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

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

For constant momentum and magnetic field,

$r\propto \frac{1}{q}$

So, the ratio of the radii of Hydrogen ion to $\alpha$-particle will be,
$\frac{r_H}{r_{\text{α}}}=\frac{q_{\text{α}}}{q_H}=\frac{2}{1}$
$r_H:r_{\text{α}}=2:1$.