JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Electrostatics

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α

particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be :

(A) $2 : 1$
(B) $22 : 1$ ✓ Correct
(C) $42 : 1$
(D) $8 : 1$

Answer: (B)

Solution

When a charged particle is accelerated through potential difference V, it gains kinetic energy

q V

.

The momentum is:

p = 2 m E = 2 m q V

For an α-particle: mass

m_{α} = 4 m_{p}

, charge

q_{α} = 2 e

For a proton: mass

m_{p}

, charge

q_{p} = e

Ratio:

\frac{p _{α}}{p _{p}} = \frac{m _{α} q _{α}}{m _{p} q _{p}} = \frac{4 m _{p} \times 2 e}{m _{p} \times e} = 8 = 22

Therefore, the ratio is

22 : 1

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Single correct option

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