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Let ν1 denote the frequency at the Lyman series limit, ν2 the frequency of the first Lyman line, and ν3 the frequency at the Balmer series limit. Which relation is correct?

1. ν1 − ν2 = ν3
2. ν1 = ν2 − ν3
3. 1/ν2 = 1/ν1 + 1/ν3
4. 1/ν1 = 1/ν2 + 1/ν3

Correct answer: ν1 − ν2 = ν3

Solution

nu1 = Rc (Lyman limit), nu2 = Rc(1 - 1/4) = (3/4)Rc (first Lyman line), nu3 = Rc/4 (Balmer limit). Then nu1 - nu2 = Rc/4 = nu3.

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