An excited hydrogen atom emits a photon of wavelength $' λ'$ in returning to the ground state. If $' R'$ is the Rydberg's constant, then the quantum number $' n'$ of the excited state is -

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$\sqrt{λR (λR - 1)}$

$\sqrt{λR - 1}$

$\sqrt{\frac{λR}{λR - 1}}$

$\sqrt{λR}$

answer is C.

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Detailed Solution

$\frac{1}{λ} = R \times [\frac{1}{1^{2}} - \frac{1}{n^{2}}] \frac{1}{Rλ} = 1 - \frac{1}{n^{2}} \frac{1}{n^{2}} = 1 - \frac{1}{λR} = \frac{λR - 1}{λR} n = \sqrt{\frac{λR}{λR - 1}}$

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