Is it possible for an atom to emit a neutron or a proton?
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google for "<particle-type>+emission"
In short, yes.
In their ground-state, nuclei will only emit neutrons or protons if they are unstable with respect to neutron or proton emission, in the same way as for alpha emission. In general, this occurs close to the neutron or proton drip-lines, respectively. That is, their neutron (proton) separation energies are negative, as shown below.
Now, when you produce nuclei via fusion, you tend to produce them with high excitation where their level densities are very high - these are called "hot compound nuclei". Nuclei in this state will release energy by evaporating one or more nucleons. Heavy compound nuclei emit neutrons, and light compound nuclei will also emit protons and other charged particles (e.g. alphas).
I am writing a book, and I said that nuclei can emit protons and neutrons, and was just checking if it is true
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