The Zeeman effect is the modification of an atomic spectrum by the application of a strong magnetic field. It arises from the interaction between applied magnetic fields and the magnetic moments due to orbital and spin angular moment a (recall the evidence provided for electron spin by the Stern-Gerlach experiment, Section 9.8). To gain some appreciation for the so-called normal Zeeman effect, which is observed in transitions involving singlet states, consider a p electron, with l= 1 and ml = 0, ±1. In the absence of a magnetic field, these three states are degenerate. When a field of magnitude B is present, the degeneracy is removed and it is observed that the state with ml = +1 moves up in energy by μBB, the state with mj = 0 is unchanged, and the state with m =-1 moves down in energy by μBB, where μB= eh/2m; = 9.274 x 10-24 J T-I is the Bohr magneton (see Section 15.1).
Therefore, a transition between a I S O term and a IP 1 term consists of three spectral lines in the presence of a magnetic field where, in the absence of the magnetic field, there is only one.
(a) Calculate the splitting in reciprocal centimeters between the three spectral lines of a transition between a I So term and alp 1 term in the presence of a magnetic field of2 T (where 1 T = 1 kg S-2A-I).
(b) Compare the value you calculated in (a) with typical optical transition wave numbers, such as those for the Balmer series of the H atom. Is the line splitting caused by the normal Zeeman effect relatively small or relatively large?