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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 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 Rdgberg formula for hydrogen could be half-integers as well as integers.

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In part (b), it can be seen that all the lines of He+ will belong to Hydrogen ...

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