MCQ
The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2 \lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :
- A$1: 8$
- B$1: 2$
- C$4: 1$
- ✓$8: 1$
✓
Answer
Correct option: D.
$8: 1$
d
$\lambda= \frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}} \Rightarrow \mathrm{v}=\frac{\mathrm{h}}{\mathrm{m} \lambda}$
$\lambda= \frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}} \Rightarrow \mathrm{v}=\frac{\mathrm{h}}{\mathrm{m} \lambda}$
$\frac{\mathrm{v}_{\mathrm{p}}}{\mathrm{v}_\alpha}=\frac{\mathrm{m}_\alpha}{\mathrm{m}_{\mathrm{p}}} \times \frac{\lambda_\alpha}{\lambda_{\mathrm{p}}}$
$=4 \times 2=8$
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