The Interaction of Light With Matter

Question 1

The Photoelectric Effect

Hertz

Answer 1

noticed that more sparks were produced when UV light shone on his apperatus

Question 2

The Photoelectric Effect

Results and Classical Physics

Answer 2

• electrons were ejected without delay as light is uniformly distributed over the surface, a low intensity should eventually eject electrons (i.e. as a result of an accumulation of energy)
• the threshold should depend on intensity but actually depends on frequency
• the electron kinetic energy should also depend on intensity but instead is proportional to frequency

Question 3

The Photoelectric Effect

Einstein

Answer 3

-assumed that photons existed
-assumed that the energy of a photon E = hf
-

Question 4

The Photoelectric Effect

Answer 4

• when photoelectrons are released from the surface of a metal when light is shone on the metal
• in a circuit when light is shone on a plate, it can knock electrons free from the plate
• these electrons are attracted to the positive plate
• they flow around the circuit generating a current that can be measured

Question 5

The Photoelectric Effect

Energy Conservation

Answer 5

1/2 mv² = hf - Φ

where
1/2 mv² = KE of an electron
hf = photon energy
Φ = work function

Question 6

Work Function

Answer 6

the minimum photon energy required to release a photoelectron from the surface of a metal

Question 7

The Photoelectric Effect

Classical Time Lag

Answer 7

• the time between when the plate is first exposed to the radiation and the time when a photoelectron is released
• this is based on the classical assumption that the energy accumulates until it is great enough to release an electron
• in actuality, when the radiation is shone on the plate, an electron will either be emitted immediately or never

Question 8

The Compton Effect

Description

Answer 8

• monochromatic xray source
• pass through a collimator creating a parallel beam
• the radiation hits an electron
• the xray photon is scattered through an angle φ
• the scattered xray photon has less energy than the incident photon, the difference in energy is transferred to the electron

Question 9

The Compton Effect

Classical

Answer 9

• EM waves should scatter without a change in wavelength/frequency
• when electrons are accelerated by EM radiation they emit radiation at the same frequency as the exciting radiation

Question 10

Relativistic Energy Equation

Answer 10

E² = ρ²c² + m0²c^4

Question 11

Relativistic Energy of a Photon

Answer 11

E² = ρ²c² + m0²c^4
-but for a photon the rest mass is 0, so:
E² = ρ²c²
E = ρc

Question 12

The Compton Effect

Conservation of Momentum

Answer 12

the momentum of the incoming photon is equal to the momentum of the scattered photon added to the momentum of the electron

Question 13

The Compton Effect

Change in Wavelength Equation

Answer 13

λs - λi = h/m0c * (1-cosθ)

λs - scattered photon wavelength
λi - incident photon wavelength
m0 - electron rest mass
θ - scattering angle

Question 14

Compton Wavelength of a Particle

Answer 14

λc = h/mc

Question 15

The Compton Effect

When to use relativistic equations

Answer 15

-using conservation of energy, Ei = Ee + Es
the energy of the electron
Ee = Ei - Es
-compare Ee to m0c²
-if E is ~1% of m0c², then we need relativistic equation, i.e. if v ~15% of c

Question 16

The Compton Effect

Change in Wavelength and Compton Wavelength Equation

Answer 16

Δλ = λc* (1-cosθ)

Δλ = change in wavelength
λc = Compton wavelength of the particle
θ = scattering angle

Question 17

Inverse Compton Scattering

Answer 17

-it is possible for the scattered photon to have higher energy than the incident photon if the electron is initially moving and then slows down after the interaction

Question 18

The Bragg Law

Producing Xrays

Answer 18

• electrons are liberated from a filament
• electrons are accelerated through appro. 40-50keV towards a target e.g. Cu
• the electrons are high enough energy to knock core electrons from the Cu atoms
• when the atoms are neutralised again, a photon is emitted with an energy that depends on the transition
• typical transitions that give rise to x rays are Kα and Kβ

Question 19

The Bragg Law

Bremmsstrahlung

Answer 19

• ‘braking radiation’
• the name given to the continuous spectrum observed
• as the accelerated electrons approach the target metal, they experience a repulsive electromagnetic force from the free electrons within the metal
• this causes them to decelerate, and they emit radiation resulting in a broad continuous background
• there are two distinct peaks above this background corresponding to the Kα and Kβ transitions
• there is a minimum wavelength, a transition where the approaching electron loses all of its kinetic energy in one event

Question 20

The Bragg Law

Equation

Answer 20

2dsinθ = nλ

d = lattice spacing in the crystal
n = path difference
λ = wavelength
θ = 1/2 total scattering angle

Question 21

The Bragg Law

Explanation of Equation

Answer 21

2dsinθ = nλ

• when xrays pass through a crystal lattice, they are scattered
• peaks of scattered intensity are observed where the angle of incidence is equal to the angle of scattering, and the path difference is an integer number of wavelengths

Question 22

Pair Production

Definition

Answer 22

• high energy photons that lose all off their energy in a collision (i.e. with a nucleus)
• a pair of particles are created (most are an electron positron pair)

Question 23

Pair Production

Conservation of Energy

Answer 23

hf = Ee + Ep

= 2m0c² + KEe + KEp

Question 24

Pair Production

Minimum Energy Required

Answer 24

-for the production of an electron positron pair:
Emin = hfmin = 2m0c²
-this assumes that all the energy from the photon is transferred to the mass of the two particles and that the two particles have 0 kinetic energy