Dual Nature Of Matter Question 6

Question 6 - 29 January - Shift 2

The ratio of de-Broglie wavelength of an $\alpha$-particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$, the value of $m$ is

(1) 4

(2) 16

(3) 8

(4) 2

Show Answer

Answer: (3)

Solution:

Formula: De Broglie wavelength

$ \begin{aligned} & \frac{\lambda _{\alpha}}{\lambda_p}=\frac{h}{\frac{\sqrt{2 m _{\alpha} q _{\alpha} V}}{h}} \\ & \frac{\lambda _{\alpha}}{\lambda_p}=\sqrt{\frac{1}{8} \quad m}=8 \end{aligned} $

Ans. 3