C. The absorption of a free-moving neutron by the atom's nucleus
In a nuclear fission reaction, the nucleus of an atom becomes unstable when it absorbs a free-moving neutron. This can cause the nucleus to break apart into two or smaller fragments, releasing a large amount of energy in the process. Other factors, such as the temperature and pressure of the surrounding environment, can also affect the stability of the nucleus, but the absorption of a neutron is typically the primary cause of instability in a nuclear fission reaction. Control rods, which are used to regulate the rate of the reaction, do not directly cause the nucleus to become unstable, and the absorption of protons by the nucleus is not typically a factor in nuclear fission reactions.