In spectral phenomena such as the Zeeman it becomes evident that transitions are not observed between all pairs of energy levels. Some transitions are "forbidden" while others are "allowed" by a set of selection rules. That a transition is forbidden does not mean that it does not happen, only that it is much less frequent than “allowed” transitions. The number of split components observed in the Zeeman effect is consistent with the selection rules:
These are the selection rules for an electric dipole transition. One can say that the oscillating electric field associated with the transitions resembles an oscillating electric dipole. When this is expressed in quantum terms, photon emission is always accompanied by a change of 1 in the orbital angular momentum quantum number. The magnetic quantum number can change by zero or one unit.
Another approach to the selection rules is to note that any electron transition which involves the emission of a photon must involve a change of 1 in the angular momentum. The photon is said to have an intrinsic angular momentum or "spin" of one, so that conservation of angular momentum in photon emission requires a change of 1 in the atom's angular momentum. The photon carries away a unit of angular momentum. The electron spin quantum number does not change in such transitions, so an additional selection rule is:
The total angular momentum may change be either zero or one.
An exception to this last selection rule it that you cannot have a transition from
to
i.e., since the vector angular momentum must change by one unit in a electronic transition,to 0 can't happen because there is no total angular momentum to re-orient to get a change of 1.