Question

Assertion :If a proton and an $\alpha$-particle enter a uniform magnetic field perpendicularly with the same speed, then the time period of revolution of the $\alpha$-particle is double than that of proton. Reason: In a magnetic field, the time period of revolution of a charged particle is directly proportional to mass.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

The magnetic force on revolving particle provides the centripetal force due make particle move in circular orbit.

Thus $\frac{m{v}^2}{R}=qvB$

$⟹\frac{v}{R}=\frac{qB}{m}$

Hence the time period of revolution, $T=\frac{2\pi R}{v}$ $=\frac{2\pi m}{qB}$

Hence $T\propto m$

The mass of $\alpha$ nucleus four times that of proton, and charge of $\alpha$ particle is double of that of proton.

Hence the time period of revolution of $\alpha$ particle is double of that of proton.