A proton, a deuteron 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 [image:11_image21.emf]

Question

Dr. Abubacker · Accepted Answer

(a) The deflection suffered by charged particle in an electric field is
$y = \frac{qELD}{mu^{2}} = \frac{qELD}{p^{2}/m}\ \ \ \ \lbrack p = mubrack$
$\Rightarrow y \propto \frac{qm}{p^{2}} \Rightarrow y_{p}:y_{d}:y_{\alpha} = \frac{q_{p}m_{p}}{p_{p}^{2}}:\frac{q_{d}m_{d}}{p_{d}^{2}}:\frac{q_{\alpha}m_{\alpha}}{p_{\alpha}^{2}}$
Since $p_{\alpha} = p_{d} = p_{p}$ [Given]
$m_{p}:m_{d}:m_{\alpha} = 1\ :2\ :4$ and$\ q_{p}:q_{d}:q_{\alpha} = 1\ :1\ :2$
$\Rightarrow y_{p}:y_{d}:y_{\alpha} = 1 	imes 1:1 	imes 2\ :2 	imes 4 = 1\ :2\ :8$

Q. A proton, a deuteron 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

Explanation

Reviewed by Dr. Abubacker

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