Question

When the hydrogen atom emits a photon in going from $n=5$ to $n=1$ state, its recoil speed is nearly

• A. ${10}^{-4}m{s}^{-1}$
• B. $2\times {10}^{-2}m{s}^{-1}$
• C. $4m{s}^{-1}$
• D. $8\times {10}^{2}m{s}^{-1}$

Answer 1

Answer: (C)

$4m{s}^{-1}$

Potential energy of the photon released is:

$\frac{1}{2}(\frac{24}{25}\times 13.6\times 1.602\times {10}^{-19})=\frac{p\times 3\times {10}^8}{2}\Rightarrow p=7\times {10}^{-27}$

is the momentum of photn which is also equal to hydrogen.

Mass of hydrogen is $m_H=1.67\times {10}^{-27}kg$
Therefore, recoil velocity is $v=\frac{7\times {10}^{-27}}{1.67\times {10}^{-27}}=4m/s$