Quantum Part 1

Question 1

What is the intensity of a black body?

Answer 1

I=σT^4

Question 2

What is Wien’s displacement law?

Answer 2

λmaxT=a constant=2.898x10^-3Km

Question 3

What is the power of a black body?

Answer 3

I=σAT^4

Question 4

What is the wavelength for a standing wave?

Answer 4

λn=2L/n

Question 5

What is Rayleigh-Jeans law?

Answer 5

For a 3D black body I(λ)=(2πck_B T)/λ^4

Question 6

What is the ultraviolet catastrophe?

Answer 6

Where for small λ the black body curve no loner follows the Rayleigh-Jeans law

Question 7

How is energy quantised?

Answer 7

En=nhf

Question 8

What is Planck’s model for the intensity?

Answer 8

I(λ,T)=(2πc^2 h)/λ^5 * 1/((e^(hc⁄(λk_B T)))-1)
I(λ,T)=(2πc^2 h)/λ^5 * <E>
I(T)=(2π^5k_B^4 T^4)/(15h^3c^2)</E>

Question 9

What is the average energy of a black body?

Answer 9

hf/(e^βhf-1)

Question 10

What is the average energy for high T?

Answer 10

kBT= hf/βhf

Question 11

What is the average energy for low T?

Answer 11

hf/e^βhf =hfe^(-hf/(k_B T))

Question 12

What is the work function?

Answer 12

How much energy is required to remove an electron from a surface
KE=hf-Φ

Question 13

What is the relativistic energy?

Answer 13

E^2=p^2c^2+m_0^2c^4

Question 14

What is the energy of a photon?

Answer 14

m_0=0 so E=pc=hf

Question 15

What is the momentum of a phton?

Answer 15

p=h/λ

Question 16

How much is one angstrom?

Answer 16

1A_o=10^-10m

Question 17

What is the change in λ for Compton scattering?

Answer 17

Δλ=h/mc*(1-cosθ) where θ is the angle of scattering

Question 18

What is the Compton wavelength?

Answer 18

h/mc=λ_C=0.024 Angstroms =2.4x10-12m

Question 19

What is the maximum change in λ for Compton scattering?

Answer 19

2λ_C=0.05 angstroms

Question 20

What is the minimum change in λ for Compton scattering?

Answer 20

0

Question 21

For what range is Compton scattering significant?

Answer 21

For x-rays (0.1 to 100) angstroms in λ

Question 22

What is the Rydberg formula?

Answer 22

1/λ=R(1/m^2-1/n^2) where m<n
With R=1.097x10^7m^-1

Question 23

What is the Rydberg formula involving the atomic number?

Answer 23

1/λ=RZ^2`(1/m^2-1/n^2)

Question 24

What is the Bohr radius?

Answer 24

a_0= roughly 0.5 angstroms

Question 25

What radius orbits are allowed for electrons orbiting the nucleus?

Answer 25

r_n=n^2a_0

Question 26

What is the quantised angular momentum?

Answer 26

L_n=nħ=m_e x v_n x r_n Where ħ=h/2π

Question 27

What are the energy levels for a hydrogen atom?

Answer 27

E_n=-13.6eV/n^2

Question 28

What is the de Broglie wavelength?

Answer 28

λ=h/p

Question 29

What is the quantum momentum?

Answer 29

p=h/λ=ħk

Question 30

What is Bragg's law?

Answer 30

nλ=2dsinθ

Question 31

What is the wave particle duality?

Answer 31

The wave description and particle description are complementary and both are required to model the nature properly

Question 32

What is the from of the TDSE?

Answer 32

(-ℏ^2)/2m (∂^2 φ)/(∂x^2 )=iℏ ∂φ/∂t

Question 33

When is the plane wave a solution to the TDSE?

Answer 33

When ℏω(k)= ℏ^2k^2/2m

Question 34

What is the probability of finding a particle between two points a and b at a time t?

Answer 34

∫|φ(x,t)|^2 dx Integrated between a and b

Question 35

What is the form of the normalisation condition?

Answer 35

|φ|^2=∫|φ(x,t)|^2 dx=1

Question 36

What is a wave packet?

Answer 36

If φ1 and φ2 are solutions then φ= Aφ1+Bφ2 is also a solution The superposition of many plane waves with wave numbers grouped around an average value k_0

Question 37

What is the form of a plane wave?

Answer 37

φ=Aexp(i(kx-ωt))

Question 38

What is Heisenberg's uncertainty principle?

Answer 38

ΔxΔp≥ℏ/2 ΔEΔt≥ℏ/2

Question 39

What is the distribution for a wave packet centred around k_0?

Answer 39

Ψ=∫dx a(k)exp⁡(i(kx-ω(k)t))

Question 40

What is the width of the wave packet in k?

Answer 40

w

Question 41

What is the width of the wave packet in s?

Answer 41

1/w

Question 42

What is w for a wave packet?

Answer 42

w=2σ√2ln2

Question 43

What is the form of the TISE?

Answer 43

(-ℏ^2)/2m (∂^2 Φ)/(∂x^2 )+VΦ=EΦ For the equation iℏ dP/dt=Ep has solution p(t)=e^((-iEt)⁄ℏ)

Question 44

What is the probability density?

Answer 44

|φ|^2

Question 45

What is a stationary state?

Answer 45

Where energy is constant and does not change with time as the probability density is independent of time due to p being a phase term. E= ℏω is constant

Question 46

For a particle in an infinite potential well what is the wave equation?

Answer 46

Φ=(2/L)^1/2b sin(nπx/L)

Question 47

What does k^2 equal to?

Answer 47

k^2=2mE/ℏ^2

Question 48

What does the energy equal to for a plane wave related to k?

Answer 48

En=(ℏ^2 k^2)/2m=(ℏ^2 n^2 π^2)/(2mL^2 )

Question 49

For a quantum particle what is necessary for the boundary condtions?

Answer 49

ψ(x) and dψ(x)/dx must be continuous at x=0 and x=L

Question 50

For a finite potential barrier what is the transmission probability?

Answer 50

T= (FF*)/(AA* ) for quantum tunnelling where EV0

Question 51

What is the transmission probability related to?

Answer 51

T ∝ e^(-2k_2 L) ∝ e^((-2L√(2m(V-E)))/ℏ) As k2=-ik’=√(2m(V-E))/ℏ

Question 52

What is the half life?

Answer 52

t^1/2=half life=ln(2)/λ

Question 53

What is the decay rate?

Answer 53

λ =decay rate=number of attempts at the barrier per second times T Ln λ =C2-C1(Z-2)/√(E_k )