(a) Hund’s first rule says that, consistent with the Pauli principle, the state with the highest total spin (S) will have the lowest energy. What would this predict in the case of the excited states of helium?
(b) Hund’s second rule says that, for a given spin, the state with the highest total orbital angular momentum (L), consistent with overall antisymmetrization, will have the lowest energy. Why doesn’t carbon have L = 2? Hint: Note that the “top of the ladder” (ML = L) is symmetric.
(c) Hund’s third rule says that if a subshell (n, l) is no more than half filled, then the lowest energy level has J = |L – S|; if it is more than half filled, then J = L + S has the lowest energy. Use this to resolve the boron ambiguity in Problem 5.12(b).
(d) Use Hund’s rules, together with the fact that a symmetric spin state must go with an antisymmetric position state (and vice versa) to resolve the carbon and nitrogen ambiguities in Problem 5.12(b). Hint: Always go to the “top of the ladder” to figure out the symmetry of a state.
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