Question

Derive the symbol for the ground state of carbon atom.

Answer 1

Answer on Question #64623, Physics / Atomic and Nuclear Physics

Derive the symbol for the ground state of carbon atom.

Answer:

Carbon, with $Z = 6$ has the 1S and 2S levels filled giving $j = 0$ as a base. It has two valence 2P electrons. Hund's first rule, maximum total S, tells us to couple the two electron spins to $S = 1$ . This is the symmetric spin state so we'll need to make the space state antisymmetric. Hund's second rule, maximum I, doesn't play a role because only the $I = 1$ state is antisymmetric. Adding two P states together, we get total $I = 0, 1, 2$ . The maximum state is symmetric, the next antisymmetric, and the $I = 0$ state is again symmetric under interchange. This means $I = 1$ is the only option. Since the shell is not half full we couple to the lowest $j = |I - S| = 0$ . So the ground state is $^3\mathrm{P}_0$ .

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