Question

An $\alpha$-particle (mass $4 \,amu$ ) and a singly charged sulfur ion (mass $32\, amu$ ) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $\alpha$-particle and the sulfur ion move in circular orbits of radii $r_{\alpha}$ and $r_{s}$, respectively. The ratio $\left(r_{s} / r_{a}\right)$ is _____.

Answer 1

$ r _{a} =\frac{\sqrt{2 m _{a} q _{a} V }}{ q _{a} B }$
$ r _{ S } =\frac{\sqrt{2 m _{ S } q _{ s } V }}{ q _{ s } B } $
$\frac{ r _{ S }}{ r _{a}} =\sqrt{\frac{ m _{ s }}{ q _{ S }} \frac{ q _{a}}{ m _{ a }}}=\sqrt{\left(\frac{32}{1}\right)\left(\frac{2}{4}\right)} $
$\frac{ r _{ s }}{ r _{a}} =4$