Application One of the waste products of a nuclear reactor is plutonium-239 (239 Pu) . This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus (4 He + 235 U), 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. (b) How much kinetic energy does each nucleus carry away? Note that the data given here are accurate to three digits only.
Step-by-step solution In this problem we have to calculate the velocities of the two nuclei,kinetic energy of the nucleus as per the data given above respectively: Step 1 of 6 (a) Plutonium is at rest initially. So, the initial momentum was zero. Step 2 of 6 The expression of conservation of momentum is Here, is mass of plutonium nucleus, is mass of helium, is mass of uranium, is initial velocity of plutonium, is final velocity of helium and is final velocity of uranium. Substitute, kg for , kg for , and 0 m/s for in the expression of conservation of momentum, Divide the expression by and rearrange, Step 3 of 6 The energy emitted by the plutonium is fully converted into the kinetic energy of the helium and uranium.