Question

How many Zeeman states are there in a paramagnetic material with a total angular momentum quantum number of J=3 ?

Is the answer a number or depends on the spin of the atom?

Answer 1

The energy states of Zeeman levels of an atom with spin and orbital angular momentum is given by

where is called the :Lande g factor  and is the Bohr magneton

goes from to

There will be energy levels corresponding to

This will not depend on the spin of the atom because lande g-factor depends on the total spin of any atom. It is only dependent on the value of J.

Only the value of energy of the Zeeman level will depend on the total spin of the atom.