# Why does beta-plus decay (positron decay) have a 1.022 MeV energy requirement rather than 0.511 MeV + the binding energy of an electron?

From my understanding, beta-plus decay is only possible when certain energy requirements are met due to the fact that the atom will need to emit a positron particle, which has a rest energy-mass equivalent of 511 KeV. Therefore the difference in the rest energy-mass equivalent of the entire daughter atom vs of the parent atom (or, in other words, its difference in binding energy) has to be at least 511 KeV in order to (in layman terms) ‘produce’ a positron.

However in most physics textbooks they go a step further and mention how the energy requirement is actually double that (1.022 MeV). They explain it’s due to the fact that positron decay converts a proton into a neutron, decreasing the atomic number by 1, meaning the daughter atom would have an excess electron that will also need to be ejected from the atom.

I can't understand how this orbital electron can influence the decay properties of its nucleus. I will illustrate what I don't understand in an imaginary counter-example:

Let's assume the parent nucleus has atomic number Z_1, neutron number N_1, and charge 0 (Z_1 electrons). Let's then assume the theoretical lower-energy daughter state has atomic number Z_2 = Z_1 - 1, neutron number N_2 = N_1 + 1, and charge -1 (Z_2 + 1 electrons). Let's finally assume the transition energy between those two states is lower than 1,022 KeV, say, 612 KeV, and that the binding energy of an electron in that daughter state is 1 KeV.

Why couldn't this nucleus go from the first (Z_1, N_1) state to the (Z_2, N_2) state, use 611 KeV to emit a positron (511 KeV would go towards the "energy-mass" of that positron and 100 KeV would be used as its kinetic energy and the neutrino), and use 1 KeV afterwards to eject one of the valence electrons from the daughter atom, for a total of 612 KeV of transition energy?

• Re: "I can't understand how this orbital electron can influence the decay properties of its nucleus." - there are a variety of reasons that orbiting electrons impact decay properties. One, of course, is electron capture (a bare Be-7 ion cannot decay by EC with no electrons to capture). There are also low energy beta decays that can only occur with a highly stripped ion because the low energy electron can't escape and has no available energy level to occupy in a neutral atom. Nature is weird... Commented Nov 4, 2022 at 14:24