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The recoil speed of a hydrogen atom after it emits a photon in going from $n = 5$ state to $n = 1$ state will be

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2.19 m/s

3.25 m/s

4.17 m/s

4.34 m/s

answer is A.

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Detailed Solution

$P = \frac{Δ E}{C} \Rightarrow m v = \frac{Δ E}{C}$

$υ = \frac{Δ E}{m C}$

$= \frac{(\frac{13.6}{1^{2}} - \frac{13.6}{5^{2}}) \times 1.6 \times 10^{- 19}}{1.6 \times 10^{- 27} \times 3 \times 10^{8}}$

$= 4.35 m / s$

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