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Q.

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $λ$ . The value of principal quantum number 'n' of the excited state will be : (R : Rydberg constant)

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a

$\sqrt{\frac{λR}{λR - 1}}$

b

$\sqrt{\frac{{λR}^{2}}{λR - 1}}$

c

$\sqrt{\frac{λ}{λR - 1}}$

d

$\sqrt{\frac{λR}{λ - 1}}$

answer is B.

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Detailed Solution

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$\begin{array}{l} \frac{- Rch}{(n)^{2}} + \frac{Rch}{1} = \frac{hc}{λ} \\ \frac{- R}{n^{2}} + R = \frac{1}{λ} \\ R - \frac{1}{λ} = \frac{R}{n^{2}} \\ \frac{λR - 1}{λ} = \frac{R}{n^{2}} \\ n^{2} = \frac{λR}{λR - 1} \Rightarrow n = \sqrt{\frac{λR}{λR - 1}} \end{array}$

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