•• Consider two energy levels of the helium atom, in both of which the two electrons’ spins are antiparallel (so that the total spin is zero, and the spins can be ignored) and one of the electrons is in the lowest (1s) orbital. In the upper level the second electron has l = 2; in the lower level the second electron has l = 1. The atom is placed in a magnetic field, and (as described in Section 9.4) the upper level splits into five equally spaced sublevels and the lower into three sublevels (with the same spacing), (a) Sketch the resulting levels, (b) There are, in principle, 15 different possible transitions from the upper (l = 2) level to the lower (l = 1) level. Show that because the sub- levels all have the same spacing, there are actually only seven distinct energy differences, (c) The selection rules for these transitions are Δl = ±1 and Δm = 0 or ±1; that is, only transitions that satisfy these rules are allowed. Indicate all of the allowed transitions on your energy level diagram, (d) How many distinct photon frequencies will result from allowed transitions between the two levels? This is the normal Zeeman effect described in Section 9.4.
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