One of the waste products of a nuclear reactor is plutonium–239 (239pu). this nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus (4he + 235u), the latter of which is also radioactive and will itself decay some time later. the energy emitted in the plutonium decay is 8.40 ✕ 10^−13 j and is entirely converted to kinetic energy of the helium and uranium nuclei. the mass of the helium nucleus is 6.68 ✕ 10^−27 kg, while that of the uranium is 3.92 ✕ 10^−25 kg (note that the ratio of the masses is 4 to 235).
a. calculate the velocities of the two nuclei, assuming the plutonium nucleus is originally at rest. (enter the magnitude of the velocities in m/s.)
b. how much kinetic energy in joules does each nucleus carry away? note that the data given here are accurate to three digits only.