Question

A hydrogen atom emits a photon corresponding to an electron transition from $n=5$ to $n=1$. The recoil speed of hydrogen atom is almost

• 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)

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

$\Delta p\times \lambda h\Rightarrow \frac{1}{\lambda }=\frac{\Delta p}{h}$
We know that $\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
$\Rightarrow m_H{v}_H=h{R}_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

$\Rightarrow v=6.26\times {10}^{-34}\times R_H\left(\frac{24}{25}\right)=4m{s}^{-1}$