Eli5: how can a proton turn into a neutron in Beta Decay?

Question

We recently touched on the subject of radioactivity in class, and we learned about all the types of radiation an atom can emit(gama/beta-+/delta), and what their products are.

What I don’t understand is in beta- a neutron turns into 1 proton and 1 electron, but in beta+ a proton turns into a neutron, how is that possible [(n=>p+e) ==(p=>n)(e?????)]? Aren’t mater and energy subject to the laws of conservation or am I missing something? Where is the electron? Thank you in advance

In: Physics

Answer 1

Neutrons have a higher rest mass than protons, so beta+ decay of an isolated proton would require an input of extra energy. Therefore, beta+ decay never happens for a single proton — as far as we know, protons are stable forever.

beta+ decay happens when an atom has a nucleus where the number of protons is so high that it is energetically possible for one of them to convert to a neutron (plus antielectron and neutrino). This can happen due to a combination of facts:

* Pauli exclusion principle: no two protons (or neutrons) can exist in the same nucleus with exactly the same quantum numbers. The first protons are in the lowest energy levels, but as you add protons to the nucleus, the new ones have to go into higher and higher energy levels. Ditto the neutrons.
* Neutrons and protons have completely separate energy levels. So (mostly) the energy level of the highest energy proton has nothing to do with the energy level of the highest energy neutron. (This isn’t exactly true, but it’s close enough unless you want to get a PhD in nuclear physics).
* Protons have a problem that neutrons don’t — they repel each other electrically, so the energy levels for protons go up faster than the energy levels for neutrons, i.e. adding one more proton into a nucleus with 50 protons adds a lot more energy than adding one more neutron into a nucleus with 50 neutrons.

As a result, it can fairly easily happen that a nucleus has a proton at such a high energy level compared to the lowest neutron energy level that isn’t occupied, that even after factoring in the energy it takes to make the antielectron, neutrino, and the extra mass of a neutron, it still has excess energy. So beta+ can happen.

​

Fun fact: there’s a competing process called electron capture, where some unfortunate electron minding it’s own business flittering around the nucleus is “eaten” by a proton to form a neutron and neutrino.