Sorry for being ignorant, but I'm in high school and our chemistry teacher barely went over beta decay. I decided to do some research and learned that in β+ decay, positrons are emitted from protons in order to turn it into a neutron. But positrons have mass, so where does that mass come from? Do protons "give it mass"? If so, why wouldn't protons lose mass, and how could they become neutrons if neutrons are more massive?
[Physics] What happens to mass during beta decay
electronsneutronsnuclear-physicsprotonsradiation
Best Answer
In beta decay, the mass difference between the parent and daughter particles is converted to the kinetic energy of the daughter particles. For instance, in the decay of the free neutron, $$ \rm n \to p + e^- + \bar\nu_e, \tag{$\beta^-$ decay} $$ the difference between the mass on the left and the mass on the right is about $0.78\,\mathrm{MeV}/c^2$, and this is the energy liberated in the decay. (If you're a chemistry person, an eV is a useful energy unit; the $E=mc^2$ conversion is roughly $1000\,\mathrm{MeV}\approx 1\,\mathrm{amu}\times c^2$.) Equivalent processes like $$ \rm p + \bar\nu_e \to n + e^+ \tag{neutrino capture} $$ don't occur unless the kinetic energy on the left side is already large enough to account for the extra mass on the right side. Since the electron/positron mass is about $0.51\,\mathrm{MeV}/c^2$, neutrino capture on protons at rest is impossible for neutrinos with less than $1.80\rm\,MeV$ kinetic energy. This means, among other things, that neutrinos emitted from neutron decay at rest will never have enough energy to cause positron emission on protons at rest elsewhere.
You get $\beta^-$ decay from free neutrons because free neutrons are heavier than free protons. However it's not the case for all nuclei that the more positive isobars are less massive. For instance, the mass difference between postassium-40 and argon-40 is about $1.50\,\mathrm{ MeV}/c^2$, with potassium (19 protons) heavier than argon (18 protons), so the decay $$ \rm ^{40}_{19}K \to {}^{40}_{18}Ar^- + \beta^+ + \nu_e + 0.48\, MeV $$ is allowed (though rarer than some other branches) and merrily proceeding inside the bananas on your kitchen counter.