Dual Nature Of Matter Question 1
Question 1 - 2024 (01 Feb Shift 1)
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 :
(1) $1: 8$
(2) $1: 2$
(3) $4: 1$
(4) $8: 1$
Show Answer
Answer: (4)
Solution:
$\lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}} \Rightarrow \mathrm{v}=\frac{\mathrm{h}}{\mathrm{m} \lambda}$
$\frac{\mathrm{v}{\mathrm{p}}}{\mathrm{v}{\alpha}}=\frac{\mathrm{m}{\alpha}}{\mathrm{m}{\mathrm{p}}} \times \frac{\lambda_{\alpha}}{\lambda_{\mathrm{p}}}$
$=4 \times 2=8$
