Find the total angular momentum of an atom in the state with `S=3//2` and `L=2` if its magnetic moment is known to be equal to zero.

Find the total angular momentum of an atom in the state with `S=3//2`

1.	Find the total angular momentum of an atom in the state with `S=3//2` and `L=2` if its magnetic moment is known to be equal to zero.
Answer» Since `mu=0` we must have either `J=0` or `g=0` is incomplete with `L=2` and `S=(3)/(2)`. Hence `g=0`. Thus `0=1+(J(J+1)+(3)/(2)xx(5)/(2)-2xx3)/(2J(J+1))` or `-3J(J+1)=(15)/(4)-6=-(9)/(4)` Hence `J=(1)/(2)` Thus `M= ħsqrt((1)/(2)xx(3)/(2))=( ħsqrt(3))/(2)`

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Find the total angular momentum of an atom in the state with `S=3//2` and `L=2` if its magnetic moment is known to be equal to zero.

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