If this were true, then there should be no limit to the number of neutrons found in stable atoms.

First, let us start with the largest stable atom.

A stable atom will have as many electrons as it has protons.

But, atoms that have too few or too many neutrons than a stable atom can be radioactive.

But for a given element, the radioactive atoms are usually slightly heavier than the stable atoms.

Glucose can be labeled with either stable or radioactive atoms.

There are no stable atoms with mass numbers 5 or 8.

There are stable atoms with all other mass numbers up to 208 with the exceptions of 147 and 151.

With the possible exception of the pair Tellurium-123 and Antimony-123, odd mass numbers are never represented by more than one stable atom.

The over-excited particles emit so much light, in fact, that their energies fall to a level at which they can combine to form stable atoms.