1. Tardigrade
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  4. An electron of stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquires as a result of photon emission is (k h R/25 m). Find k. (Here, m= Mass of electron, h= Planck's constant and R= Rydberg constant)

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Q. An electron of stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquires as a result of photon emission is $\frac{k h R}{25 \,m}$. Find $k$.
(Here, $m=$ Mass of electron, $h=$ Planck's constant and $R=$ Rydberg constant)

Atoms

Solution:

$p=m v$
$\frac{h}{\lambda}=m v$;
$ \because \frac{1}{\lambda}=R\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$
$ \Rightarrow m v=h R\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
$v=\frac{h R}{m}\left[\frac{1}{1^{2}}-\frac{1}{5^{2}}\right]=\frac{24 h R}{25 m}$