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When Carbon-14 emits a beta particle, the Carbon-14 atom becomes a Nitrogen-14 Atom.
The Mass Number for any isotope is the addition of all the protons and neutrons in the nucleus.
Notice that the farther away the Mass Number gets from 12-13, the faster they break down (The blue numbers indicate half-lives, the time it takes for one half of the atoms in a sample to break down.).
So the farther the carbon is from the norm, the more unstable it is. They have too many neutrons so they breakdown, releasing a beta particle which effectively converts a neutron into a proton.
Neutrons that come from these fragmented molecules run into other molecules.
When a neutron collides into a Nitrogen-14 atom, the Nitrogen-14 turns into Carbon-14 along with a proton.
Thus the breakdown of radioactive atoms is a self-corrective process; those Isotopes which have too many neutrons loose a neutron in the beta decay, and those Isotopes which have too few neutrons gain a neutron in the positron decay.