Cyclotron with 1500 V between the two dees

[gsquare567]

Homework Statement

A cyclotron is designed to accelerate deuterium nuclei. (Deuterium has one proton and one neutron in its nucleus.)
[ANSWERED] (a) If the cyclotron uses a 2.0-T magnetic field, at what frequency should the dee voltage be alternated?
[ANSWERED] (b) If the vacuum chamber has a diameter of 0.90 m, what is the maximum kinetic energy of the deuterons?
(c) If the magnitude of the potential difference between the dees is 1500 V, how many orbits do the deuterons complete before achieving the energy from part (b)?

Homework Equations

frequency of particles in a cyclotron = (q * B) / (2 * PI * m), where q is the charge of the particle, B is the magnetic field of the cyclotron, and m is the mass of the particle

radius of a particle's circular motion in a cyclotron = (m * v) / (q * B)

The Attempt at a Solution

I have (what I think are) solutions for (a) and (b):
(a) f = qB/(2PIm) = eB/(2PIm) = 1.52 * 10^7 revolutions per second
(b) r = 0.45m = m * v-max / (qB)
v-max = 4.31 * 10^7 m/s
KE-max = 1/2mv-max^2 = 3.10 * 10^-12 J
(c)
...
I have no idea how to use the voltage to determine their speed or KE, all i know is:
electric potential = qV
but i don't know how, or if that helps.

 

[Delphi51]

The particle gains energy qV each time it crosses from one dee to the other. Would that be twice per orbit? Set n*2qV = KEmax from (b) and solve for n.

 

[gsquare567]

Thanks so much! I didn't know that it gains qV every time. I guess that's because the cyclotron is doing qV work on the particle when it is passed from one dee to the other?

 

[Delphi51]

Yes, you could work it out that way. Or use the definition of electric potential difference as the "energy per charge".