A cyclotron designed to accelerate protons has an outer radius of $0\mathrm{.}570$ m$.$ The protons are emitted nearly at rest from a source at the center and are accelerated through $600$ V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is $0\mathrm{.}400$ T$.$

$($a$)$ Find the cyclotron frequency for the protons in this cyclotron.

Your response differs from the correct answer by more than $10\%.$ Double check your calculations. rad$/$s

$($b$)$ Find the speed at which protons exit the cyclotron.

m$/$s

$($c$)$ Find their maximum kinetic energy.

eV

$($d$)$ How many revolutions does a proton make in the cyclotron?

revolutions

$($e$)$ For what time interval does one proton accelerate?

s