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 $ms^{-1}$
• B. 7.418 $ms^{-1}$
• C. 4.178 $ms^{-1}$
• D. 7.148 $ms^{-1}$

Answer 1

Answer: (C)

4.178 $ms^{-1}$

Answer 2

$E = R \, hc \left( 1 - \frac{1}{25} \right)$ 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 $p$. $m \nu = p$ $\nu = \frac{p}{m} \frac{(1.097 \times 10^7)(6.626 \times 10^{-34})24}{(25)(1.67 \times 10^{-27})}$ $\therefore$ $\nu = 4.178 \, ms^{-1}$