A stationary hydrogen atom emits a photon corresponding to first line of Lyman s

Question

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

Options:

A . 7.29 m/s

B . 2.79 m/s

C . 3.2 m/s

D . 5.32 m/s

Answer: Option C
:
C

P = \frac{E}{C} = \frac{(13.6 - 3.4)}{3 \times 10^{8}} 1.6 \times 10^{- 19}

= \frac{10.2 \times 1.6 \times 10^{- 19}}{3 \times 10^{8}}

V = \frac{p}{m} = \frac{3.4 \times 1.6 \times 10^{- 19}}{1.67 \times 10^{- 27} \times 10^{8}} = V = 3.2 m s^{- 1}

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