A proton, an electron, and a Helium nucleus, have the same energy.

(2) As $m v r=q v B \Rightarrow r=\frac{m v}{q B}=\frac{\sqrt{2 m K . E .}}{q B}$

$\left[\right.$ As $: \frac{1}{2} \mathrm{mv}^{2}=\mathrm{K} . \mathrm{E} .$

$\Rightarrow \mathrm{m}^{2} \mathrm{v}^{2}=2 \mathrm{~m} \mathrm{~K} . \mathrm{E} .$

$\Rightarrow \mathrm{mv}=\sqrt{2 \mathrm{~m} \mathrm{~K} . \mathrm{E} .}]$

For proton, electron and $\alpha$-particle,

$\mathrm{m}_{\mathrm{He}}=4 \mathrm{~m}_{\mathrm{p}}$ and $\mathrm{m}_{\mathrm{p}} \gg \mathrm{m}_{\mathrm{e}}$

Also $\mathrm{a}_{\mathrm{He}}=2 \mathrm{q}_{\mathrm{p}}$ and $\mathrm{q}_{\mathrm{p}}=\mathrm{q}_{\mathrm{e}}$

$\therefore$ As $\mathrm{KE}$ of all the particles is same then,

$\mathrm{r} \alpha \frac{\sqrt{\mathrm{m}}}{\mathrm{q}}$

$\therefore \mathrm{r}_{\mathrm{He}}=\mathrm{r}_{\mathrm{p}}>\mathrm{r}_{\mathrm{e}}$