A proton , a deuteron and an $\alpha -$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. if  $r_p,r_d and{r}_a$ denote respectively the radii of the trajectories of these particles, then

In the situation described in question we have kinetic energies of the particles

$k_p=k_d=k_a=k\left(say\right)$

We know that charges on particles are

And         $m_p=m,m_d=2mand{m}_a=4m$

In uniform magnetic field radius of circular motion is given as

$r=\frac{mv}{qB}=\frac{\sqrt{2mK}}{qB}$

$\Rightarrow$  $r_P=\frac{\sqrt{2mK}}{eB}$

$\Rightarrow$    $r_d=\frac{\sqrt{2\left(2m\right)K}}{eB}$

$\Rightarrow$    $r_a=\frac{\sqrt{2\left(4m\right)K}}{\left(2e\right)B}{r}_p$

$\Rightarrow$     $r_a=r_p<r_d$