The recoil speed of a hydrogen atom after it emits a photon in going from
Question:

The recoil speed of a hydrogen atom after it emits a photon in going from $\mathrm{n}=5$ state to $\mathrm{n}=1$ state will be:

1. (1) $4.17 \mathrm{~m} / \mathrm{s}$

2. (2) $4.34 \mathrm{~m} / \mathrm{s}$

3. (3) $219 \mathrm{~m} / \mathrm{s}$

4. (4) $3.25 \mathrm{~m} / \mathrm{s}$

Correct Option:

Solution:

(1)

momentum $(P)=\frac{\Delta E}{C}=\frac{(13.6-0.54) \mathrm{eV}}{3 \times 10^{8}}$

$\mathrm{mv}=\frac{(13.06) \times 1.6 \times 10^{-19}}{3 \times 10^{8}}$

$\mathrm{v}=\frac{(13.06) \times 1.6 \times 10^{-19}}{3 \times 10^{3} \times 1.67 \times 10^{-27}} \Rightarrow 4.17 \mathrm{~m} / \mathrm{sec}$