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PX156 > Quantum Part 1 > Flashcards

Quantum Part 1 Flashcards

1
Q

What is the intensity of a black body?

A

I=σT^4

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2
Q

What is Wien’s displacement law?

A

λmaxT=a constant=2.898x10^-3Km

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3
Q

What is the power of a black body?

A

I=σAT^4

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4
Q

What is the wavelength for a standing wave?

A

λn=2L/n

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5
Q

What is Rayleigh-Jeans law?

A

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

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6
Q

What is the ultraviolet catastrophe?

A

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

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7
Q

How is energy quantised?

A

En=nhf

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8
Q

What is Planck’s model for the intensity?

A

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>

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9
Q

What is the average energy of a black body?

A

hf/(e^βhf-1)

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10
Q

What is the average energy for high T?

A

kBT= hf/βhf

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11
Q

What is the average energy for low T?

A

hf/e^βhf =hfe^(-hf/(k_B T))

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12
Q

What is the work function?

A

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

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13
Q

What is the relativistic energy?

A

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

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14
Q

What is the energy of a photon?

A

m_0=0 so E=pc=hf

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15
Q

What is the momentum of a phton?

A

p=h/λ

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16
Q

How much is one angstrom?

A

1A_o=10^-10m

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17
Q

What is the change in λ for Compton scattering?

A

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

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18
Q

What is the Compton wavelength?

A

h/mc=λ_C=0.024 Angstroms =2.4x10-12m

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19
Q

What is the maximum change in λ for Compton scattering?

A

2λ_C=0.05 angstroms

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20
Q

What is the minimum change in λ for Compton scattering?

A

0

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21
Q

For what range is Compton scattering significant?

A

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

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22
Q

What is the Rydberg formula?

A

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

23
Q

What is the Rydberg formula involving the atomic number?

A

1/λ=RZ^2`(1/m^2-1/n^2)

24
Q

What is the Bohr radius?

A

a_0= roughly 0.5 angstroms

25
Q

What radius orbits are allowed for electrons orbiting the nucleus?

A

r_n=n^2a_0

26
Q

What is the quantised angular momentum?

A

L_n=nħ=m_e x v_n x r_n
Where ħ=h/2π

27
Q

What are the energy levels for a hydrogen atom?

A

E_n=-13.6eV/n^2

28
Q

What is the de Broglie wavelength?

29
Q

What is the quantum momentum?

A

p=h/λ=ħk

30
Q

What is Bragg’s law?

A

nλ=2dsinθ

31
Q

What is the wave particle duality?

A

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

32
Q

What is the from of the TDSE?

A

(-ℏ^2)/2m (∂^2 φ)/(∂x^2 )=iℏ ∂φ/∂t

33
Q

When is the plane wave a solution to the TDSE?

A

When ℏω(k)= ℏ^2k^2/2m

34
Q

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

A

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

35
Q

What is the form of the normalisation condition?

A

|φ|^2=∫|φ(x,t)|^2 dx=1

36
Q

What is a wave packet?

A

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

37
Q

What is the form of a plane wave?

A

φ=Aexp(i(kx-ωt))

38
Q

What is Heisenberg’s uncertainty principle?

A

ΔxΔp≥ℏ/2
ΔEΔt≥ℏ/2

39
Q

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

A

Ψ=∫dx a(k)exp⁡(i(kx-ω(k)t))

40
Q

What is the width of the wave packet in k?

41
Q

What is the width of the wave packet in s?

42
Q

What is w for a wave packet?

A

w=2σ√2ln2

43
Q

What is the form of the TISE?

A

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

44
Q

What is the probability density?

45
Q

What is a stationary state?

A

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

46
Q

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

A

Φ=(2/L)^1/2b sin(nπx/L)

47
Q

What does k^2 equal to?

A

k^2=2mE/ℏ^2

48
Q

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

A

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

49
Q

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

A

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

50
Q

For a finite potential barrier what is the transmission probability?

A

T= (FF)/(AA ) for quantum tunnelling where E<V0
T= (BB)/(AA ) for reflection where E>V0

51
Q

What is the transmission probability related to?

A

T ∝ e^(-2k_2 L) ∝ e^((-2L√(2m(V-E)))/ℏ)

As k2=-ik’=√(2m(V-E))/ℏ

52
Q

What is the half life?

A

t^1/2=half life=ln(2)/λ

53
Q

What is the decay rate?

A

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

PX156 (10 decks)

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