Question

The recoil speed of a hydrogen atom after it emits a photon in going from $n=5$, state to $n=1$ state is

• A. 4.718 $m{s}^{-1}$
• B. 7.418 $m{s}^{-1}$
• C. 4.178 $m{s}^{-1}$
• D. 7.148 $m{s}^{-1}$

Answer 1

Answer: (C)

$E=Rhc\left(1-\frac{1}{25}\right)$
Momentum of photon emitted is
$p=\frac{E}{c}=R_{\infty }h\left(\frac{24}{25}\right)$
Recoil momentum of H atom will also be $p$.
$m\nu =p$
$\nu =\frac{p}{m}\frac{(1.097\times 10^7)(6.626\times 10^{-34})24}{(25)(1.67\times 10^{-27})}$
$\therefore$ $\nu =4.178m{s}^{-1}$