Why are spectral lines divided when the magnetic field is applied?

“Split” is probably a more common word than “divided” in this context. If an atom has a net angular momentum (due to spin and orbital angular momenta of its constituent particles) then it also has a net magnetic dipole moment. The energies corresponding to the different possible quantized orientations of this magnetic moment in the magnetic field are seen as small increases or decreases in the transition energies between two states of the atom. Even if the net angular momentum and magnetic moment are zero, in a very strong magnetic field the magnetic moments of the constituent particles will interact independently with the magnetic field, producing a different splitting pattern than the pattern that is observed in a weak magnetic field.

By - Mel Siegel, from Carnegie Mellon University