The maximum velocity to which a proton can be accelerated in a cyclotron of $10\, MHz$ frequency and radius $50\, cm$ is

Bohr model is applied to a particle of mass '$m$' and charge '$q$' moving in a plane under the influence of a transverse magnetic field '$B$'. The energy of the charged particle in the $n^{th}$ level will be ($h$ = Planck's constant).

$A$ cyclotron's oscillator frequency is $n$ and the radius of the dees is $r$. The operating magnetic field $(B)$ for accelerating protons of charge $q$ and the kinetic energy of the protons produced by the accelerator are respectively ($m$ and $v$ are the mass and velocity of the proton).

$A$ charged particle moves along a circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to $4$ times its initial value. What will be the ratio of the new radius to the original radius of the circular path of the charged particle?

In a cyclotron experiment, if we assume that the maximum radius attained by any charged particle is equal to the radius of the dees, then the minimum kinetic energy gained by the particles will be for

The cyclotron frequency of an electron gyrating in a magnetic field of $1\, T$ is approximately