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Unformatted text preview: 1 Problem 1 For the atomic term 3 P , what are the energy diﬀerences between the levels
arising due to spinorbit coupling. 1.1 Solution For the atomic term 3 P , show the energy diﬀerences between the levels
arising due to spinorbit coupling.
Answer For this term, the values of J that arise are 0,1,2 and these
correspond to L = 1, S = 1. Thus, E0,1,1 =
E1,1,1 =
E2,1,1 = hA
hA
[0 − 2 − 2] = −4
2
2
hA
hA
[2 − 2 − 2] = −2
2
2
hA
hA
[6 − 2 − 2] = 2
2
2
(1) The energies between levels can be determined by simple subtraction of the
values between the J = 0andJ = 1 states and the J = 1andJ = 2 states.
The results are hA and 2hA. 2 Problem 2 For the oxygen atom in the ground state, what terms are possible? What
is the degeneracy of each term? If spinorbit coupling is taken into account,
what levels arise? What is the degeneracy of each level? 2.1 Solution For the oxygen atom in the ground state, what terms are possible? What
is the degeneracy of each term? If spinorbit coupling is taken into account,
what levels arise? What is the degeneracy of each level?
Answer Atomic electronic conﬁguration of oxygen atom is: 1s 2 , 2s2 , 2p4 ;
thus, it’s an np4 conﬁguration. From Handbook, the possible terms are
1 S,1 D,3 P .
The degeneracy of each term is determined by g = (2S + 1)(2L + 1). Thus,
for the 3 terms just mentioned, the degeneracies are (1)(1) = 1, (1)(5) = 5,
and (3)(3) = 9 . 1 In order to determine the levels arising from spinorbit coupling, we have to
determine the possible values of J for each term. For the 1 S there is only
one value of J = L + S = 0 + 0 = 0, so the level is 1 S0 . In like manner, the
levels for the 1 D are 1 D2 , and for the 3 P term the levels are 3 P0 ,3 P1 ,3 P2 .
The degeneracies for levels are determined by the J values by g J = 2J + 1:
gJ =0 = 1
gJ =1 = 3
gJ =2 = 5
(2) 2 ...
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 Fall '08
 Dybowski,C
 Physical chemistry, Atom, pH

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