Question

An alpha particle and a Proton have same velocity when they enter a uniform magnetic field the period of revolution of Alpha particle will be _______time of protone

Answer 1

time period of charged particle is given by, $T=\frac{2\pi m}{qB}$

where m is mass of charged particle, q is charge and B is magnetic field in which enters the charged particle.

charge on proton, $q_p$ = 1e

charge on alpha particle, $q_{\alpha}$ = 2e

[ here e indicates 1.6 × 10^-19C [/tex]

mass of proton, $m_p$ = 1/4 × mass of alpha particle, $m_{\alpha}$

so, $\frac{\textbf{time period of proton}}{\textbf{time period of alpha particle}}=\frac{m_pq_{\alpha}}{m_{\alpha}q_p}$

= $\frac{m_p}{4m_p}\times\frac{2q_p}{q_p}$

= 1/4 × 2 = 1/2

hence, time period of alpha particle = 2 × time period of proton.