Which process generates nuclear power by splitting an atom's nucleus?

The process that generates nuclear power by splitting an atom's nucleus is fission. In fission, a heavy atomic nucleus, such as that of uranium-235 or plutonium-239, absorbs a neutron and becomes unstable, leading it to split into two smaller nuclei along with a few additional neutrons and a significant amount of energy. This energy release is what is harnessed in nuclear power plants to generate electricity.

Fission is distinct from fusion, which is the process of combining two light atomic nuclei to form a heavier nucleus, releasing energy as well, but it typically occurs under extremely high temperatures and pressures found in stars. Radiation refers to the emission of energy as electromagnetic waves or subatomic particles and is a byproduct of many nuclear processes but isn't a method in itself for generating nuclear power. Nuclear reactions encompass both fission and fusion processes, but the specific action of splitting an atomic nucleus is what defines fission, making it the correct answer in the context of the question.