An atom in the state with quantum numbers `L=2,S=1` is located in a weak magnetic field. Find its magnetic moment if the least possibel angle between the angular momentum and the field direction is known to be equal to `30^(@)`.

Explanation

The angular between the angular momentum vector and field direction is the least when the angular mommentum vector and the field direction is the least when the angular mommentum projection is maximum i.e., `j ħ`
Thus `j ħ=sqrt(J(J+1)) ħ cos 30^(@)`
or `sqrt((J)/(J+1))=(sqrt(3))/(2)`
Hence `J=3`
Then `g=1+(3xx4+1xx2-2xx3)/(2xx3xx4)=1+(8)/(24)=(4)/(3)`
and `mu=(4)/(3)sqrt(3xx4)mu_(B)=(8)/(sqrt(3))mu_(B)`.