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  • when a hydrogen atom initially a rest emits a photon resulting in transition ,  

when a hydrogen atom initially a rest emits a photon resulting in transition \mathrm{n=5 \rightarrow n=1},  its recoil speed is about

Option: 1

10^{-4} \mathrm{~m} / \mathrm{s}


Option: 2

2 \times 10^{-2} \mathrm{ra} / \mathrm{s}


Option: 3

4.2 \mathrm{~m} / \mathrm{s}


Option: 4

3.8 \times 10^-2 \mathrm{~m} / \mathrm{s}


Answers (1)

best_answer

\mathrm{\text{Energy of photon}=13.6\left(\frac{1}{1^{2}}-\frac{1}{5^2}\right) \mathrm{ev} }
\mathrm{=13.6 \times \frac{24}{25} \mathrm{eV}=13.056\, \mathrm{eV} }
\mathrm{=20.89 \times 10^{-19} \mathrm{~J}=p . c . }

\mathrm{p= \frac{20.89 \times 10^{-19}}{3 \times 10^8} \mathrm{~kg}\, \mathrm{m} / \mathrm{s}=6.96 \times 10^{-27} \mathrm{kg} / \mathrm{ms} }

Momentum of hydrogen aton is same as that of photon

\mathrm{\Rightarrow m v=6.96 \times 10^{-27} }
\mathrm{\Rightarrow v=\frac{6.96 \times 10^{-27}}{1.67 \times 10^{-27}} \mathrm{~m} / \mathrm{s}=4.2 \mathrm{~m} / \mathrm{s}}

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Rishi

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