An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

Energy of photon liberated = loss in energy of electron

${\mathrm{E}}_{\text{photon selected}}=\mathrm{R}[\frac{1}{{\mathrm{N}}_1^2}-\frac{1}{{\mathrm{N}}_2^2}]\times \mathrm{hC}$

$=\mathrm{RhC}[\frac{1}{1^2}-\frac{1}{5^2}]$

Momentum of the Photon is 

$\mathrm{P} = \frac{\mathrm{E}}{\mathrm{C}} = \mathrm{Rh}\frac{24}{25}$

From Conservation of momentum :

 Initial momentum of system (atom + photon) = final momentum of system

$0={\overline{\mathrm{P}}}_{\text{photons}}+{\overline{\mathrm{p}}}_{\text{atoms}}$

$\Rightarrow \left|{\mathrm{P}}_{\text{atom}}\right|=|-{\mathrm{P}}_{\text{photon}}|$

${\mathrm{m}}_{\text{atom}}{\mathrm{V}}_{\text{atom}}=\frac{24\mathrm{Rh}}{25}$

${\mathrm{V}}_{\text{atom}}=\frac{24\mathrm{Rh}}{25\mathrm{m}}$