Week 1

Question 1

What is energy density?

Answer 1

How much energy is in each wavelength or frequency
- energy of mode x density of states for photons x probability mode is occupied

Question 2

What frequencies can a light inside a box have?

Answer 2

• As n lambda = 2 L, frequency = nc/(2L)

Question 3

Momentum of photon

Answer 3

H bar *k

Question 4

What are optical modes / densities of state?

Answer 4

The available modes at a given point or frequency range
- or polarisation states per volume

Question 5

Equation for density of states/optical modes.

Answer 5

From equation for frequency solved for n, and then dn and surface area of sphere

N(v) do = 2 x 4Pi/8 (2Lv/c)^2(2L/c) dv

Question 6

Energy density equation in words

Answer 6

Number of modes x Mode energy/Volume

Or density of modes x average number of photons per mode

Question 7

Equation for energy per mode E (T)?

Answer 7

Integral from 0 to infinity of Probability [E) x E dE

Question 8

How would you normalise energy per mode?

Answer 8

Integral A divided by integral B

integral A= zero to infinity of Pe(T) x E dE

Integral B as above but not multiplied by E

Question 9

What is Pe (T)?

Answer 9

As fgiven by I statistical physics, A e^(-E/kbT)

Question 10

What is the result of integral zero to infinity e^-ax dx?

Answer 10

1/a

Question 11

What is the result of integral zero to infinity xe^-ax dx?

Answer 11

1/(a^2)

Question 12

What is energy per mode according to statistical physics?

Answer 12

E bar (T) = Kb T

Question 13

What is the ultraviolet catastrophe?

Answer 13

An ideal black body would emit infinite energy as wavelength decreases

Question 14

How was ultraviolet catastrophe solved?

Answer 14

Quantisation of energy makes it harder to put into high frequency modes, decreasing overall energy

Question 15

What is the quantum effect?

Answer 15

An effect which is predicted by classical physics, but is predicted by quantum theory

Question 16

What is radiation pressure ?

Answer 16

Mechanical pressure applied to an object as momentum is transferred between object and light

Question 17

What is DeBroglie’s momentum?

Answer 17

H bar K

Question 18

What are 3 consequences of radiation quantisation?

Answer 18

• Solution of UV catastrophe
• Photoelectric effect
• Compton scattering

Question 19

What does momentum of light in Compton scattering depend on?

Answer 19

Wavelength

Question 20

What happens when light collides with an electron?

Answer 20

Wavelength changes

Question 21

What happens when an electron changes energy states?

Answer 21

It absorbs or emits an electron

Question 22

What is the energy of an emitted photon when electrons change energy states?

Answer 22

H v = Em - En

Question 23

What did Bohr suggest about electron angular momentum

Answer 23

Quantised

Question 24

Bohr’s equation for angular momentum

Answer 24

Me V(velocity) r (orbital radius) = n hbar

Question 25

How to derive Bohr radius?

Answer 25

balance coloumb and centripetal forces

Question 26

How to calculate energy of electron?

Answer 26

Kinetic energy - Coulomb energy

Question 27

What is energy of a level proportional to ?

Answer 27

1/ (n^2)

Question 28

What is En for hydrogen?

Answer 28

- 13.6eV/n^2

Question 29

How to apply En to other 1 electron systems such as ionised helium and positronium?

Answer 29

Replace Me with reduced mass

Question 30

What is Debroglie wavelength?

Answer 30

H/P and applies to matter and waves

Question 31

What is the dispersion relation for light?

Answer 31

The relationship between frequency and wave-vector - v = ck

Question 32

What is the dispersion relation for matter?

Answer 32

V = h bar (k^2)/ 2m

Question 33

What predicts a wavepacket?

Answer 33

The dispersion relation

Question 34

How does a wave packet move?

Answer 34

With group velocity I.E. packet moves with particles velocity

Question 35

What does the width of the wavepacket depend on?

Answer 35

The particle’s momentum as h is very small

Question 36

What happens to the wavepacket when wavelength is really small?

Answer 36

When DeBroglie wavelength is really small, wavepacket looks like a particle moving through space so wave nature does not affect behaviours

Question 37

What does the DeBroglie wavelength of an electron in metal correlate to?

Answer 37

Roughly the interatomic spacing

Question 38

How to find DeBroglie wavelength of gas?

Answer 38

Use 3/2 Kb T and wavelength = h/sqrt (2mE)

Question 39

How are waves and particles different?

Answer 39

Waves can undergo interference as not localised (I.E constructive/ destructive

Question 40

4 steps to derive Planck’s Radiation Law (ρ (v,T) eV

Answer 40

1. from notes sub in E bar (T) into ρ (V,T)dev 2. Cancel and factor until have hv ∑me^-x/e^-x 3. Use summation formulae 4. Factor out e^-x (so can cancel and have “1” in numerator)

Question 41

How to prove wavelength shift when photon and energy collide?

Answer 41

convert equation of change in energy to one in terms of λ-λ’

Question 42

Magnitude of momentum transfer in Compton

Answer 42

E/c

Question 43

Mechanism of Compton

Answer 43

Photons transfer momentum

Question 44

Mechanism of photoelectric

Answer 44

Energy from light radiation transferred to electrons in metals

Question 45

Free free scattering

Answer 45

Charges particle interacts with another free particle

Question 46

How to calculate number of scattering events

Answer 46

- Δλ = ℏ/ mc ( 1- cos θ) - Small angle approx of cos θ~ θ^2/2 - Δλ = ℏ θ^2/ 2mc (Will have been asked/given wavelengths) - Assume equal λ; N = Δλ total / Δλ per photon (calculated above)

Question 47

Time photons spend in sun?

Answer 47

- Distance travelled = mean free path X Number of scatters - Time = Distance /c

Question 48

Maximum electron energy from stopping potential

Answer 48

Voltage * J/ eV (i.e. *1.6 * 10^-19)

Question 49

Sign of harmonic energy level

Answer 49

- Electron energy level, proportional to 1/n^2

Question 50

Energy of “harmonic” energy levels

Answer 50

En = (- z^2 e^4 me)/ [2 * (4 π εo)^2 (n ℏ)^2 ] - me = reduced mass for ionised helium, positronium etc - Z = valency - e = charge

Question 51

What does negative sign of Bohr electron energy signify?

Answer 51

Bound state

Question 52

Bohr Radius value

Answer 52

= ao = 0.53 x 10^-10m for Z =1

Question 53

Energy spacing between m and n (M>N)

Answer 53

En = (- z^2 e^4 me)/ [2 * (4 π εo)^2 ℏ^2 ] * [(1/n^2) - (1/m^2) ]

Question 54

Find how adjacent Bohr energy level spacing scale

Answer 54

Δ E proportional to [1/(n^2) - 1/(n+1)^2] ->>Scales to 2/n^3 ->>>looks continuous

Question 55

Relate KE to momentum for non relativistic

Answer 55

P = sqrt (2m KE)

Question 56

How to verify if operator is linear

Answer 56

- Sub in (aF + bG) - Check if L(af+bg)=aL(f)+ bL(g)