For some isotopes of some very heavy nuclei, including nuclei of thorium, uranium, and plutonium, the nucleus will fission
(split apart) when it absorbs a slow-moving neutron.
For example, plutonium-241, with 94 protons and 147 neutrons, can fission when it absorbs a neutron and becomes
plutonium-242. The two fission fragments, called “daughter” nuclei, can be almost any two nuclei whose charges Q1 and
Q2 add up to 94e (where e is the charge on a proton), and whose nucleons add up to 242 protons and neutrons (Pu-242,
formed from Pu-241 plus a neutron).
One of the possible fission modes involves nearly equal fragments, silver nuclei (Ag-121) each with electric charge Q1 =
Q2 = 47e. The rest masses of the two daughter nuclei add up to less than the rest mass of the original parent nucleus. (In
addition to the two main fission fragments there are typically one or more free neutrons in the final state; in your analysis
make the simplifying assumption that there are no free neutrons, just two daughter nuclei.)
Objects involved in the reaction, where the rest mass is given in atomic mass units, and 1 amu = 1.66054 × 10−27 kg:
There are three states you should consider in your analysis: (1) The initial state of the Pu-242 nucleus, before it fissions. (2) The state just after fission, when the two silver nuclei are close together, and momentarily at rest. (3) The state when the silver nuclei are very far away from each other, traveling at high speed. A: The final speed of the fission products Your first task is to determine the final speed of each of the daughter nuclei in state (3), when they are far from each other. Figure 6.74 shows three important states in the process: