Question

An electron in H-atom makes a transition from $n=3$ to $n=1$. The recoil momentum of $H$-atom will be

• A. 6.45 x 10${}^{-27}$ N/m
• B. 6.8 x 10${}^{-27}$ N/m
• C. 6.45 x 10${}^{-24}$ N/m
• D. 6.8 x 10${}^{-24}$ N/m

Answer 1

The correct option is A 6.45 x 10${}^{-27}$ N/m

The wavelength emitted due to transition of an electron from $n=3$ to $n=1$is given by:
$\frac{1}{\lambda }=R[\frac{1}{1^2}-\frac{1}{3^2}]$
$\frac{1}{\lambda }=R[1-\frac{1}{9}]$
$\frac{1}{\lambda }=R\left[\frac{8}{9}\right]$
$\lambda =\frac{9}{8R}$
$\lambda =\frac{9}{8\times 10.97\times {10}^6}$
$\lambda =1024\times {10}^{-10}=1024A^{\circ }$

Now, the momentum is:
$p=\frac{h}{\lambda }$
$p=\frac{6.6\times {10}^{-34}}{1024\times {10}^{-10}}$

$p=0.006445\times {10}^{-24}$

$p=6.45\times {10}^{-27}N{m}^{-1}$