Question 322: Atoms & Nuclei

Question

When a hydrogen atom going from $$n=2$$ to $$n=1$$ emits a photon, its recoil speed is $$\frac{x}{5} \mathrm{~m} / \mathrm{s}$$. Where $$x=$$ ________. (Use, mass of hydrogen atom $$=1.6 	imes 10^{-27} \mathrm{~kg}$$)

Accepted Answer

$$\begin{aligned}
& \Delta \mathbf{E}=\mathbf{1 0 . 2} \mathrm{eV} \
& 	ext { Recoil speed }(\mathrm{v})=\frac{\Delta \mathrm{E}}{\mathrm{mc}} \
& =\frac{10.2 \mathrm{eV}}{1.6 	imes 10^{-27} 	imes 3 	imes 10^8} \
& =\frac{10.2 	imes 1.6 	imes 10^{-19}}{1.6 	imes 10^{-27} 	imes 3 	imes 10^8} \
& \mathrm{v}=3.4 \mathrm{~m} / \mathrm{s}=\frac{17}{5} \mathrm{~m} / \mathrm{s}
\end{aligned}$$
Therefore, $$x=17$$

Atoms & Nuclei

When a hydrogen atom going from $n=2 to n=1 emits a photon, its recoil speed is \frac{x}{5} \mathrm{~m} / \mathrm{s}. Where x= ________. (Use, mass of hydrogen atom =1.6 \times 10^{-27} \mathrm{~kg}$)

Integer / Numeric Answer Type