$A$ cyclotron's oscillator frequency is $10 \text{ MHz}$ and the operating magnetic field is $0.66 \text{ T}$. If the radius of its dees is $60 \text{ cm}$, then the kinetic energy of the proton beam produced by the accelerator is: (in $\text{ MeV}$)

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

$A$ 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 $m_{p} = 1.6 \times 10^{-27}\,kg, e = 1.6 \times 10^{-19}\,C$]

Explain the working of a cyclotron and give its uses.

$A$ cyclotron's oscillator frequency is $10 \; MHz$. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is $60 \; cm$,what is the kinetic energy (in $MeV$) of the proton beam produced by the accelerator? $(e = 1.60 \times 10^{-19} \; C, m_p = 1.67 \times 10^{-27} \; kg, 1 \; MeV = 1.6 \times 10^{-13} \; J)$

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).