Consider a hydrogen atom electron in a d$-$orbital

a$.$ Calculate the magnitude of the angular moment and that of the magnetic moment.

b$.$ Determine the possible orientations of the angular moment in space. Calculate the angles between the angular moment vector and the $xy-$plane.

c$.$ What is the effect of having $Lx$ and Ly indeterminate?

d$.$ What is the effect of external magnetic field on the energy of the d$-$electron?

$\backslash$table$[[I,m,{}_m(),{}_m()$