The Zeeman effect is the modification of an atomic spectrum by the application of a

Chapter 10, Problem 10.9

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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 momenta (recall the evidence provided for electron spin by the SternGerlach experiment, Section 9.8). To gain some appreciation for the socalled 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 BB, the state with ml = 0 is unchanged, and the state with ml = 1 moves down in energy by BB, where B = e$/2me = 9.274 1024 J T 1 is the Bohr magneton (see Section 15.1). Therefore, a transition between a 1S0 term and a 1P1 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 centimetres between the three spectral lines of a transition between a 1S0 term and a 1P1 term in the presence of a magnetic field of 2 T (where 1 T = 1 kg s2 A1). (b) Compare the value you calculated in (a) with typical optical transition wavenumbers, 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?