Find the possible values of total angular momenta of atoms in the states `.^(4)P` and `.^(5)D`.

Explanation

For the state `4p, L=1, S=(3)/(2)` (since `2s+1=4`). For the state `5d,L=2,s=2`
The possible values of `J` are
`J:(5)/(2),(3)/(2),(1)/(2)` for 4p
`J:4,3,2,1,0 for 5d`
The value of the magnitude of angular momentum is `ħ sqrt(J(J+1))`. Substitution gives the values
`4P`:
`ħ sqrt((1)/(2).(3)/(2))=(ħsqrt(3))/(2),ħsqrt((3)/(2).(5)/(2))=(ħsqrt(15))/(2)`
and`ħsqrt((5)/(2).(7)/(2))=(ħsqrt(35))/(2)`
`5D:0,ħsqrt(2),ħsqrt(6),ħsqrt(12),ħsqrt(20)`