Question

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

• A. $\frac{3}{4}\frac{Rh}{M}$
• B. $\frac{Rh}{4M}$
• C. $\frac{Rh}{2M}$
• D. $\frac{Rh}{M}$

Answer 1

The correct option is A $\frac{3}{4}\frac{Rh}{M}$

Transition from n=2 to 1 (first line), photon emitted with momentum
$p_{photon}=\frac{h}{\lambda }=Rh(1-\frac{1}{n^2})=\frac{3R}{4}$
Apply Momentum Conservation
$p_{photon}=p_{atom}$
$\frac{3Rh}{4}=MV$
$V=\frac{3Rh}{4M}$