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. $6.8 \times 10^{-27} N m$
• 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 $p=h R\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right) p$
$=6.6 \times 10^{-34} \times 1.0974 \times 10^{7}\left(\frac{1}{1^{2}}-\frac{1}{4^{2}}\right)$
$p=6.8 \times 10^{-27} N m$