Assume that a group of explorers traveled to the Orion Nebula, a star-forming cloud at a distance of 1,300 light-years, using revolutionary technology that allowed them to travel at a speed very close to the speed of light. Observers back on Earth would say it took them to get there, but the travelers would say it took them to get there.

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-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?