Atomic Physics Question 5
Question 5 - 2024 (29 Jan Shift 1)
When a hydrogen atom going from $\mathrm{n}=2$ to $\mathrm{n}=1$ emits a photon, its recoil speed is $\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}$. Where $\mathrm{x}=$ . (Use : mass of hydrogen atom $=1.6 \times 10^{-27} \mathrm{~kg}$ )
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Answer: (17)
Solution:
$\Delta \mathbf{E}=10.2 \mathrm{eV}$
Recoil speed $(\mathrm{v})=\frac{\Delta \mathrm{E}}{\mathrm{mc}}$
$=\frac{10.2 \mathrm{eV}}{1.6 \times 10^{-27} \times 3 \times 10^{8}}$
$=\frac{10.2 \times 1.6 \times 10^{-19}}{1.6 \times 10^{-27} \times 3 \times 10^{8}}$
$\mathrm{v}=3.4 \mathrm{~m} / \mathrm{s}=\frac{17}{5} \mathrm{~m} / \mathrm{s}$
Therefore, $x=17$
