Question

An electron and a proton are projected with same velocity perpendicular to a magnetic field. Which particle have greater frequency?

Answer 1

The centripetal acceleration is provided by the magnetic field. Hence,

$\frac{m{v}^2}{r}=qvB$

$⟹mv=qBr$

The frequency of revolving particle,$f=\frac{v}{2\pi r}$

$=\frac{qB}{2\pi m}$

$f\propto \frac{1}{m}$

Hence electron has higher frequency because of its lower mass.