Why does the daughter nucleus have more binding energy
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Answer:
I don't think it's quite right to say that "binding energy must increase" in a decay. That's a pretty good rule for heavy nuclei, but you're correct that the proton and neutron both have zero binding energy if they are free particles. There are plenty of other decays, like π→νμ or μ→eνν, where it doesn't make sense to talk about the binding energy on either side of the reaction.
The real rule is that the rest mass of the particle that decays must be heavier than the combined rest masses of all the particles produced in the decay. That's why a few neutron can decay to a proton but not the other way around. The way that binding energy works in nuclei can change this relationship, however. For example, a potassium-40 nucleus is heavier than an argon-40 nucleus, and also heavier than a calcium-40 nucleus, so potassium-40 undergoes both positive and negative beta decay.
Explanation: