A proton starts out at the central point of a cyclotron with radius R $=50$ cm

in which a uniform magnetic field B $=1$ T is established perpendicular to the plane of

motion of the proton. Determine: a$)$ the cyclotron frequency; b$)$ the maximum velocity

of the proton in terms of the speed of light c; c$)$ the maximum kinetic energy in eV;

d$)$ the number of full cycles the proton makes before reaching its maximum energy; e$)$ the

amount of time the proton spends in the cyclotron; f$)$ how will your answers change if

instead of the proton, it is a deuteron $($a $2$H nucleus, which has the same charge e and

roughly twice the mass of the proton mp$)$ that is being accelerated?