Q.On the basis of even-odd of protons and neutrons, what type of nuclides are most stable?

Step 1. Tallying naturally occurring stable nuclides by whether Z and N are each even or odd gives four groups: even-Z/even-N = 165 nuclides, even-Z/odd-N = 55, odd-Z/even-N = 50, odd-Z/odd-N = only 4.

Step 2. The even-Z/even-N group is overwhelmingly the largest, accounting for about 85% of the Earth's crust by nuclide count -- direct evidence of its stability.

Step 3. The physical reason is nucleon pairing: protons tend to pair up with other protons, and neutrons pair up with other neutrons (not with each other), and each such pairing adds extra binding/stability to the nucleus. An even-even nuclide has every proton and every neutron paired off, with none left over.

Step 4. By contrast, a nuclide with one odd count (either Z or N) has exactly one unpaired nucleon, and a nuclide with both Z and N odd has two separate unpaired nucleons (an unpaired proton and an unpaired neutron, which do not pair with each other) -- explaining why odd-odd nuclides are rarest of all.

Read off the relative sizes of the four even/odd Z-N groups and connect the largest group (even-even) to the nucleon-pairing explanation for stability.

• Thinking pairing occurs between a proton and a neutron rather than separately within the proton population and within the neutron population.
• Overlooking that even-Z/odd-N and odd-Z/even-N groups are nearly equal in size, which is itself evidence that protons and neutrons behave similarly regarding pairing.