Q. The ratio of momenta of an electron and an $\alpha -$particle which are accelerated from rest by a potential difference of $100\ volt$ is
A) 1
B) $\sqrt{\frac{2m_{e}}{m_{\alpha}}}$
C) $\sqrt{\frac{m_{e}}{m_{\alpha}}}$
D) $\sqrt{\frac{m_{e}}{{2m}_{\alpha}}}$
Explanation
(d) Momentum $p = \sqrt{2mk}$; where $K =$ kinetic energy $= Q.V$
$\Rightarrow p = \sqrt{2mQV} \Rightarrow p \propto \sqrt{mQ} \Rightarrow \frac{p_{e}}{p_{\alpha}} = \sqrt{\frac{m_{e}Q_{e}}{m_{\alpha}Q_{\alpha}}} = \sqrt{\frac{m_{e}}{2m_{\alpha}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.