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
As /u/polaris2acrux mentioned, there is indeed an additional (anti-)electron created during the p->n beta decay, but I’d like to mention something else with regards to this part of your post:
>Aren’t mater and energy subject to the laws of conservation or am I missing something?
If you look up the proton and neutron masses, you’ll find that the neutron is heavier than the proton. Since the electron and positron, as well as the electron neutrino and electron anti-neutrino, are equally massive, this means that there is mass gain during the p->n decay. Thus, this decay will only occur if it is possible for a bound state (such as an atom nucleus) to reach a lower energy level by this conversion. A free proton would never decay to a neutron.
They are subject to conservation; what you’re missing is that in beta+ decay a positron is also emitted: (p=>n & e+) in sort of your notation. The positron is basically an electron but antimatter version, with a positive charge, balancing that conservation law.
(Bear in mind, to fully conserve everything you also have to look at the spin charge, which is one of the things that led people to believe a “neutrino” was also being emitted.)
There’s another variant of beta+ decay called electron capture, where the reaction is more like (p & e => n) which is also balanced, just backwards.
It doesn’t make sense because you’re missing a few end products! Your intuition was spot on. Beta positive produces a positron and electron neutrino. A positron is an anti-electron–the positive charged counterpart to an electron. edit: (beta negative produces an electron anti-neutrino as well fwiw). I’ll let someone with a stronger background in this part of physics do an explanation of the weak nuclear force and what’s going on at a deeper level here.
edits: for clarity and improving the tone–which was more terse than I wanted the first time!
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.
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