Question

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

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (A)

The period of a charged particle in a magnetic field is given by $T=\frac{2\pi m}{qB}, i.e., T \propto \frac{m}{q}$
We know that, $m_{p} = m, m_{\alpha} = 4m, q_{p} = e, q_{\alpha} = 2e$
$\therefore \frac{T_{p}}{T_{\alpha}}=\frac{1}{2}$ or $T_{\alpha}=2T_{p}$