Question

A proton,a deutron and an $\alpha$-particle have equal kinetic energies. Compare the radii of their paths when a normal magnetic field is applied.

Answer 1

$r=\frac{\sqrt{2km}}{Bq}orr\propto \frac{\sqrt{m}}{q}$
$r_p:r_d:r_{\alpha }={(\frac{\sqrt{m}}{q})}_p:{(\frac{\sqrt{m}}{q})}_d:{(\frac{\sqrt{m}}{q})}_{\alpha }$
$=\frac{\sqrt{1}}{1}:\frac{\sqrt{2}}{1}:\frac{\sqrt{4}}{2}$
$=1:\sqrt{2}:1$