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:
$\lambda=\frac{h}{p}=\frac{h}{mv} \Rightarrow v=\frac{h}{m \lambda}$
$\frac{v _p}{v _{\alpha}}=\frac{m _{\alpha}}{m _p} \times \frac{\lambda _{\alpha}}{\lambda _p}$
$=4 \times 2=8$
