A stationary hydrogen atom emits a photon corresponding to first line of Lyman series. The velocity of recoil of the atom is

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3.2m/s

5.32m/s

2.79m/s

7.29m/s

answer is C.

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Detailed Solution

P_H–atom = P_photon ; $∴ MV = \frac{h}{λ}$
$\begin{array}{l} ∴ MV = h ({Rz}^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]) \\ ∴ V = \frac{{hRz}^{2}}{M} (\frac{1}{1^{2}} - \frac{1}{2^{2}}) \\ ∴ V = \frac{6 .6 \times 10^{- 34} \times 1.09 \times 10^{7} \times (1)^{2}}{1 .67 \times 10^{- 27}} (\frac{3}{4}) ∴ V = 3 .2 {ms}^{- 1} \end{array}$

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