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I believe that the Rydberg Equation can only be used for hydrogen atoms (or hydrogen-like species containing only one atom) because it stems from the Bohr model of a hydrogen atom. The Bohr model doesn't account for more than one electron or electron-electron interactions. Because He+ only has one electron, the Rydberg Equation should work for that ion.
This works for hydrogen only. There are some "corrections" that need to be made when doing this for other elements. I'm pretty sure we're just focusing on hydrogen but there's some information on this in the textbook.
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