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Find the value of wave number bar v in terms of Rydberg's constant, when transition of electron takes place between two levels of He^+ ion

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Find the value of wave number (\(\bar{v}\)) in terms of Rydberg's constant, when transition of electron takes place between two levels of He+ ion whose sum is 4 and difference is 2.

(a) \(\frac{8R}{9}\)

(b) \(\frac{32R}{9}\)

(c) \(\frac{3R}{9}\)

(d) None of these

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Correct answer: (b) \(\frac{32R}{9}\)

Explanation:

n1 + n2 = 4; n2 - n1 = 2;

∴ n1 = 1, n2 = 3

\(\bar{v}\) = R\((2)^2\)\(\Big[\frac{1}{1^2}- \frac{1}{3^2} \Big]\)

= \(\frac{32R}{9}\)

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