Question

Write the spectral designation of the term whose degeneracy is equal to seven and the quantum numbers L and S are interrelated as L = 3S.

Answer 1

The degeneracy is 2J + 1. So we must have J = 3. From L = 3 S, we see that S must be an integer since L is integral and S can be either integral or half-integral. If S = 0 then L = 0 but this is consistent with J = 3. For S ≥ 2, L ≥ 6 and then J = 3. Thus the state is ³F₃