Calculate the Land'e `g` factor for atoms
(a)`.^(6)F_(1//2)`, (b) `.^(4)D_(1//2)`, (c )`.^(5)F_(2)`, (d) `.^(5)P_(1)`, (e ) `.^(3)P_(0)`

Explanation

(a)`.^(6)F_(1/2) Here S=(5)/(2), L=3, J=(1)/(2)`
`g=1+((3)/(4)+(35)/(4)-12)/(2xx(3)/(4))=1+(38-48)/(6)=-(2)/(3)`
(b) `.^(4)D_(1//2)`: Hence `S=(3)/(2),L=2,J=(1)/(2)`
`g=1+((3)/(4)+(15)/(4)-6)/(2xx(3)/(4))=1+(18-24)/(6)=-(2)/(3)`
(c )`.^(5)F_(2)` Here `S=2, L=3, J=2`
`g=1+(6+6-12)/(2xx6)=1`
(d)`(5)P_(1)` Here `S=2,L=1,J=1`
`g=1+(2+6-2)/(2xx2)=(5)/(2)`
(e ) `.^(3)P_(0)`. For states with `J-0, L=S` the `g` gactor is indeterminate.