Question

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

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

Answer 1

Answer: (C)

$\sqrt{\frac{m_e}{m_{\alpha }}}$

Since both particles are accelerated by same potential difference, their kinetic energies are equal.

Thus $\frac{1}{2}{m}_e{v}_e^2=\frac{1}{2}{m}_{\alpha }{v}_{\alpha }^2$

$⟹\frac{v_e}{v_{\alpha }}=\sqrt{\frac{m_{\alpha }}{m_e}}$

Thus the ratio of their momenta=$\frac{m_e{v}_e}{m_{\alpha }{v}_{\alpha }}=\sqrt{\frac{m_e}{m_{\alpha }}}$

Hence correct answer is option C.