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=3S`, we see that `S` must be an integer since `L` is intergal and `S` can be either intergal or half intergal. If `S=0` then `L=0` but this is consistent with `J=3`. For `S ge2,L ge6` and then `J=3`. Thus the state is
`.^(3)F_(3)`