Question

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 speed of recoil of the atom after the emission of the photon is

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

Answer 1

Answer: (A)

From conservation of momentum $\overset{ \rightarrow }{p}_{H}+\overset{ \rightarrow }{p}_{photon}=0$
$\left|\left(\overset{ \rightarrow }{p}\right)_{H}\right|=\left|\left(\overset{ \rightarrow }{p}\right)_{photon}\right|=\frac{h}{\lambda }=hR\left(\frac{1}{1^{2}} - \frac{1}{2^{2}}\right)=\frac{3 R h}{4}$
$v_{H}=\frac{3 R h}{4 M}$