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(9 pts.) Proton Racetrack. (a) A cyclotron with radius R and magnetic field strength B is used to accelerate ions of mass m and charge q to non-relativistic velocities. In order for the cyclotron to operate effectively, its frequency f must be set to qB f = 1 2mm Using elementary ideas from Physics I and Physics II, show clearly where this result comes from. (b) As the ions accelerate, they spiral outwards. In terms of the variables above, how fast are the ions moving when they reach the outer edge of the cyclotron (at a distance R from the center)? (c) Suppose that the cyclotron parameters are adjusted to produce protons with kinetic energies of 0.6 MeV. If the same cyclotron (potentially operated at a different frequency) is then used to accelerate He++ ions, what will the Helium ion kinetic energies be? The Helium ion kinetic energies will be (circle one): approximately four times the proton kinetic energies. (approximately three times the proton kinetic energies. (iii) approximately twice the proton kinetic energies. (approximately 3/2 the proton kinetic energies. (v) approximately 4/3 the proton kinetic energies. (vi) about the same as the proton kinetic energies. (vii) approximately 3/4 the proton kinetic energies. (viii) approximately 2/3 the proton kinetic energies. (x) approximately 1/2 the proton kinetic energies. approximately 1/3 the proton kinetic energies. Be sure to explain how you arrived at your answer.