An $\alpha$ - particle moving with a velocity u in a uniform magnetic field is moving in a circular path at frequency $\text{'}f\text{'}$ called the cyclotron frequency. The cyclotron frequency of a proton moving with a speed 2u in the same magnetic field will be

The cyclotron frequency is given by

$f=\frac{q B}{2\pi m}$

It is independent of the speed of the particle and the radius of its circular path. Now $v\propto q/m$. The charge of a proton is half that of an $\alpha$-particle and the mass of a proton is one-fourth. Therefore, v will be doubled.