Q. A proton and an $\alpha$-particle are accelerated through a potential difference of $100\ V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is
A) $\sqrt{2}\ :1$
B) 2 :1
C) $2\sqrt{2}\ :1$
D) $\frac{1}{2\sqrt{2}}:1$
Explanation
(c) $\lambda = \frac{h}{\sqrt{2mQV}} \Rightarrow \lambda \propto \frac{1}{\sqrt{mQ}} \Rightarrow \frac{\lambda_{p}}{\lambda_{\alpha}} = \sqrt{\frac{m_{\alpha}Q_{\alpha}}{m_{p}Q_{p}}}$
$= \sqrt{\frac{4m_{p} \times 2Q_{p}}{m_{p} \times Q_{p}}} = 2\sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.