Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• When the spectrum of once-ionized helium, He+, was first observed, it was interpreted as a newly discovered part of the hydrogen spectrum. The following two questions illustrate this confusion: (a) Show that alternate lines in the Balmer series of He+ — that is, those lines given by the Rydberg formula (5.30) with the lower level n′ = 2 — coincide with the lines of the Lyman series of hydrogen, (b) Show that all lines of He+ could be interpreted (incorrectly) as belonging to hydrogen if one supposed that the numbers n and n′ in the Rydberg formula for hydrogen could be half-integers as well as integers.
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