Q. 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
A) $24hR/25m$
B) $25hR/24m$
C) $25m/24hR$
D) $24m/25hR$
Explanation
(a) For emission
$\frac{1}{\lambda} = Rz^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)$
$= R\left( \frac{1}{1^{2}} - \frac{1}{5^{2}} \right)$
$\frac{1}{\lambda} = R\frac{24}{25}$
Linear momentum
$P = \frac{h}{\lambda} = h \times R \times \frac{24}{25}$
$= mv = \frac{24hR}{25}$
$\Rightarrow v = \frac{24hR}{25m}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.