The Interaction of Light With Matter Flashcards
The Photoelectric Effect
Hertz
noticed that more sparks were produced when UV light shone on his apperatus
The Photoelectric Effect
Results and Classical Physics
- 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
The Photoelectric Effect
Einstein
-assumed that photons existed
-assumed that the energy of a photon E = hf
-
The Photoelectric Effect
- 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
The Photoelectric Effect
Energy Conservation
1/2 mv² = hf - Φ
where
1/2 mv² = KE of an electron
hf = photon energy
Φ = work function
Work Function
the minimum photon energy required to release a photoelectron from the surface of a metal
The Photoelectric Effect
Classical Time Lag
- 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
The Compton Effect
Description
- 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
The Compton Effect
Classical
- 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
Relativistic Energy Equation
E² = ρ²c² + m0²c^4
Relativistic Energy of a Photon
E² = ρ²c² + m0²c^4
-but for a photon the rest mass is 0, so:
E² = ρ²c²
E = ρc
The Compton Effect
Conservation of Momentum
the momentum of the incoming photon is equal to the momentum of the scattered photon added to the momentum of the electron
The Compton Effect
Change in Wavelength Equation
λs - λi = h/m0c * (1-cosθ)
λs - scattered photon wavelength
λi - incident photon wavelength
m0 - electron rest mass
θ - scattering angle
Compton Wavelength of a Particle
λc = h/mc
The Compton Effect
When to use relativistic equations
-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
The Compton Effect
Change in Wavelength and Compton Wavelength Equation
Δλ = λc* (1-cosθ)
Δλ = change in wavelength λc = Compton wavelength of the particle θ = scattering angle
Inverse Compton Scattering
-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
The Bragg Law
Producing Xrays
- 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
The Bragg Law
Bremmsstrahlung
- ‘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
The Bragg Law
Equation
2dsinθ = nλ
d = lattice spacing in the crystal n = path difference λ = wavelength θ = 1/2 total scattering angle
The Bragg Law
Explanation of Equation
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
Pair Production
Definition
- 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)
Pair Production
Conservation of Energy
hf = Ee + Ep
= 2m0c² + KEe + KEp
Pair Production
Minimum Energy Required
-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
