserve momentum and so they'll travel off in opposite directions.
How can you tell what the charge of a particle is from its track?
You can use Fleming's left hand rule, the direction of the motion of the particle and the magnetic field to calculate the direction of current. If current is in the same direction that the particle is moving then the charge is positive. If it curves in the other direction it is negative. A particle with no charge won't leave a track
How do we produce alternating current?
You have a coil of wire that you are continually turning inside a magnetic field due to a turbine turning. As the wire is moving in an electric field a current is produced. However, as the motion of the wire compared to the magnetic field keeps changing, so does that direction of the e.m.f. so you produce an alternating current.
How can we take account of background radiation in our calculations?
You have to subtract the background count rate from the measured count
Young's experiment
Young proved the wave nature of light by having sunlight shine through one slit (yo make it coherent) and then put it through two slits to show diffraction patterns. As only waves diffract, light must be a wave.
How can you calculate the frequency of a cyclatron and what does it depend on?
f=1/T T=2π/w T=2πr/v r=mv/Bq T=2πmv/Bqv T=2πm/Bq So the frequency only depends on the charge and mass of the particle and the strength of the electric field, it doesn't depend on the radius.
Work done
force × distance moved in the direction of the force It is measured in Joules. This is the same as energy transferred
How can we calculate the gravitational field strength g?
g = F/m This field strength is what we used to call acceleration due to gravity.
How can we calculate the energy stored in a capacitor?
is equal to the area under a charge vs p.d. graph. E=½QV This is different from our previous equation of E=QV as this equation assumes that charge and voltage are constant, but in our capacitor we start with a charge and voltage of 0 and gradually build up.
Kinetic energy
the energy an object has by virtue of its movement = ½mv²
How can you calculate field strength?
the force felt by a charged particle per unit of charge, E=F/Q
How can we derive the equations of displacement, velocity and acceleration for an object in SMH?
x = rcosθ but as θ = ωt x = rcosωt We can differentiate to find the other equations: v = -rωsinωt a = -rω²cosωt ∴ a = -ω²x where r = amplitude
How does a charged particle act in a magnetic field?
A charged particle will feel a force acting perpendicularly to it's motion (current) when it moves in a magnetic field due to the motor effect. This results in the circular motion of the particle, perpendicularly to the direction of the magnetic field.
How can we get charged particles to move in a circle?
A charges particle moving in a magnetic field will move in a circle.
What is an elastic collisions?
A collision where both kinetic energy and momentum is conserved.
What is an inelastic collision?
A collision where only momentum is conserved, kinetic energy isn't.
What is red shift?
Red shift is the fractional increase in wavelength received by an observer, due to the source receding from the observer.
What does red shift tell us and what is z?
Red shift tells us that galaxies are moving away from us. The amount of red shift, z, tells us how quickly it is moving away. z = ∆λ/λ = ∆f/f = v/c
Diffraction patterns
There is a central maxima in the middle (where the light is the most intense) and then a pattern of minima (dark areas) and smaller maxima. These patterns are created because light rays moving at different angles interfere with each other. Where this interference is destructive at the screen, you have a minima. Where it is constructive, there is a maxima. Double slit diffraction occurs the same way. When this is done with coloured light, violet is to the central side of each maxima and red light on the other side
Momentum
p=mv (momentum is the product of mass and velocity)
What are the two versions of the gas law?
pV=NkT pV=nRT
Equation for speed of a transverse wave on a string
V = √T/µ
How do you calculate potential in a radial field?
V=Q/4πεr (watch out, this r isn't squared)
How can we calculate gravitational potential energy?
Vgrav = -Gm/r
Displacement time graph
upward slope - constant positive velocity flat line - stationary downward slope - negative constant velocity It can often be easier to just draw a distance-time graph.
What is the quark constitution of a proton?
uud
How can we find instantaneous velocity using angular velocity?
v = rω
What is resonance?
when very large amplitude oscillations occur because the driving frequency matches the natural frequency of a system
Calibrating a Thermistor: Safety
- Boiling water is hot so don't touch beaker when its hot - Don't exceed voltage limit of thermistor - Keep leads away from hot things as plastic covering could melt - Support thermistor so it doesn't cause the beaker to tip over
Determining speed of sound: Improvements
- Change timebase so only one wave is shown to reduce uncertainties - Find frequency from oscilloscope as this bypasses uncertainties in the signal generator
Determining g: Method
- Clamp a ruler so that it stands vertically above a table - Attach a light gate underneath the ruler at the zero point - Attach the light gate to a data logger to measure velocity - Drop a dowel from a certain height and use a stopwatch to time the time taken for it to fall from the height to the light gate - Repeat 3 times and then repeat for heights of 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 cm
Determining Resistivity: Errors
- Crocodile clip may not be directly in contact with the wire - Crocodile clip may have a poor connection to the wire, e.g. if its dirty the measured resistance will be higher. - If the wire becomes hot resistivity will change as it is constant for a certain temperature
Determining speed of sound: Safety
- Don't make the sound too loud to protect ear drums
Determining g: Improvements
- Dowel may not take a vertical route so blue tack the bottom to give it more stability - Use larger distances to increase t in order to reduce uncertainties
What happens when particles try to move the speed of light?
- Einstein said that nothing can move faster than the speed of light. - Bertozzi proved that at very high speeds, particles' mass will increase rather their speed, thus still increasing KE. - E=mc²
What are the problems with fusion?
- Forcing two positively charged particles together requires very high temperatures - There has to be a very high density of protons for it to work
Why would fusion be such a good source of energy?
- Fusing hydrogen to make helium releases a lot of energy - It could use hydrogen from water in the sea. - The only by product would be helium which is an inert gas that can be let into the atmosphere.
Calibrating a Thermistor: Improvements
- Heat slowly as it allows the semiconductor time to adjust - Read temperature from thermometer at eye level to avoid parallax error - Check meter for zero error by connecting a lead across the terminals - Use small current and switch off circuit between readings so that there isn't an additional heating effect
Determining viscosity: Errors
- High uncertainties due to human reaction times - If ball falls close to wall flow won't be laminar - If velocity for second reading is higher terminal velocity hasn't been reached
Determining Specific Latent Heat: Improvements
- Ice must be crushed so it cools the water quickly so less heat is transferred to surroundings
Calibrating a Thermistor: Errors
- If fixed resistors resistance is too high V out may not vary enough - If it is too small it may vary across a bigger range than the voltmeter can handle - Simultaneous readings of two variables can lead to systematic errors
How can we derive the equation pV=¹/₃ mN<c²>
- Imagine a particle inside square box of size L - Consider the particle having a velocity in the x direction Ux - When it collides and rebounds the change of momentum will be -2mUx because the collision was elastic - As force is rate of change of momentum F = (2mUx)/t - v = s/t and s=2L (as the particle moves the lengths of the box, collides and then moves back again) - ∴ t = s/v = 2L/Ux - ∴ (m(Ux)²)/L - p = F/A = (m(Ux)²)/L³ - To find the overall pressure we have to find the force exerted by all of the gas particles - Total pressure = sum of the pressure of all of the particles - p = m/L³ * ((U₁x)²+ (U₂x)² + (UNx)² - ∴ p = (mN<Ux²>)/L³ - As we have only considered velocity in the x direction, it only accounts for ¹/₃ of the overall pressure - p = (¹/₃ mN<c²>)/L³ - ∴ pV=¹/₃ mN<c²>
What are advantages of using nuclear power?
- It's an alternative (but still non-renewable) energy source to fossil fuels - It can produce a lot of power from relatively little uranium
Investigating Momentum: Safety
- Keep feet away from under falling masses and trolleys
Determining EMF and r: Improvements
- Keep temperature constant by disconnecting the circuit between readings - Check for zero errors on ammeter and voltmeter
Determining viscosity: Improvements
- Keep temperature same as it may affect viscosity - Ensure timing the same part of the ball (e.g. always the bottom) - Larger distances between the bands reduces uncertainties
Analysing Collisions: Method
- Measure masses and diameters of spheres - Set up digital camera to record collisions - Collide one sphere with another at varying angles - Use "tracker" to measure the velocities - Multiply by mass to find momentum and show that momentum was conserved
Determining Young Modulus: Method
- Measure the diameter of a piece of copper wire in 3 different places and calculate the mean - Place one end of wire between two wooden blocks and clamp these blocks onto the table - Place the other end of the wire over a pulley at the end of the table - Tie a loop in the end of the wire and attach a mass hanger - Place a metre ruler underneath the wire - Put two sticky labels on the wire as markers - Measure the extension of the wire for every new mass that you add
Determining Specific Latent Heat: Safety
- Melted ice may drip on floor and be a slipping hazard, ensure there is a beaker there to catch it
What are the assumptions of an ideal gas?
- Molecules have negligible size - Molecules are identical - All collisions are perfectly elastic and time of collisions is significantly smaller than the time between collisions - Molecules exert no forces on each other except during collisions - Are enough molecules that statistics can be applied - The motion of the molecules is random
Determining Resistivity: Method
- Place a piece of wire along a metre ruler and sellotape it in place - Place the crocodile clip at the zero point of the ruler - Place the lead at 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 cm and measure the resistance at these different lengths using an ohmmeter - Repeat these measurements 3 times - Measure the diameter of the wire in 3 different places and find the mean
Determining Specific Latent Heat: Method
- Place ice in a funnel and allow it to reach zero - Determine mass of empty dry beaker - Add 100 cm³ of water to the beaker and measure the new mass - Measure temperature of water - Add roughly 20 cm³ of ice at 0 C and stir it into the water - Measure the lowest temperature that this mixture reaches - Determine the final mass
Determining wavelength of light: Method
- Place laser 4m away from blank wall with a diffraction grating in front of it - Measure the distance between the diffraction grating and the wall - Turn on laser and identify the zero order maximum (straight ahead) - Measure the distance between it and the two first order maxima and take a mean of the readings - Repeat for increasing orders - Repeat with different diffraction gratings
Determining wavelength of light: Improvements
- Place laser far enough away to get a good spread of dots
How can you calculate acceleration in an electric field?
as F=EQ and F=ma, ma=EQ a=EQ/m
Determining speed of sound: Method
- Set the oscilloscope to show two traces, one from the loudspeaker and the other the signal received from the microphone - Place microphone next to oscilloscope and place the speaker about 50 cm away - Adjust the spacing on the screen and the distance of the speaker until the tough of one wave touches the peak of the other wave, the waves are antiphase - Measure this distance - Move speaker back until the waves are antiphase again - Measure the new distance - Difference in distances is one wavelength - Keep repeating this
Determining EMF and r: Method
- Set up a cell next to a small resistor and treat the whole thing as you cell (as actual r often too small to measure) - Place voltmeter parallel to 'cell' - Place an ammeter and variable resistor in series - Vary the resistance and measure the voltage an current
Investigating Momentum: Method
- Set up a trolley with a card on it on a tilted ramp - Attach a string to the trolley and put it over a pulley at the end of the table - Attach a mass hanger onto the end of the string - Place the mass hanger on the floor and pull the trolley back until the string is tight. Place a light gate at this position and have it measure velocity - Pull the trolley back until the mass hanger touches the pulley - Blue tack 5 10g masses onto the trolley so that they are secure - Record the hanging mass m - Release the trolley and using a stopwatch measure the time taken for the trolley to reach the light gate - Move one mass from the trolley to the slotted hanger and repeat. continue until all masses have been moved. - Measure the distance from the starting position to the light gate - Measure the mass of the entire system - Theory suggests that mgT = Mv so plot a graph with gradient M/g which should be a constant
Calibrating a Thermistor: Method
- Set up circuit with power source, fixed resistor, waterproof thermistor and voltmeter - Set up a bunsen burner, tripod, gauze, beaker with ice, stirring rod and thermometer to 0.5 C - Measure the resistance for temperature in 2-5 C intervals from 1 to 100 C - Use potential divider circuit to calculate resistance in thermistor - Plot a calibration curve of resistance against temperature
Determining viscosity: Safety
- Spilled washing liquid is extremely slippery and any spills should immediately be cleaned
Investigating Momentum: Improvements
- Tilt ramp to compensate for friction
Investigating Standing Waves: Errors
- Uncertainty at node measurements when measuring the wavelength due to blur
What are the disadvantages of nuclear power?
- Uranium reserves are found predominantly in 3 countries, thus affecting supply - Uranium is a finite resource - Hazards are extreme, Chernobyl and Fukushima - Very large commissioning and decommissioning costs - Produces a lot of dangerous radioactive waste
Determining Young Modulus: Improvements
- Use a large distance between your markers to reduce uncertainty in extension measurements - Use a wire thick enough to give a range of readings - Use smaller masses for more precise readings - Use a set square to avoid parallax errors in measurements
Determining Resistivity: Improvements
- Use an ohmmeter rather than a voltmeter and ammeter with a power supply as it reduces uncertainty - Avoid pressing hard on the wire as you could deform it - Ensure that the wire is straight (sellotape it on) so that the length measurements are accurate
Investigating Capacitors: Safety
- Use low voltages to avoid capacitor blowing
Investigating Standing Waves: Improvements
- Use small masses so that the frequencies needed remain low
Investigating Capacitors: Improvement
- Using a larger resistor will slow down the discharge making the percentage uncertainties in time measurements smaller
Determining EMF and r: Safety
- Variable resistor may get hot so disconnect between readings - Don't pull out leads from the wires as this breaks the connection inside the lead
What was the alpha particle scattering experiment?
-Alpha particles where aimed at extremely thin gold foil to detect where the alpha radiation would come out
What is the exchange boson for the strong nuclear force?
-Boson: Gluon -Symbol: g -Charge: 0
What is the exchange boson for gravity?
-Boson: Graviton Properties are undetermined as they haven't actually been discovered yet
What is the exchange boson for the electromagnetic force?
-Boson: Photon -Symbol: γ -Charge: 0
What is the exchange boson for the weak nuclear force?
-Boson: W or Z boson -Symbol: Z, W⁺,W⁻ -Charge: 0,+1,-1
Explaining resistance due to particles
-Cation lattices vibrate more as temperature increases -Leads to more collisions with delocalised electrons -Therefore harder for electrons to pass through -So greater resistance
Beta Particles
-Composed of a high-speed electron -Moderately ionising as it is smaller and doesn't have as large a charge -Beta particles move several meters through air and can be stopped by a thin sheet of aluminium
Alpha Particles
-Composed of two protons and two neutrons -Highly ionising as it has a large positive charge and is a large particle -Alpha particles move a few centimeters through air and can be blocked by skin or a sheet of paper as they lose KE quickly because they are so ionising
Determining Resistivity: Safety
-Disconnect wires between readings as the wire may get hot -Small voltages and current so little danger of shock
What are some similarities between electric fields and gravitational fields?
-Equation for force F = (Gm₁m₂)/r² F = (kQ₁Q₂)/r² -Equation for field strength g = Gm/r² g = kQ/r² -Equation for potential Vgrav = -Gm/r V = kQ/r
What happens to the speed, frequency and wavelength during refraction?
-Frequency stays the same -Speed increases -Wavelength increases
What are some differences between electric fields and gravitational fields?
-Gravitational fields are always attractive -The electromagnetic force is a lot stronger -Charged particles can be shielded from electric fields
What are the four fundamental forces?
-Gravity -Strong Nuclear Force -Weak Nuclear Force -Electromagnetic
Gamma Decay
-High energy, high frequency, electromagnetic radiation -Not very ionising as the photons have no mass or charge and as such rarely interact with other particles -They can never be completely absorbed their energy can be significantly reduced by several metres of concrete or cms of lead
What about conservation of strangeness?
-If strangeness is conserved it is strong interaction -If strangeness isn't conserved it is a weak interaction
What factors would increase the centripetal force?
-If the rotating object has a larger mass -if the object rotates faster -If the object is further from the centre of the circle.
Image formed outside 2F
-Inverted -Diminished -Real
Image formed between 2F and F
-Inverted -Magnified -Real
Image formed at 2F
-Inverted -Same size -Real
Laminar flow
-Layers are parallel to each other (don't mix) -No abrupt changes in direction -Fluid has a small velocity
Turbulent flow
-Layers mix -Fluids move at a high velocity -Abrupt changes in speed and direction -Eddies
What are applications of the motor effect?
-Mass spectrometers -Cyclotrons
What must be conserved in particle reactions?
-Mass/energy -Charge -Baryon Number -Lepton Number
What where the results of the alpha particle scattering experiment?
-Most particles went straight through, as expected -Some particles were diverted by quite large angles -Very few even repelled back
What is special about conserving lepton numbers?
-Muons, taons and electrons all have their different types of leptons that must be conserved in a reaction.
Pulses
-Pulses have a short duration so that you can differentiate between the pulse and the echo.
Image formed between F and lens
-Right way up -Magnified -Virtual
What factors affect capacitance?
-Size of plate -Size of separation -Nature of insulator
Why do scientists think that dark matter exists?
-Stars in galaxies all rotate at the same speed, regardless of their distance from the centre (which is very different from our solar system). The stars in galaxies experience a centripetal force but the mass of all of the stars only accounts for 10% of the necessary force, so scientists think that there must be more mass that doesn't emit light. Things like black holes or interstellar gases are contenders for some of this mass, but there are too few of them to account for the majority of dark matter. -Large masses deform space-time and so accelerates things. When this affects light coming from galaxies behind it we can detect it as gravitational lensing. This is another evidence for dark matter. as we can see its affect on light from galaxies.
Determining g: Safety
-Take care that falling objects don't fall on feet -Use clamps to secure metre ruler so it doesn't topple
What are 3 of the possible fates of the universe?
-The closed option (the big crunch) -The open option (the big freeze) -The flat option
Optical fibres problems
-The waves undergo material dispersion as they are moving at different speeds. To reduce this, an infrared laser is used that emits waves with a very narrow range of wavelengths -The wave can also undergo modal (multipath) dispersion as different light rays can take different paths through the fibre. To reduce this monomode fibres with an extremely small core is used
How does a cyclatron work?
-There are two D shaped electrodes (called dees) in a magneic field with a small gap between them. -The magnetic field makes the charged particle move in a circle -The electrons are accelerated across the gap between the dees by an alternating voltage with a constant frequency -Therefore the particle keeps spiraling and accelerating until it leaves the cyclatron
How do nuclear reactors produce energy?
-They use uranium-235 -The uranium absorbs a slow moving neutron (thermal neutron) -This produces two smaller, radioactive nuclei and some neutrons that continue the chain reactions
Terminal velocity equation derivation
-Weight = upthrust + stokes law -m(s)g = weight of fluid displaced + 6πηrv(t) -W(s) = 4/3 x π r^3 p(f) g + 6πηrv(t) 4/3 x π r^3 p(s) g = 4/3 x π r^3 p(f) g + 6πηrv(t) Rearranged to make V(t) the subject and simplified you get: v(t) = (2r^2 x g (p(s)-p(f)))/9η
Fundamental rules in circuits
-conservation of charge -conservation of energy
Resistance in parallel
1/R=1/R₁+1/R₂+1/R₃ This is because: R=V/I 1/R=I/V 1/R=(I₁+I₂)/V 1/R=I₁/V₁ + I₂/V₂ Therefore: 1/R=1/R₁+1/R₂
Lens Equation
1/u + 1/v = 1/f u = Object distance v = Image distance f = focal length
Where does background radiation come from?
50% comes from radon gas in the atmosphere, the rest comes from: -Cosmic rays -Food and drink -Medical -Ground and buildings The radon gas comes from the decay of uranium in rocks, specifically granite, so there are higher concentrations of it in different places.
Power
= energy transferred/time taken Measured in Watts
Accelaration
=(v-u)/t Where v is initial velocity and u is final velocity
Speed
=distance / time
Efficiency
=useful energy out/total energy in =useful power output/total power input
What was Rutherford's Model?
A positive nucleus with electrons orbiting it and a lot of empty space.
Precision Definition
A quality denoting the closeness of agreement (consistency) between values obtained by repeated measurements. A measurement is precise if the values cluster closely together
What is a photon?
A quantum packet of electromagnetic radiation
What is the life cycle of a massive star?
A star larger than the sun will start off as a protostar and main sequence star as well. However, once the star contracts after running out of helium to fuse, a large star gets hot enough to fuse carbon and it forms a red supergiant that goes through cycles of collapsing and then expanding as it fuses new elements up until iron as iron cannot be fused to release energy. As the star collapses under the massive force of gravity, electrons collapse into protons to form neutrons. This means that the core is very hard and made of neutrons, so it is called a neutron star. The envelope of the star bounce off the rigid core and form a type II supernova. This explosion can create elements larger than iron. If the star is exceptionally large, it will collapse further to produce a black hole rather than a neutron star.
What determines a stars colour?
A stars temperature will determine its peak intensity wavelength, which will determine its colour.
What is a standard candle?
A stellar object of known luminosity
What is a critically damped system?
A system that occurs when damping is such that the oscillator returns to equilibrium position as fast as possible without going past that point.
What is absolute zero?
Absolute 0 is 0 on the Kelvin scale of temperature. It is the point when the particles have no more kinetic energy and as such cannot be reached.
Where does uncertainty come from?
Any measurements will have some uncertainty about the result, this will come from variation in the data obtained and be subject to systematic or random effects.
How does trigonometric parallax work?
As the earth orbits around the sun, closer stars seem to move across the background of more distant stars. We know that in six months the earth will have completed half of its orbit and will therefore be 2 AU away from its original position. Using background stars, we can measure the angle between the star and the earth. These measurements enable us to use trigonometry to calculate the distance to the star. As the angle is so small, we tend to use arc seconds. A parsec is the distance a star must be from the sun for the angle to be 1 arc second.
Potential difference along a uniform wire
As the wire becomes longer, the resistance increases and the current remains constant, therefore the potential difference increases
What are root-mean-square values?
As we need to be able to compare AC to DC, we try to find a way to measure the total power that AC current supplies. To do this, we square the values (so that it's all positive) find the mean of that and then root our answer. To find the RMS value from a peak value, divide it by root 2
internal resistance
Every cell has a very small internal resistance. This means that it uses some of the emf, so the terminal potential difference that reaches the circuit isn't actually the EMF because there are some "lost volts" due to the current across the cell and the internal resistance.
What is electric potential?
Every charged particle has electric potential energy per unit of charge by virtue of it's position in the field. V=E/Q
What does Farraday's Law state?
Farraday's Law states that the e.m.f. induced is proportional to the rate of change of flux linkage. Therefore: ε= -d(BAN)/dt If B A or N are constants, you can pull them out to the front. At A-level you just use changes in rather than differentiating.
What is the process of fission?
Fission can be triggered when a nucleus absorbs another particle (usually a neutron) which makes it unstable
Analysing Collisions: Errors
Friction cannot be accounted for
What is the closed option?
Gravity could possibly slow down expansion and cause the universe to contract back into one point again, and the universe would continually pulsate. Whether or not this will happen depends on the density of matter. If the matter in the universe has a mass greater than a critical mass the universe will contract.
What was the Greeks theory of atoms?
Greeks believed that every known material could be broken down until it was indivisible and then what was left was called an atom. This model was solid.
How is energy conserved in a pendulum in a closed system?
Green line is total energy which remains constant. Red line is GPE which has a maximum value at the outsides but is 0 at the equilibrium position. Blue line is KE, which is O at the top of the swing but has its maximum value at the equilibrium position.
What was Milikan's oil drop experiment?
He determined the charge of a single electron, less than 1% away from the value that we know it to be today. -He squirted oil droplets into a container. -These oil droplets got an electrostatic charge through friction. This was an unknown multiple of the charge of an electron -He had a uniform field that acted upwards and gravity pulled the droplets downwards. -He changed the strength of the field until the droplets were suspended (as well as many other variations of the same experiment)
How do the properties of stars change with their temperature?
Hotter stars tend to have a larger mass, are larger and are more luminous as the large gravitational pressure at the centre makes fusion go very fast.
What forms between two charged plates?
If we have two plates of opposite charges we create an electric field between them with parallel and equally spaced field lines. This produces a uniform electric field.
Superconductivity
If you cool a metal enough, it has 0 resistance and is called a superconductor. This is used when the current used is so large that the heat produced would melt the equipment or waste too much energy.
What is impulse?
Impulse is the change in momentum Impulse (Ns) = Force (N) x time (s) ∆p=Fx∆t
Conservation of linear momentum
In a closed system the sum of total momentum before a collision/explosion is the same as the sum of total momentum after the collision/explosion.
Why does fission work?
In fission a large nucleus splits to form smaller nuclei which have a greater binding energy per nucleon and therefore a larger mass deficit. Therefore, like in fusion, energy is released
Intensity of waves
Intensity is inversely proportional to the amplitude squared. I = P/A (where A = area and P = power)
What is dark matter?
Inter stellar mass that doesn't emit light.
What are some common astronomical units?
Light year = 10¹⁶ m AU (Astronomical unit) = 1.5 x 10¹¹ m Parsec =
What is magnetic flux density?
Magnetic flux density, B, is another way of refering to the magnetic field strength. Its unit is the tesla (T)
Magnification Formula
Magnification = Image size/Object size or: m = v/u
What is nuclear decay and why does it happen?
Many nuclei are slightly unstable so there is a probability, each second, that they will decay. This means that a nucleon may change into another or the energy state of the whole nucleus may change.
Momentum and newtons third law
Momentum is responsible for Newtons third law. As momentum in a closed system (in this case a very big system such as our whole earth etc.) must be conserved, if a force increases momentum in one direction there must be another force increasing it in the other direction, therefore there is always an equal and opposite force.
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Resistance in negative temperature coefficient thermistors
Normally resistance increases as temperature increases, however in negative temperature coefficient thermistors it decreases as although the heat adds extra resistance it also moves more electrons into the conduction band and so as there are more electrons available to carry charge resistance decreases.
Power
P=IV This can be used with V=IR to derive the equations: P=I²R and P=V²/R
Investigating Capacitors: Method
Part 1: - Set up a capacitor parallel to a cell and resistor of known resistance with a switch so that the capacitor is either in series with the resistor or the cell - Use oscilloscope to measure the emf of the cell - Move switch to capacitor charges and record this p.d. as V₀ - Flip switch so it discharges and using the lap function on a stopwatch measure the time taken for it to drop to 5V, 4V, 3.5V, 3V, 2.5V, 2V, 1.75V, 1.5V, 1.25V Part 2: - Set the power supply unit (PSU) to provide an AC current - Attach the oscilloscope parallel to resistor so it measures the pd across it - Sketch the graph of the oscilloscope - Repeat with different resistors
In the standard model, what are the two main categories of particles?
Particles can be split into leptons and hadrons.
Where does the linac get its particles from?
Particles like electrons can be produced by thermionic emission or something like a Van de Graaff generator.
What are exchange bosons?
Particles that are constantly exchanged between particles to produce the four forces.
What are baryons?
Particles that are made of 3 quarks
What are mesons?
Particles that are made of a quark and anti quark pair. (Such as a pion or kaon)
Potential divider circuits
Potential difference in multiple parallel circuits splits in proportion to the resistance in each circuit. Therefore you can calculate the way that the potential difference will split
Power of a Lens
Power (d) = 1/F For thin lenses in combination, the total power is found by adding the separate powers
What is Boyle's law?
Pressure exerted by a gas is indirectlu proportional to its volume. Constants: -Temperature -Mass p₁V₁=p₂V₂
What is the pressure law?
Pressure of a gas is proportional to its absolute temperature Constants: -Mass -Volume p₁/T₁ = p₂/T₂
Resistance in series
R=R₁+R₂+R₃ This is because: R=V/I R=(V₁+V₂)/I R=V₁/I₁ + V₂/I₂ Therefore: R=R₁+R₂
Resistivity
R=ρl/A is used to find resistivity (ρ) as resistivity is constant for length and area (but changes with temperature) and so is more useful.
What are radians?
Radians are a unit for measuring angles, θ=s (length of arc)/r (radius)
Snell's Law
Refraction follows snell's law: n1 x sinθ1 = n2 x sinθ2 where n represents the refractive index of teh medium, and θ the angle with the normal
Refractive index
Refractive index (n) is given by: n=c/v where v is the speed of light in the medium.
Resistance
Resistance is found by V=IR
How can we find out the speed of a particle from its track?
Slower moving particles are more ionising and so have thicker tracks
What are the two equations to calculate the period of oscillating objects?
T = 2π√(m/k) T = 2π√(l/g)
How can we plot a straight line graph of decay?
Take logs of both sides and rearrange it into the equation into a y=mx+c equation
What does luminosity depend on?
Temperature and size
What does the kinetic theory say?
Temperature is the kinetic energy of the particles that make an object
What are equipotentials?
The locations in an electric field that all have the same potential can be connected by dotted lines called equipotentials. These are used like contour lines on a map, how close equipotential lines are show how rapidly electric potential is shifitng.
What is background radiation?
The low-level radiation that we always experience from the environment
What happens to this mass deficit?
The mass deficit is converted into binding energy that holds the nucleus together.
What is the peak value of AC electricity?
The maximum value that AC current can have. This can be either the maximum voltage or the maximum current.
Drift velocity
The mean velocity of electrons moving in a conductor found using I = nqvA
True Value Definition
The value that would have been obtained in an ideal measurement - with the exception of fundamental constants, true values are considered unknowable
What is angular displacement?
The vector measurement of an angle through which something has moved.
How can we calculate centripetal acceleration?
a = rω² a = v²/r You need to know this derivation, it's in the text book page 24
Acceleration-time graph
a graph describing motion of an object, with acceleration on the vertical axis and time on the horizontal axis. upward slope - increasing acceleration flat line - constant acceleration downward slope - decreasing acceleration
electron volt
one electron volt is1.6 x 10-¹⁹ Joules.
What are damped oscillations?
oscillations that occur when there is a loss of energy which reduces the amplitude over time
Kinematics
s = displacement u = initial velocity v = final velocity a = acceleration t = time. All of the equations apart from s = (u+v)/2 xt are given in the formula book. Just use them.
Moments
the turning, movement of a force. =force x perpendicular distance from the pivot.
What is u?
u is the approximate mass of one nucleon. u=1.66x10⁻²⁷
What is the quark constitution of a neutron?
udd
How is the average kinetic energy of a molecule linked to the temperature?
½mv² = ³/₂ kT where k is the Boltzmann constant.
Strain
ε=∆x/x where x is the original length of the material and ∆x is the extension
What is Wien's Law?
λmaxT = 2.898 x 10-³ 2.898 x 10-³ is Wien's constant.
Stress
σ=F/A where F is force and A is cross sectional area
How can we calculate magnetic flux density?
φ=B x sinθ x A Where A is the area and θ is the angle between the plane and the flux lines.
What is angular velocity?
ω = θ/t ω = 2π/T ω = angular velocity θ = angular displacement t = time T = time period
Elastic Strain Energy
∆E(el) = F∆x As this is the area under a force extension graph.
How can we calculate the energy required to heat a substance?
∆E=mc∆θ - θ is temperature - c is specific heat capacity
Hooke's Law
∆F = k∆x where k is the stiffness of the object