Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

3rd Year Oxford Physics > Atomic, Molecular, and Laser Physics > Flashcards

Atomic, Molecular, and Laser Physics Flashcards

1
Q

Bohr equation for hydrogen

/\E =

/\ is a delta

A

hbar w =

Rhc( Z2/n2 - Z2/m2 )

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

relate wavenumber and wavelength

A

v = 1/lambda

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Rhc =

A

e2/4πe0 . 1/2a0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

bohr radius

a0 =

A

hbar2 / (e2/4πe0)me

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

fine structure constant

A

alpha = ve/c

= e2/4πe0 . 1/(hbar.c)

~1/137

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

energy of a magnetic dipole in a magnetic field

A

E =

-mu.B

mu is the magnetic dipole

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Bohr magneton

A

muB=

e hbar/2me

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

TISE

A

{-hbar2/2me \/2 + V(r)} phi = E phi

\/ is nabla

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

To solve schrodiger for hydrogen atom (angular part)

A
  • express \/2 in spherical polar also using operator l2 to contain angular terms
  • separation of variables
  • start with angular, separate again with constant m2
  • use PHI(phi + 2π) = PHI(phi) => integer m
  • apply raising operators to Y until l+Y = 0 (mmax = l )
  • show Y≈ sinl(theta)eilø
  • apply lowering ops to find the rest
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Y0,0 =

A

SQRT (1/4π)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Y1,0 =

A

SQRT ( 3/4π ) cos(theta)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Y1,1

Y1,-1

A

-SQRT( 3/8π ) sin(theta) e+iø

+SQRT( 3/8π ) sin(theta) e-iø

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

how do we solve shrodinger eqn for a many electron atom

A
  • ignore electron spin
  • include a SUM of mutual repulsions
  • invent a centrally symmetric potential V(r)
  • modify H = H0 + H1

such that H0 centrally symmetric

  • eqns are now separable

H0 >> H1

perturbation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

central field approximation

A

ignore the risidual el. static interaction from multi atom Hamiltonian.

H1 = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Pauli Exclusion Principle. How does it lead to configurations

A

2 identical fermions cannot occupy the same quantum state simultaneously.

It limits the number of electrons you can put in each state. Otherwise all electrons would be in n=1 l=0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the quantum defect

A

a correction applied to the equations of a hydrogenic atom to take into account the fact that inner electrons do not entirely screen their associated charge in the nucleus.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

electron configuration notation

A

nlx

n = shell = 1, 2, 3

l = orbital = s, p, d, = 0, 1, 2…

x = number of electrons, this has maximum 2*(2l + 1)

factor of 2 for the spin

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

why does a higher l correspond to higher (nearer 0) energy state

A

lower l electrons penetrate closer to the nucleus. Hence electrons with high l are further from the nucleus.

This means that outer electrons are more effectively screened <=> the effective charge experienced is lower.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

trick for finding energies of first excited state of helium

A

1s12s1

first electron experiences no screening

2nd experiences perfect screening

1st has the form of hydrogen with z=2

2nd with z=1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

in helium does the singlet or triplet state have higher energy and why?

A

singlet

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

can the triplet state in helium

1s12s1 3S

decay into the singlet state

1s12s1 1S

A

no. both states are metastable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

tell me about the sequence of perturbations:

Hatom = H0 + H1 + HSO +[HHFS]

A

H0 is from the central field, it gives the configuration (nl)

H1 is the residual due to electron repulsion + screening, ot gives the term (2S+1L) [singlet-triplet splitting]

  • together these two make the gross tructure

HSO is the fine structure due to spin orbit interaction, it gives the level (2S+1LJ) [triplet state is split into 3 levels]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Briefly outline the cause of the fine structure

A

The combination of the spin and orbital angular momenta.

The spin of the electron gives rise to a magnetic dipole moment, this sits in the magnetic field of the orbiting electrons. This leads to a shift in energy.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

electron magnetic moment

mu =

and its energy in a magnetic field

A

-gs . muB/hbar . s

gs ≈ 2 = Londé factor

E = -mu . B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

in the fine structure, where does the magnetic field come from? In hydrogen, is it parallel or antiparallel to the angular momentum of the electron?

A

the charged electrons are moving in the electric field of the nucleus and thus create a magnetic field.

NB

B = - 1/c2 v ^ E (from SR)

Parallel

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Biot Savart Law

A

B = mu0/4π x I x int [r ^ ds / r2]

the path integral around the loop

current I =

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

when deriving the energy shift in the fine structure of hydrogen, what must you remember?

A

gs -> (gs - 1)

due to Thomas Precession

  • it is relativistic motion in an accelerated frame because the electron is orbiting the nucleus
28
Q

how to find

< s . l >/hbar2

A

j = l + s

j2 - l2 - s2 = 2l.s

use expectation values of LHS:

<j>2&gt; = hbar2 j (j+1) ...</j>

< s . l >/hbar2 =

1/2 [j(j+1) - l(l+1) - s(s+1)]

29
Q

in fine structure, what are the possible values of J and why?

A

J is the total angular momentum

J = L + S

so Jmax = L + S

<span>J</span>min = | L-S |

30
Q

how does the fine structure splitting change for large nuclei

A

it gets bigger

31
Q

what is L-S coupling used for? (it is also known as Russel-Saunders Coupling)

A

fine structure of multi electron atoms

  • easiest case is with 2 valence electrons (eg magnesium)
32
Q

what are L and S and why are they important in LS coupling

A

L = Σ_l_i

S = Σ_s_i

L2 and S2 both commute with the hamiltonian H1 (residual electrostatic ham)

[L2, H1] = [Lz, H1] = 0

similarly for S

33
Q

how to find the ‘terms’ for

Si … 3p14p1

A

l1=1, l2=1 => L = 0, 1, 2

s1=1/2, s2=1/2 => S = 0, 1

so

1S, 1P, 1D, 3S, 3P, 3D

34
Q

what is the condition for LS coupling?

A

the energies resulting from the residual electrostatic interaction must be larger than the corresponding energies from the spin-orbit interaction:

<h>1&gt; &gt;&gt; <h>SO&gt;</h></h>

35
Q

Fine structure in LS coupling.

what is the ‘projection’ of

< s1 . l1 >

A

< s1 . S > S / S(S+1) . < l1 . L > L​ / L(L+1)

( = some scalar times S . L )

36
Q

ESO =

A

betaLS / hbar2 * <S . L>

37
Q

what are the differences between LS and jj coupling?

A

LS:

You couple l1 and l2 to L (l1 + l2 = L), and s1 and s2 to S, and then you couple L with S to get LS (L + S = J)

JJ:

You couple l1 and s1 to j1 (l1 + s1 = j1), and l2 and s2 to j2, and then couple j1 and j2 to get JJ (j1 + j2 = J)

when ESO >≈ Eres use jj coupling

38
Q

what is the ionisation energy of an alkali atom?

A

-hcR/(n-dl)2

dl is the quantum defect

note that there is no Z as the inner electrons shield (almost) all the nucleus

39
Q

how does the quantum defect change for large l.

Does it depend on n?

A

dl -> 0

barely

40
Q

read

32S1/2

A

three - doublet - S - one half

41
Q

What is the dependece on Z in the spin orbit interaction in

1) hydrogen-like atoms
2) alkali atoms

A

1) Z4
2) Z2

42
Q

in alkali atoms, what kind of splitting is there due to the spin orbit interaction?

A

there is a single e- so S=1/2

thus, if

l =/= 1 (so for P, D, F, …)

we get a doublet

43
Q

Zeeman effect energy shift

A

EZe = - mu . B

44
Q

for orbiting electron

mu =

< HZe > =

A

mu = - muB/hbar l

< HZe > =

muB/hbar B < l . z >

= muB B ml

45
Q

for spinning electron

mu =

< HZe > =

A

mu = - gs muB/hbar s

< HZe > =

muB/hbar B < s . z >

= 2 muB B ms

46
Q

Zeeman effect in LS coupling

< HZe > = ?

A

mu = - muB/hbar ( L + S )

this is hard to evaluate, but

< mu . j > = constant of motion

< HZe > = - < mu . j > / (hbar2 j(j+1)) j . B

then sub in mu in terms of S and L

EZe = gj muB B Mj

gj = 3/2 + [S(S+1) - L(L+1)]/2J(J+1)

47
Q

what is the normal Zeeman effect

A

S=0

=> J = L => gJ = 1

48
Q

is the Zeeman effect always valid?

A

it works only if

< HZe > << < HSO > << < H1 >

otherwise we use the Paschen-Back effect

49
Q

Describe the Paschen-Back effect

A

the external B-field is stronger than the spin-orbit coupling. L and S precess independently about the B-field axis

-muB/hbar [< L . B > - 2< S . B >]

so

EPB = muB B ( ML + 2 MS )

50
Q

what quantum numbers are important when there is an applied B field that is:

weak

strong

A

MJ (Zeeman effect)

ML and MS (Paschen-Back effect)

51
Q

EHFS

A

EHFS = - muI . Be

B is parallel to J

muI = gI muN/hbar I

muN = muB me/Mp

52
Q

when is nuclear spin I non-zero

A

for half integer I

<=> odd # of protons OR neutrons

I = 0 if # of p and n both even

53
Q

What is the cause of the hyperfine structure?

A

the spinning nucleus inside the electronic B-field

54
Q

hyperfine structure contributions to Be

A

1) closed shells do not contribute
2) major contribution from s-electron since the wavefunction is non zero at r=0

55
Q

hyperfine structure s-electron

Be =

A

-2/3 mu0 gs |phins (r=0)|2 muB/hbar s

56
Q

outline IJ-coupling

A

F = I + J

I and J precess about F

57
Q

< I . J > =

A

hbar2/s { F(F+1) - I(I+1) - J(J+1) }

58
Q

hyperfine structure fot l<0

Be =

A
59
Q

Born-Oppenheimer approximation

A

the motion if the electron and nuclei is treated separately because of the great disparity between their masses.

60
Q

order of magnitude of electronic energy

A

_/_p ≈ hbar/a

a = atomic radius

Ee ≈ p2/2m

a few eV

61
Q

order of magnitude of vibrational energy

A

U(x) = 1/2 mu wv2 x2

mu is the reduced mass

when x is of the order of a, the energy must be of the order Ee

1/2 mu wv2 a2 = hbar2/2ma2

solve for wv

Ev ≈ hbar wv

= SQRT (m/mu) Ee

62
Q

order of magnitude of rotationl energy

A

Er = 1/2 I wr2

I = mu a2

the rot frequency is such that:

mu a2 wr ≈ hbar

=>

Er = (m/mu) Ee

63
Q

condition for optical gain

A

N2/g2 > N1/g1

64
Q

necessary (but not sufficient) condition for steady-state population inversion

A

A21 < g1/g2 1/t1

65
Q

describe the features of the lineshape function

A

g(w - w0)

looks like a stretched delta function with FWHM of gamma and centred around w0

66
Q

How are the lineshapes for absorption and spontaneous and stimulated emission related

A

they are the same

<=> they have the same frequency dependance

67
Q
A

3rd Year Oxford Physics (4 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions