Modern Physics Chapter 3
Destructive Interference
- When the crest of the wave from one slit to arrive at a point on the screen simultaneously with the trough (valley) of the wave from the other slit. When this happens, the two waves cancel, giving a dark region on the screen - The existence of destructive interference at intensity minima immediately shows that we must add the electric field vectors E of the waves from the two slits, and not their powers P, because P can never be negative. - Destructive interference occurs whenever the distances X1 and X2 are such that the phase of one wave differs from the other by one-half cycle, or by one and one-half cycles, two and one-half cycles, and so forth: |X₁-X₂|=(n+½)λ
Diffraction Grating
- device for observing the interference of light waves - used to learn the different wavelengths or colors contained in a beam of light - usually consists of thousands of narrow, closely spaced parallel slits (or grooves) - wave fronts pass through a barrier that has many slits (often thousands or tens of thousands) and then recombine
Wave Number
- the number of wavelengths per unit distance (equivalently, the number of cycles per wavelength), where λ is the wavelength, sometimes termed the spectroscopic wavenumber vectorv=1/λ - the number of radians per unit distance, sometimes termed the angular wavenumber or circular wavenumber, but more often simply wavenumber k = 2π/λ
1. Celsius to Kelvin 2. Fahrenheit to Celsius
1. Celsius + 273.15 2. (Fahrenheit - 32) * 5 / 9
Classical Information of dependence of I on λ
1. The box is filled with electromagnetic standing waves 2. The number of standing waves with wavelengths between λ and λ + dλ is: N(λ) dλ = 8πV/λ⁴ dλ where V is the volume of the box. 3. Each individual wave contributes an average energy of kT to the radiation in the box.
Three Classical Wave THeory Predictions vs Experimental Results
1. The maximum kinetic energy of the electrons should be proportional to the intensity of the radiation. vectorF=vectorE*-e - Result: For a fixed value of the wavelength or frequency of the light source, the maximum kinetic energy of the emitted photoelectrons (determined from the stopping potential) is totally independent of the intensity of the light source. 2. The photoelectric effect should occur for light of any frequency or wavelength - Result: The photoelectric effect does not occur at all if the frequency of the light source is below a certain value. 3. The first electrons should be emitted in a time interval of the order of seconds after the radiation begins to strike the surface. - Result: The first photoelectrons are emitted virtually instantaneously (within 10−9s) after the light source is turned on. The wave theory predicts a measurable time delay, so this result also disagrees with the wave theory
Two Properties of Thermal Radiation
1. The total intensity radiated over all wavelengths (that is, the area under each curve) increases as the temperature is increased. I=σT⁴ 2. The wavelength λmax at which the emitted intensity reaches its maximum value decreases as the temperature is increased, in inverse proportion to the temperature: λmax inversely proportional to T λmaxT = 2.8978 × 10⁻³ m·K
5 Basic Properties of Photons
1. like an electromagnetic wave, photons move with the speed of light; 2. they have zero mass and rest energy; 3. they carry energy and momentum, which are related to the frequency and wavelength of the electromagnetic wave by E = hf and p = h/λ 4. they can be created or destroyed when radiation is emitted or absorbed; 5. they can have particle-like collisions with other particles such as electrons.
Quantum
1. the smallest quantity of radiant energy, equal to Planck's constant times the frequency of the associated radiation. 2. the fundamental unit of a quantized physical magnitude, as angular momentum.
Blackbody
A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
Ultraviolet Catastrophe
A blackbody is an idealized object which absorbs and emits all frequencies. Classical physics can be used to derive an equation which describes the intensity of blackbody radiation as a function of frequency for a fixed temperature--the result is known as the Rayleigh-Jeans law.
Rayleigh Jeans Formula
A classical law approximately describing the intensity of radiation emitted by a blackbody, derived by Rayleigh and Jeans by counting the number of standing wave modes in an enclosure. It corresponds to the Planck law in the case of small frequencies, in which case allows the approximation
Complex Wave Number
A complex-valued wavenumber can be defined for a medium with complex-valued permittivity ε, permeability μ0 and refraction index n as: k=k₀√(ε)=k₀n
Photon
A photon is an elementary particle, the quantum of all forms of electromagnetic radiation including light. It is the force carrier for electromagnetic force, even when static via virtual photons.
Plane Wave
A plane wave is a wave of constant frequency and amplitude with wavefronts that are an infinitely long straight line. Plane waves travel in the direction perpendicular to the wavefronts(a surface containing points affected in the same way by a wave at a given time.)
Positron
A positron is a particle that is identical in mass to the electron but has a positive electric charge
Radiometer
A radiometer is a device for measuring the intensity of thermal radiation at selected wavelengths, enabling a determination of temperature.
Angular Frequency
Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity. One revolution is equal to 2π radians ω=2π/T=2πƒ in rad/s T - Period f - frequency
Intensity and its General Property in Waves
Average power per unit area General Property of Waves: the intensity is proportional to the square of the amplitude
The diameter of an atomic nucleus is about 10 × 10⁻¹⁵ m. Suppose you wanted to study the diffraction of photons by nuclei. What energy of photons would you choose? Why?
Diffraction of light by the nucleus occurs only when the wavelength of the photon is smaller or of the order of the size of the nucleus, λ ~ D (D = diameter of the nucleus). Hence, the minimum energy of the photon would be E = hc/λ ~ hc/D ~ 120 MeV.
Energy Photon Equations
E=hƒ=hc/λ p=E/c → p=h/λ Kmax= hƒ − φ
Plane Electromagnetic Wave Equations
Electric Field vectorE=E₀sin(kz-ωt) Magnetic Field vectorB=B₀sin(kz-ωt)
Electric Field
Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge. E=F/q
I(λ)=
I(λ)=(2πhc²)/(λ⁵e^(hc/λkT)-1)
Radiant Intensity
I(λ)=(c/4)u(λ) u(λ) - energy density (energy per unit volume) per unit wavelength interval The quantity I(λ) dλ is the radiant intensity in the small interval dλ at the wavelength λ.
Total Intensity Emitted in Region
I(λ₁:λ₂)=∫ I(λ) dλ between λ₁ and λ₂ Total emitted set limits at 0 to ∞
Principle of Superposition
If two or more traveling waves are moving through a medium, the resultant value of the wave function at any point is the algebraic sum of the values of the wave functions of the individual waves.
Azimuthal
In land navigation, azimuth is usually denoted alpha, , and defined as a horizontal angle measured clockwise from a north base line or meridian. Azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line. ε₀=8.8541878176×10⁻¹² C/Vm [Coulombs per Volt-Meter]
Cutoff Frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced (attenuated or reflected) rather than passing through. ƒcutoff = φ/h →λcutoff=c/ƒcutoff=hc/φ The cutoff wavelength represents the largest wavelength for which the photoelectric effect can be observed for a surface with the work function φ.
Quanta
In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization".
Diffraction
It is defined as the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle. In classical physics, the diffraction phenomenon is described as the interference of waves according to the Huygens-Fresnel principle.
Power Entering Receiver
P=SA=(1/µ₀)E₀B₀Asin²(kz-ωt)=(1/µ₀c)E₀²Asin²(kz-ωt) S - Magnitude of Poynting vector A - Sensitive Area Perpendicular to Poynting Vector
Do photons carry momentum?
Photons carry linear momentum as well as energy, and thus they share this characteristic property of particles. Because a photon travels at the speed of light, it must have zero mass. Otherwiseits energy and momentum would be infinite. Similarly, a photon's rest energy E₀= mc² must also be zero.
Bragg's Peak
The Bragg peak is a pronounced peak on the Bragg curve which plots the energy loss of ionizing radiation during its travel through matter. For protons, α-rays, and other ion rays, the peak occurs immediately before the particles come to rest.
Compton Effect
The Compton effect (also called Compton scattering) is the result of a high-energy photon colliding with a target, which releases loosely bound electrons from the outer shell of the atom or molecule. The scattered radiation experiences a wavelength shift that cannot be explained in terms of classical wave theory, thus lending support to Einstein's photon theory.
Stefan-Boltzmann constant
The Stefan-Boltzmann constant (also Stefan's constant), a physical constant denoted by the Greek letter σ (sigma), is the constant of proportionality in the Stefan-Boltzmann law
Wave-particle Duality
The behaviors of the electron does not allow for it to be observable as a particle and as a wave. The two sided nature of the electron is known as the Wave-Particle Duality: The property of particles behaving as waves and the property of waves behaving as particles as well as waves.
Wave Mechanics
The branch of theoretical physics that mathematically represents subatomic particles as waves in fields, as in the theory of quantum electrodynamics.
Cutoff Wavelength
The cutoff wavelength represents the largest wavelength for which the photoelectric effect can be observed for a surface with the work function φ. ƒcutoff = φ/h →λcutoff=c/ƒcutoff=hc/φ
Single Photoelectron
The entire energy of the photon is delivered instantaneously to a single photoelectron.
Permeability of Free Space
The magnetic permeability determines a material's response to an applied magnetic field. The permeability in the Ampere- Maxwell law is that of free space (or ''vacuum permeability''), which is why it carries the subscript zero. µ₀=4π×10⁻⁷ Vs/Am [Volt-seconds per Amp-meter]
Permittivity of Free Space
The permittivity of a material determines its response to an applied electric field - in nonconducting materials (called ''insulators'' or ''dielectrics''), charges do not move freely, but may be slightly displaced from their equilibrium positions. The relevant permittivity in Gauss's law for electric fields is the permittivity of free space (or ''vacuum permittivity''), which is why it carries the subscript zero.
Photoelectric Effect
The photoelectric effect refers to the emission, or ejection, of electrons from the surface of, generally, a metal in response to incident light. Cannot be explained by light wave theory.
Stefan's Law
The principle that the energy radiated per second by unit area of a black body at thermodynamic temperature T is directly proportional to T⁴. The constant of proportionality is the Stefan constant, equal to 5.670400 × 10⁻⁸ Wm⁻² K⁻⁴ Also called Stefan-Boltzmann law.
Stopping Potential
The stopping potential is defined as the potential necessary to stop any electron (or, in other words, to stop even the electron with the most kinetic energy) from 'reaching the other side' - [Vs] is determined by increasing the magnitude of the voltage until the ammeter current drops to zero -Vs=Kmax/e[lectric charge of electron]
Thermal Radiation
Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero. It represents a conversion of thermal energy into electromagnetic energy.
Robert Millikan
United States physicist who isolated the electron and measured its charge (1868-1953). Won the 1923 Nobel Prize in physics for experiments on the photoelectric effect
Wave mechanics
a method of analysis of the behavior of atomic phenomena with particles represented by wave equations.
Laue Pattern
a photographic record of the diffraction pattern formed when a beam of X rays passes through a thin crystal plate
Nuclear Gamma Rays
a photon of penetrating electromagnetic radiation (gamma radiation) emitted from an atomic nucleus
Poynting Vector
a quantity describing the magnitude and direction of the flow of energy in electromagnetic waves. It is named after English physicist John Henry Poynting, who introduced it in 1884. vector S=(1/µ₀)(vector E × vector B) Plane wave: vector S = E₀B₀sin²(kz-ωt)* unit vector k
Photoelectrons
an electron emitted from an atom by interaction with a photon, especially an electron emitted from a solid surface by the action of light.
Dif. Grating Equation
d sin θ = nλ d - slit spacing n - order number (integer)
Back Scattering
deflect (radiation or particles) through an angle of 180°
Bremsstrahlung
electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the accelerated particles increases.
Planck's Constant
h = 6.6260696 × 10⁻³⁴ J · s fundamental physical constant characteristic of the mathematical formulations of quantum mechanics, which describes the behavior of particles and waves on the atomic scale, including the particle aspect of light.
Thermal Radiation
is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero. It represents a conversion of thermal energy into electromagnetic energy. Note: Most objects at room temperature emit radiation in the infrared region of the spectrum
Work Function(psi)
minimum quantity of energy needed to remove an electron -values are typically a few electron-volts (between 2 and 7)
According to Einstein, why is a photoelectron released
photoelectron is released as a result of an encounter with a single photon
Pair Production
process that can occur when photons encounter atoms in which the photon loses all its energy and in the process two particles are created: an electron and a positron.
Quantum Mechanics
the branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles, incorporating the concepts of quantization of energy, wave-particle duality, the uncertainty principle, and the correspondence principle.
Interference
the combination of two or more electromagnetic waveforms to form a resultant wave in which the displacement is either reinforced or canceled
Constructive Interference
the interference of two or more waves of equal frequency and phase, resulting in their mutual reinforcement and producing a single amplitude equal to the sum of the amplitudes of the individual waves.
Bragg's Law
the principle that when a beam of X-rays of wavelength λ enters a crystal, the maximum intensity of the reflected ray occurs when sin θ = nλ/2d, where θ is the complement of the angle of incidence, n is a whole number, and d is the distance between layers of atoms.
Electron-Positron Annihilation
the process that occurs when a subatomic particle collides with its respective antiparticle, such as an electron colliding with a positron. Energy and momentum are conserved, and the annihilated particles are replaced by photons, electromagnetic wave quanta with zero rest mass
Wien's Displacement Law
the wavelength of thermal radiation most copiously emitted by a blackbody is inversely proportional to the absolute temperature of the body
Two Failures of the Wave Theory
two of the failures of the wave theory: the existence of the cutoff frequency and the lack of any measurable time delay
Compton Wavelength of the Electron
λ'-λ=(h/mc)(1-cosθ)≅.002426nm
Relationship between Stefan's Law and the Stefan Boltzmann Constant
σ=(2π⁵k⁴)/(15c²h³)
hc = ?
≈1240 eV*nm
