Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. These cyclotrons typically accelerate H− (the hydride ion, which has one proton and two electrons) to an energy of 5 MeV to 20 MeV. This ion has a mass very close to that of a proton because the electron mass is negligible-about 1/2000 of the proton’s mass. A typical magnetic field in such cyclotrons is 1.9 T.
a) What is the speed of a 5.0−MeVH−?
b) If the H has energy 5.0 MeV and B = 1.9 T, what is the radius of this ion’s circular orbit?