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Rather than considering what happens to individual nuclei it is perhaps easier to consider a hypothetical nucleus that can undergo many of the major forms of radioactive decay. This hypothetical nucleus is shown below:
Firstly we can see two protons and two neutrons being emitted together in a process called alpha-decay. Secondly, we can see that a proton can release a positron in a process called beta-plus decay, and that a neutron can emit an electron in a process called beta-minus decay. We can also see an electron being captured by a proton. Thirdly we can see some energy (a photon) being emitted which results from a process called gamma-decay as well as an electron being attracted into the nucleus and being ejected again. Finally there is the rather catastrophic process where the nucleus cracks in half called spontaneous fission.
We will now describe each of these decay processes in turn.