Proton beta plus decay -proton proton chain

[gooey science]

proton beta plus decay --proton proton chain

Im a biologist so forgive the ignorance.

In beta-plus decay, a proton decays into a neutron and emmits a β+ and an electron neutrino. If the neutron is more massive than the proton where did the extra mass come from?

Im asking in the context of the proton-proton chain. The first step in the stellar core creates a di-proton that decays (rarely) into a deuterium (more massive than the di-proton), and emits a β+ and an electron neutrino (both have mass). So, the reaction actually emits massive particles and still produces a more massive end product. what am I missing that explains how this happens? do vacuum fluctuations contribute this mass increase? is the radius of a neutron larger than a proton? providing more "room" for vacuum fluctuations, or do quarks alone account for the mass difference?

And, I have heard the "we are all stardust" and "stars are reactors that build heavier atoms" anecdotes. But, because free neutrons decay into protons, and since neutrons are needed to create the more massive atoms that known life requires, isn't it more correct to say that stars produce neutrons? granted they are in nuclei, but still, does my point register? yes they build heavier elements, especially in their deaths, but main sequence stars are really building neutrons. right?

 

[Bill_K]

In beta-plus decay, a proton decays into a neutron and emmits a β+ and an electron neutrino. If the neutron is more massive than the proton where did the extra mass come from?

From the binding energy of the nucleus. You have to take into count the entire mass of the parent and daughter nuclei, not just the one proton and neutron. The mass of a nucleus is less than the sum of the masses of the protons and neutrons that make it up. This difference is called the binding energy.

Nuclei prefer to have a certain ratio of protons to neutrons. The nuclei with this ratio have the greatest binding energy and are the most stable. This is called the valley of stability. Nuclei with 'too many' protons are not as tightly bound, and they can increase their binding energy by turning a proton into a neutron (positron emission). Nuclei with 'too few' protons are also not as tightly bound, and they can increase their binding energy by turning a neutron into a proton (electron emission).

The increase in binding energy supplies the energy needed to make the decay possible.