Question

A proton, a deutron and an $\alpha$-particle having the same momentum, enters a region of uniform electric field between the parallel plates of a capacitor. The electric field is perpendicular to the initial path of the particles. Then the ratio of deflections suffered by them is

• A. 1 : 2 : 8
• B. 1 : 2 : 4
• C. 1 : 1 : 2
• D. None of these

Answer 1

The correct option is A 1 : 2 : 8

The deflection suffered by charged particle in an electric field is $y=\frac{qELD}{m{u}^2}=\frac{qELD}{p^2/m}$ $(p=mu)$
$\Rightarrow y\propto \frac{qm}{P^2}\Rightarrow y_p:y_d:y_{\alpha }=\frac{q_p{m}_p}{P_p^2}:\frac{q_d{m}_d}{P_d^2}:\frac{q_{\alpha }{m}_{\alpha }}{P_{\alpha }^2}$
Since $P_{\alpha }=P_d=P_p$ (given)
$m_p:m_d:m_{\alpha }=1:2:4$ and $q_p:q_d:q_{\alpha }=1:1:2$
$\Rightarrow y_p:y_d:y_{\alpha }=1\times 1:1\times 2:2\times 4=1:2:8$