# Binding energy of the daughter nucleus

In radioactivity, the total binding energy of parent nucleus must be greater than the daughter nucleus. In alpha decay, uranium has greater binding energy because it is large but in beta plus decay (positron) proton changes to neutron then binding energy of the daughter nucleus must increase so how can this happen?

• Why must the binding energy of the nucleus increase after $\beta^+$ decay? May 16 '18 at 23:07

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 $\pi\to\nu\mu$ or $\mu\to e\nu\nu$, where it doesn't make sense to talk about the binding energy on either side of the reaction.