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Q.
The recoil speed of a hydrogen atom after it emits a photon in going from $n = 5$, state to $n = 1$ state is
Atoms
Solution:
$E = R \, hc \left( 1 - \frac{1}{25} \right)$
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 $ $\nu = 4.178 \, ms^{-1}$