The permanent magnetic moment of a molecule is due to the presence of unpaired electron spins in that molecule.
The magnitude of the magnetic moment, m, of a single electron is given by the relationship below, where s is the spin angular momentum.
ge is the electron’s g-factor and μB is the Bohr magneton,
In a molecule there is more than electron, and the total spin of the molecule determines the magnetic moment, not the spin of individual electrons. Therefore the total spin, S, replaces the individual electron spin, s, in the expression above. Hence, the spin contribution to the molar magnetic susceptibility is
The total spin, S, in a system with N unpaired electrons is N/2, and so the determination of the magnetic susceptibility can tell us the number of unpaired electrons in a molecule. This can be very important in determining the electronic structures of d-metal complexes, where the Ligand Field splitting means that different configurations are possible for a given number of electrons.