Question

When an electron jumps from a level $n=4$ to $n=1$, the momentum of the recoiled hydrogen atom will be

• A. $6.5\times {10}^{-27}kgm{s}^{-1}$
• B. $12.75\times {10}^{-19}kgm{s}^{-1}$
• C. $13.6\times {10}^{-27}kgm{s}^{-1}$
• D. $Zero$

Answer 1

Answer: (A)

$6.5\times {10}^{-27}kgm{s}^{-1}$

Momentum of the recoiled hydrogen atom
$=$ momentum of the emitted photon $=\frac{h\nu }{c}=\frac{h}{\lambda }$
$=hR[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
$=6.6\times {10}^{-34}\times {10}^7[\frac{1}{1^2}-\frac{1}{4^2}]$
$=6.5\times {10}^{-27}kgm{s}^{-1}$