Assertion: If a proton and an α-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of α - 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.

Question

Assertion: If a proton and an α-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of α - 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

Tardigrade Admin · Accepted Answer

The period of a charged particle in a magnetic field is given by T=(2π m/qB), i.e., T propto (m/q) We know that, mp = m, mα = 4m, qp = e, qα = 2e ∴ (Tp/Tα)=(1/2) or Tα=2Tp

If both assertion and reason are true and reason is the correct explanation of assertion

If both assertion and reason are true but reason is not the correct explanation of assertion

If assertion is true but reason is false

If both assertion and reason are false

The period of a charged particle in a magnetic field is given by T=qB2πm​,i.e.,T∝qm​ We know that, mp​=m,mα​=4m,qp​=e,qα​=2e ∴Tα​Tp​​=21​ or Tα​=2Tp​

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