Question

The ratio of momenta of an electron and an $\alpha -particle$ which are accelerated from rest by a potential difference of 100 V is

• A. $1$
• B. $\sqrt{2m_e/m_{\alpha }}$
• C. $\sqrt{m_e/m_{\alpha }}$
• D. $\sqrt{m_e/2m_{\alpha }}$

Answer 1

The correct option is D $\sqrt{m_e/2m_{\alpha }}$

By energy conservation, kinetic energy = electric potential energy

or $\frac{p^2}{2m}=qV$ or $p=\sqrt{2mqV}$

Here, $m_e=$ mass of electron and $m_{\alpha }=$ mass of alpha particle.

Magnitude of charge of electron , $q_e=e$ and $q_{\alpha }=2e$

and potential difference is constant i.e 100 V.

Thus, $\frac{p_e}{p_{\alpha }}=\frac{2m_{e}eV}{2m_{\alpha }\left(2e\right)V}=\sqrt{m_e/2m_{\alpha }}$