Ionized hydrogen atoms and α -particles with same momenta enters...

The radius of a charge particle $q$ moving in a magnetic field is given by,

$r = \dfrac{mv}{qB} = \dfrac{p}{qB}$; where $m$ is mass, $v$ is velocity and $p$ is momentum of the charge particle.

For constant momentum and magnetic field,

$r ∝ \dfrac{1}{q}$

So, the ratio of the radii of Hydrogen ion to $\alpha$-particle will be,
$\dfrac{{r}_{H}}{{r}_{\text{\alpha}}} = \dfrac{{q}_{\text{\alpha}}}{{q}_{H}} = \dfrac{2}{1}$
${r}_{H}: {r}_{\text{\alpha}} = 2: 1$.