How many and which values of the quantum number `J` can an atom possess in the state with quantum numbers `S` and `L` equal respectively to
(a) 2 and 3, (b) 3 and 3,(c )`5//2` and 2?

Explanation

The rule is that if `vec(J)=vec(L)+vec(S)` then `J` takes the values
`|L-S| to L+S`
in step of 1. Thus :
(a) The values are `1,2,3,4,5`
(b)The values are `0,1,2,3,4,5,6`
(c )The values are `(1)/(2),(3)/(2),(5)/(2),(7)/(2),(9)/(2)`.