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 $20 MHz$. The operating magnetic field for accelerating protons is (charge of proton $= 1.6 \times 10^{-19} C$,mass of proton $= 1.67 \times 10^{-27} kg$). (in $T$)

$A$ cyclotron is used to accelerate protons. If the operating magnetic field is $1.0\,T$ and the radius of the cyclotron 'dees' is $60\,cm$,the kinetic energy of the accelerated protons in $MeV$ will be.
[use $m_{p} = 1.6 \times 10^{-27}\,kg, e = 1.6 \times 10^{-19}\,C$]

Verify that the cyclotron frequency $\omega = \frac{eB}{m}$ has the correct dimensions of $[T]^{-1}$.

An alternating electric field,of frequency $f$,is applied across the dees (radius $\approx R$) of a cyclotron that is being used to accelerate protons (mass $\approx m$). The operating magnetic field $(B)$ used in the cyclotron and the kinetic energy $(K)$ of the proton beam,produced by it,are given by:

In a cyclotron,the angular frequency of a charged particle is independent of