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 portion. 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. 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Time period of revolution $T=\frac{2\pi r}{v}$

using $Bqr=mv$ $⟹T=\frac{2\pi m}{Bq}$

$\therefore$ $T\propto \frac{m}{q}$

Hence reason statement is correct.

As $m_{\alpha }=4m_p$ and $q_{\alpha }=2q_p$

$\therefore$ $\frac{T_{\alpha }}{T_p}=\frac{m_{\alpha }{q}_p}{q_{\alpha }{m}_p}$

$\frac{T_{\alpha }}{T_p}=\frac{4m_p{q}_p}{2q_p{m}_p}$ $⟹T_{\alpha }=2T_p$

Thus Assertion is also correct and the reason explains the assertion very well.