- #1
boyu
- 20
- 0
The ground state electron configuration of Carbon atom is [tex]1s^{2}2s^{2}2p^{2}[/tex]
For the electrons, [tex]1s^{2}2s^{2}[/tex], [tex]L=0[/tex], [tex]S=0[/tex]
So only consider electrons of [tex]2p^{2}[/tex], and
[tex]s_{1}=s_{2}=1/2 ---> S=0,1[/tex]
[tex]l_{1}=l_{2}=1 ---> L=0,1,2[/tex]
For S=0, L=0; J=0, so we have [tex]^{1}S_{0}[/tex]
For S=0, L=1; J=1, so [tex]^{1}P_{1}[/tex]
For S=0, L=2; J=2, so [tex]^{1}D_{2}[/tex]
For S=1, L=0; J=1, so [tex]^{3}S_{1}[/tex]
For S=1, L=1; J=0,1,2, so [tex]^{3}P_{0}, ^{3}P_{1}, ^{3}P_{2}[/tex]
For S=1, L=2; J=1,2,3, so [tex]^{3}D_{1}, ^{3}D_{2}, ^{3}D_{3}[/tex]
The above is based on my derivation. However, the correct answer is actually:
[tex]^{1}S_{0}, ^{1}D_{2}, ^{3}P_{0}, ^{3}P_{1}, ^{3}P_{2}[/tex]
My question is: where are all the other possible terms? Where is wrong in my derivation:
For the electrons, [tex]1s^{2}2s^{2}[/tex], [tex]L=0[/tex], [tex]S=0[/tex]
So only consider electrons of [tex]2p^{2}[/tex], and
[tex]s_{1}=s_{2}=1/2 ---> S=0,1[/tex]
[tex]l_{1}=l_{2}=1 ---> L=0,1,2[/tex]
For S=0, L=0; J=0, so we have [tex]^{1}S_{0}[/tex]
For S=0, L=1; J=1, so [tex]^{1}P_{1}[/tex]
For S=0, L=2; J=2, so [tex]^{1}D_{2}[/tex]
For S=1, L=0; J=1, so [tex]^{3}S_{1}[/tex]
For S=1, L=1; J=0,1,2, so [tex]^{3}P_{0}, ^{3}P_{1}, ^{3}P_{2}[/tex]
For S=1, L=2; J=1,2,3, so [tex]^{3}D_{1}, ^{3}D_{2}, ^{3}D_{3}[/tex]
The above is based on my derivation. However, the correct answer is actually:
[tex]^{1}S_{0}, ^{1}D_{2}, ^{3}P_{0}, ^{3}P_{1}, ^{3}P_{2}[/tex]
My question is: where are all the other possible terms? Where is wrong in my derivation: