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  4. A stationary hydrogen atom of mass M emits a photon corresponding to the first line of Lyman series. If R is the Rydberg's constant, the velocity that the atom acquires is

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Q. A stationary hydrogen atom of mass $M$ emits a photon corresponding to the first line of Lyman series. If $R$ is the Rydberg's constant, the velocity that the atom acquires is

Atoms

Solution:

From conservation of momentum:
$M V=\frac{h}{\lambda}=h R\left(1-\frac{1}{4}\right)$
$ \Rightarrow V=\frac{3}{4} \frac{h R}{M}$