Electronic spectroscopy Flashcards
(40 cards)
Selection rules for an atom
ΔS = 0
ΔL = 0, +/- 1
ΔJ = 0, +/- 1
L = 0 <-> L = 0 forbidden
J = 0 <-> J = 0 forbidden
Δn = anything consistent with Δl
n quantum number
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, …
s quantum number
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.
S total spin
Clebsh gordan series
S = s1 + s2, s1 + s2 -1, …, s1 - s2
Magnitude of total spin angular momentum, S
{S(S+1)} 1/2 h
l quantum number
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.
Total orbital angular momentum, L
Is the result of coupling the individual orbital angular momenta of unpaired electrons
L = l1 + l2, l1 + l2 - 1, …, l1 - l2.
Magnitude of total orbital angular momentum, L
{L(L+1)}1/2 h
Magnetic moment quantum number ML
specifies the z-component of the orbital angular momentum
quantum number j
Total angular momenta
j = l+s, l+s-1, …, |l-s|
How to calculate J with weak spin orbit coupling (Russell Saunders coupling)
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
How to calculate J with strong spin orbit coupling (jj-coupling) (when atoms heavy with large Z)
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
ml
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
ms
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
mj
2j +1 values of mj
mj = j, j-1, j-2, …, -j
Microconfiguration
specified one of the possible combinations of ml and ms in a configuration. Each microconfig defines an L, S, J and MJ state
Term
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
Level
used to describe what arises when spin orbit coupling has been taken into account. i.e. where L, S and J are accounted for
State
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
Multiplicity
Is the number of levels in a term for S<L the multiplicity equals 2S +1 for S>L multiplicity equals 2L +1
Spin orbit interaction energy, E
E = 1/2 hcA {j(j+1) -l(l+1) -s(s+1)
Why do paired electron have overall spin of zero?
the 2 electrons have their spin angular momentum vectors oriented spin that the resultant spin is 0
How to find the lowest energy microconfiguration of electron config?
Microconfiguration that maximises both Ml and Ms
Overall L and S for filled/closed shell
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
