Changes

*Lepton number.  The lepton numbers can be thought of as "electron-ness", "mu-ness", and "tau-ness".  Electrons and positrons have electron-ness of +1 and -1 respectively (and zero for the other two).  Here is where the neutrinos come into play.  An electron neutrino has an electron-ness of +1, while and anti-neutrino has -1.  That's why the neutron-to-proton-and-electron transformation needs to create the antineutrino to carry off the -1, compensating for the +1 of the electron.

*Lepton number.  The lepton numbers can be thought of as "electron-ness", "mu-ness", and "tau-ness".  Electrons and positrons have electron-ness of +1 and -1 respectively (and zero for the other two).  Here is where the neutrinos come into play.  An electron neutrino has an electron-ness of +1, while and anti-neutrino has -1.  That's why the neutron-to-proton-and-electron transformation needs to create the antineutrino to carry off the -1, compensating for the +1 of the electron.

==What can happen==

==The general principle==

With these preliminaries out of the way, the general rule can be stated:

With these preliminaries out of the way, the general principle can be stated:

:Any beta transformation will happen, with some probability, if the conservation laws are satisfied and the masses of the results add up to less than the masses of the original particle(s).

:Any beta transformation will happen, with some probability, if the conservation laws are satisfied and the masses of the results add up to less than the masses of the original particle(s).  If it '''can''' happen, it '''will''' happen.

The mass of the neutron is 1.008664916 amu, that of the proton is 1.007276467 amu, and that of the electron is .000548579909070 amu.  (The pass of the antineutrino is negligible.)  The lost mass is .00083986909093, which is carried off in the kinetic energy of the result particles, in accordance with [[E=mc²]].

The mass of the neutron is 1.008664916 amu, that of the proton is 1.007276467 amu, and that of the electron is .000548579909070 amu.  (The pass of the antineutrino is negligible.)  The lost mass is .00083986909093, which is carried off in the kinetic energy of the result particles, about 0.78 MeV, in accordance with [[E=mc²]].

 

*A: Yes, a neutron, standing alone, is unstable.  It has a [[half-life]] of about 15 minutes.  To see why this doesn't happen for neutrons inside a nucleus, keep reading.

The reverse transformation, turning a proton into a neutron, positron, and neutrino, has a negative energy budget, so it does not occur.

The reverse transformation, turning a proton into a neutron, positron, and neutrino, has a negative energy budget, so it does not occur.