Determine the spin angular momentum of an atom in the state `D_(2)` if the maximum value of the magnetic moment projection in thatl state is equal to four Bohr magnetons.

Explanation

The expression for the projection of the magnetic moment is
`mu_(z)= gm_(J)mu_(B)`
where `m_(J)` is the projection of `vec(J)` on the `Ƶ`-axis.
Maximum value of the `m_(J)` is `J`. Thus
`gJ=4`
Since `J=2`, we get `g=2`. Now
`2=1+(J(J+1)+S(S+1)-L(L+1))/(2J(J+1))`
`=1+(6+S(S+1)-6)/(2xx6), as L=2`
`=1+(S(S+1))/(12)` ltnrgt Hence `S(S+1)=12 or S=3`
Thus `M_(s)= ħsqrt(3xx4)=2sqrt(3) ħ`.