Question

In hydrogen atom, electron makes transition from $n=4$ to $n=1$ level, recoil momentum of H-atom will be :

• A. $6.8\times 10^{-24}Nm$
• B. $3.4\times 10^{-24}Nm$
• C. $6.8\times 10^{-27}Nm$
• D. $3.4\times 10^{-27}Nm$

Answer 1

Answer: (C)

For hydrogen atom $\frac{1}{\lambda }=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
According to de Broglie $p=\frac{h}{\lambda }$
Momentum $p=hR\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)p$
$=6.6\times 10^{-34}\times 1.0974\times 10^7\left(\frac{1}{1^2}-\frac{1}{4^2}\right)$
$p=6.8\times 10^{-27}Nm$