Question

Find recoil speed (approximately in $m{s}^{-1}$) when a hydrogen atom emits a photon during the transition from $n=5$ to $n=1$

Answer 1

First we calculate $\lambda$:

$\frac{1}{\lambda }=R(\frac{1}{{n_2}^2}-\frac{1}{{n_1}^2})$

$\frac{1}{\lambda }=R(\frac{1}{1}-\frac{1}{25})=\frac{24R}{25}nm$

Photon carries the momentum:

$p=\frac{h}{\lambda }=\frac{25h}{24R\times {10}^{=9}}kg.m/s$

Speed $v=\frac{p}{m}=\frac{25h}{24Rm}=\frac{25\times 6.63\times {10}^{-34}}{24\times 1.097\times {10}^7\times 1.67\times {10}^{-27}\times {10}^{=9}}=4m/s$