Actually one should answer that neutrons do decay inside the nucleus, but, as they are bound to other nucleons (protons and neutrons) this can happen with a different constrain with respect to free neutrons: for a free neutron the decay is allowed because its mass is larger than the sum of the masses of decay products (a proton, an electron and an antineutrino), whereas the mass difference is converted into kinetic energy shared among the three final particles. On the other hand, when a neutron is bound inside a nucleus, it can be transformed in the same final particles only if the mass of the parent nucleus, into which it is bound, is larger than the mass of the daughter nucleus plus the electron and the antineutrino masses (the proton remains bound in the daughter nucleus). This circumstance, in turn, is related to the binding energy of the two nuclei (parent and daughter), which depends on their structure (volume, surface, charge, pairing). One should note that for bound protons, similar considerations lead to the beta-plus decay, while free proton decay is forbidden. apart from a very slight effect not yet experimentally proven.

You can try do argue with the energy balance. Decay of a neutron will be a beta-minus decay. You will get one p more. If this state is lower in energy, the decay happens. If the daughter nucleus is higher in energy, the n-decay is forbidden.

Actually one should answer that neutrons do decay inside the nucleus, but, as they are bound to other nucleons (protons and neutrons) this can happen with a different constrain with respect to free neutrons: for a free neutron the decay is allowed because its mass is larger than the sum of the masses of decay products (a proton, an electron and an antineutrino), whereas the mass difference is converted into kinetic energy shared among the three final particles. On the other hand, when a neutron is bound inside a nucleus, it can be transformed in the same final particles only if the mass of the parent nucleus, into which it is bound, is larger than the mass of the daughter nucleus plus the electron and the antineutrino masses (the proton remains bound in the daughter nucleus). This circumstance, in turn, is related to the binding energy of the two nuclei (parent and daughter), which depends on their structure (volume, surface, charge, pairing). One should note that for bound protons, similar considerations lead to the beta-plus decay, while free proton decay is forbidden. apart from a very slight effect not yet experimentally proven.

@Filippo,

you are right, of course you have to consider the whole decay energy (mass equivalents and kinetic energies).

Protons have not been observed to decay, but neutrons decay all the time. The lifetime of a neutron all by itself is about 886 seconds. Neutrons decay into a proton, an electron, and an electron-type antineutrino. This decay proceeds by the (mostly) understood process of the weak interaction, by exchange of a virtual W- boson between a down-type quark in the neutron (changing it into an up-type quark), and the electron and antineutrino. There are still some mysteries about the weak interaction (Why is it there? Why is it weak? Which can be formulated as -- why is the W boson heavy? It has a mass of about 80 proton masses.). Neutrons weigh just a little more than protons so this process proceeds. If protons were heavier, it would be protons that decayed via the weak interaction and not neutrons.

• Neutrons decay when by themselves but do not do so when bound inside of atomic nuclei (well, many kinds of nuclei. Some nuclei in fact decay in exactly this way -- one of the neutrons decays). The energy levels inside nuclei are such that if a neutron were to decay into a proton, it would have to find a place in a higher-energy level (because of Pauli's exclusion principle keeping it out of lower-lying energy levels), and the total energy doesn't add up to enough to allow the neutron to decay. But in some nuclei, neutron decay is possible and favored.

The Beta decay of a free neutron is a spontaneous phenomenon and as any other spontaneous phenomenon in nature, it requires a lower energy for the final state (part of the mass-energy of the the decaying neutron is transformed in kinetic energy of the decaying products).

If the neutron is part of a nucleus, the energy gained from its decaying could be less than the growth of the coulombian energy due to the subsequent presence in the nucleus of the proton resulting from the decaying of the neutron.

The decay of a neutron in a nucleus is possible if the process is energetically favourable, as for heavy isotopes.