[PoetryInMotion]

Problem. What's the term symbol for ground state carbon?

My thoughts. I know that the configuration for ground state carbon is [He]2s²2p².

According to Hund's rule the two p-electrons must have parallel spins. Thus, I know that S=1 and that the ground state is a triplet.

When it comes to the orbital angluar momentum, I know that l=1 for the two p-electrons. Thus, I know that L=0,1 or 2. I'm not sure if I should take the s-electrons into account as well, or if I should just care about the outer electrons, but since l=0 for the s-electrons it really doesn't matter.

So, this far we have seen that the ground state must be either ³S, ³P or ³D. I do, however, not know which of these that actually describes the ground state.

Any suggestions? 

[Corribus]

State with maximal L and S is the lowest energy level. Full subshells do not contribute to the term symbol. Don't forget your J value.

[PoetryInMotion]

Maximal S=1 (triplet), and maximal L=2 (D). The 2p shell is less than half-filled, which means we have J=|L-S|=1.  So the right answer should be ³D₁. But as far as I have learned before, it should be ³P₀. Hmm.

Also, is there any reason that maximal L is equivalent with minimal energy?

[Corribus]

Maybe it's because there is no ³D state.

(Think about it, for there to be a triplet state with total orbital momentum of 2, then both electrons would have to have the same spin in the same orbital, which does not make Mr. Pauli very happy.) 

You are in luck that the carbon example is worked out in all its glory on Wikipedia: http://en.wikipedia.org/wiki/Term_symbol

(see section "Term symbols for an electron configuration").