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

For fifth energy level, $n_2=5$  and for ground level,  $n_1=1$. The wavelength $\lambda$ of radiation emitted is given by 
 $\frac{1}{\lambda }=R{z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})=R\times 1^2(\frac{1}{1^2}-\frac{1}{5^2})=\frac{24R}{25}$
Linear momentum of photon emitted 
 $p=\frac{h}{\lambda }=h\times \frac{24R}{25}$
As hydrogen atom is stationary, therefore momentum acquired by electron as a result of photon emission $=mv=p=\frac{24hR}{25}$
$v=\frac{24hR}{25m}$