Electronic spectroscopy

Question 1

Selection rules for an atom

Answer 1

ΔS = 0
ΔL = 0, +/- 1
ΔJ = 0, +/- 1
L = 0 <-> L = 0 forbidden
J = 0 <-> J = 0 forbidden
Δn = anything consistent with Δl

Question 2

n quantum number

Answer 2

The principal quantum number describes the electron shell of an electron. The value of n ranges from 1 to the shell containing the outermost electron of that atom
n = 1, 2, 3, …

Question 3

s quantum number

Answer 3

Spin quantum number (s) because electrons behave as if they were spinning in either a clockwise or counterclockwise fashion. One of the electrons in an orbital is arbitrarily assigned an s quantum number of +1/2, the other is assigned an s quantum number of -1/2.

Question 4

S total spin

Answer 4

Clebsh gordan series
S = s1 + s2, s1 + s2 -1, …, s1 - s2

Question 5

Magnitude of total spin angular momentum, S

Answer 5

{S(S+1)} 1/2 h

Question 6

l quantum number

Answer 6

orbital angular momentum = quantum number describes the shape of a given orbital. Its value is equal to the total number of angular nodes in the orbital. The value of l can indicate either an s, p, d, or f subshell which vary in shape
ℓ = 0 is s orbital, ℓ = 1, p orbital, ℓ = 2, d orbital, and ℓ = 3, f orbital.

Question 7

Total orbital angular momentum, L

Answer 7

Is the result of coupling the individual orbital angular momenta of unpaired electrons
L = l1 + l2, l1 + l2 - 1, …, l1 - l2.

Question 8

Magnitude of total orbital angular momentum, L

Answer 8

{L(L+1)}1/2 h

Question 9

Magnetic moment quantum number ML

Answer 9

specifies the z-component of the orbital angular momentum

Question 10

quantum number j

Answer 10

Total angular momenta
j = l+s, l+s-1, …, |l-s|

Question 11

How to calculate J with weak spin orbit coupling (Russell Saunders coupling)

Answer 11

1) individual orbital angular momenta, l, couple to give total L
2) individual spin angular momenta, s, couple to give total S
3) Only at this stage do S and L couple to give J
J = L + S, L + S - 1, …, L - S

Question 12

How to calculate J with strong spin orbit coupling (jj-coupling) (when atoms heavy with large Z)

Answer 12

1) Individual orbital and spin angular momenta, l and s, couple to give individual j
2) The individual total angular momenta, j and j couple to give J

Question 13

ml

Answer 13

The magnetic quantum number describes the specific orbital within the subshell, and yields the projection of the orbital angular momentum along a specified axis
Values of mℓ range from −ℓ to ℓ, with integer intervals

Question 14

ms

Answer 14

The spin magnetic quantum number describes the intrinsic spin angular momentum of the electron within each orbital and gives the projection of the spin angular momentum S along the specified axis
Values of ms range from −s to s, where s is the spin quantum number

Question 15

mj

Answer 15

2j +1 values of mj
mj = j, j-1, j-2, …, -j

Question 16

Microconfiguration

Answer 16

specified one of the possible combinations of ml and ms in a configuration. Each microconfig defines an L, S, J and MJ state

Question 17

Term

Answer 17

Commonly applied to describe what arises from an approximate treatment of the electronic configuration in which just L and S are accounted for i.e. ignoring spin-orbit interactions

Question 18

Level

Answer 18

used to describe what arises when spin orbit coupling has been taken into account. i.e. where L, S and J are accounted for

Question 19

State

Answer 19

Takes account of not only L, S and J but also MJ. Number of states is therefore the same as number of microconfigurations. In absence of external field all states within particular level have same energy with degeneracy of 2J + 1

Question 20

Multiplicity

Answer 20

Is the number of levels in a term for S<L the multiplicity equals 2S +1 for S>L multiplicity equals 2L +1

Question 21

Spin orbit interaction energy, E

Answer 21

E = 1/2 hcA {j(j+1) -l(l+1) -s(s+1)

Question 22

Why do paired electron have overall spin of zero?

Answer 22

the 2 electrons have their spin angular momentum vectors oriented spin that the resultant spin is 0

Question 23

How to find the lowest energy microconfiguration of electron config?

Answer 23

Microconfiguration that maximises both Ml and Ms

Question 24

Overall L and S for filled/closed shell

Answer 24

L=0 and S=0
For a single electron outside a closed shell values of S and L are the same as s and l for that electron

Question 25

In absence of external field what degeneracy does each J level have?

Answer 25

2J + 1 degeneracy arising from 2J + 1 MJ states

Question 26

What multiplicity lies lowest in energy?

Answer 26

Term of greatest multiplicity lies lowest in energy (Triplet lower than Singlet)
Is a result of spin correlation and the tendency of electrons with parallel spin to stay apart

Question 27

What value of L lies lowest in energy?

Answer 27

The term with the highest value of L lies lowest in energy

Question 28

For atoms with less than half filled subshell which level lies lowest in energy?

Answer 28

Lowest J value will lie lowest in energy - normal multiplet

Question 29

For atoms with more than half filled subshell which level lies lowest in energy?

Answer 29

Highest J value will lie lowest in energy - inverted multiplet

Question 30

How to triplet and singlet states occur

Answer 30

The spins of 2 electrons may be aligned or paired with aligned spins corresponding to s=1 (triplet) or s=0 (singlet)

Question 31

Zeeman Effect

Answer 31

In presence of magnetic field
J precesses round field direction and becomes poorly defined. System is instead defined by MJ. Each MJ value splits into a different energy level
Degeneracy is completely lifted

Question 32

Stark effect

Answer 32

In presence of electric field J precesses round field direction and becomes poorly defined. System is instead defined by MJ. Only partial lifting of degeneracy as +/- MJ have same energy

Question 33

Orbital angular momentum, Why is l no longer a good quantum number?

Answer 33

In a diatomic molecule, the electron experiences an axially symmetric electric field generated by the 2 nuclei.
l couples so strongly to electric field that use ml as still well defined.
Classify MOs according to 𝛌 = ml = 0, +/- 1, +/- 2, +/- 3. etc

Question 34

For a filled orbital/ closed shell what is the value of 𝛬

Answer 34

𝛬 = 0, either because both electrons have 𝛌 = 0 or bc there are equal number of electrons with 𝛌 = 1 and 𝛌= -1
Therefore filled shell will have term symbol Σ

Question 35

What is inversion symmetry of diatomics

Answer 35

orbitals labelled with g or u depending on whether the change sign upon inversion
Overall parity in multielectron homonuclear diatomic found by multiplying parity of each occupied orbital
g x g = g
u x u = g
u x g = u

Question 36

Symmetry under reflection in a plane, term symbol post superscript

Answer 36

All linear molecules possess a mirror plane containing the internuclear axis
Overall symmetry with respect to reflection is found by assigning +1 to each electron in symmetric orbital and -1 to antisymmetric then multiply

Question 37

Total angular momentum along internuclear axis in linear molecule, Ω

Answer 37

Ω = 𝛬 + Σ
Where 𝛬 = equiv to term symbol
Where Σ = S, S-1, S-2, …, -S

Question 38

Selection rules concerned with a linear molecule

Answer 38

Δ𝛬 = 0, +/- 1
ΔS = 0
ΔΣ = 0
ΔΩ = 0, +/- 1

Question 39

Symmetry requirements for transition for linear molecule

Answer 39

+ > - forbidden
- > - allowed
+ > + allowed
g > g forbidden
u > u forbidden
g > u allowed