Even-Odd Nature of Proton and Neutron Numbers

Whether the proton count $Z$ and neutron count $N$ of a nuclide are each individually even or odd turns out to be a strong predictor of nuclear stability. Tallying up the naturally occurring stable nuclides by this even/odd split gives four groups: 165 nuclides have both $Z$ and $N$ even; 55 have $Z$ even and $N$ odd; 50 have $Z$ odd and $N$ even; and only 4 have both $Z$ and $N$ odd.

Even-$Z$, even-$N$ nuclides make up about 85% of the mass of the Earth's crust, and their sheer abundance is itself the evidence that this combination is the most stable: protons tend to pair up with other protons, and neutrons with other neutrons, and these paired-up (even-even) configurations impart extra stability to the nucleus, much as paired electrons impart extra stability in atomic and molecular structure.

Where only one of $Z$ or $N$ is odd, the count of stable nuclides drops to roughly a third of the even-even count -- 55 versus 50, which are nearly equal to each other. That near-equality is itself informative: it shows protons and neutrons behave similarly with respect to pairing and stability, since in either case exactly one nucleon (a proton in one group, a neutron in the other) is left without a same-type partner. …