When mantle rocks near the radioactive core are heated, they become less dense than the cooler, upper mantle rocks. these warmer rocks rise, while the cooler rocks sink. this movement of warmer and cooler mantle rocks creates pockets of circulation within the mantle called which are thought to be the force behind the movement of tectonic plates over the asthenosphere.

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?