It is known thai in `F` and `D` states the number of possible values of the quantum number `J` is the same and equal to five. Find the spin angular momentum in these states.

Explanation

For the `f` state `L=3` , For `d` state `L=2`. Now if the state has spin `s` the possible angular momentum are
`|L-S| to L+S`
The number of `J` angular momentum values is `2S+1` if `L ge S` and `2L+1` if `Llt S`. Since the number of states is `5`, we must have `S ge L=2` for `D` state while `S le 3` and `2S+1=5` in ply`S=2` for `F` state. Thus for the`F` state total spin angular momentum
`M_(s)= ħsqrt(2.3)= ħsqrt(6)`
while for `D` state `M_(s) ge ħsqrt(6)`.