Chapter 8, Problem 82E

As is done for helium in Table 8.3, determine for a carbon atom the various states allowed according to LS coupling. The coupling is between Carbon’s two 2p electrons (its filled 2s subshell not participating), one of which always remains in the 2p state. Consider cases in which the other is as high as the 3d level. (Note: When both electrons are in the 2p, the exclusion principle restricts the number of states. The only allowed states are those in which $s_T$ and ${\mathcal{l}}_T$ are both even or both odd.)