Q.The nuclides with odd number of both protons and neutrons are the least stable. Why?

Step 1. Stability from nucleon pairing works WITHIN each type of nucleon separately: protons pair with protons, and neutrons pair with neutrons -- a proton does not pair with a neutron in this sense.

Step 2. In a nuclide with an odd number of protons, one proton is inevitably left without a partner; in a nuclide with an odd number of neutrons, one neutron is likewise left unpaired.

Step 3. A nuclide with BOTH Z and N odd therefore has two separate unpaired nucleons at once -- one lone proton and one lone neutron -- so it misses out on two independent sources of pairing stabilisation, rather than just one.

Step 4. This is reflected directly in the observed count of stable nuclides: only 4 stable odd-Z, odd-N nuclides are known (about 2% of the Earth's crust), far fewer than any of the other three even/odd combinations.

Apply the same-type-only nucleon-pairing rule to an odd-Z, odd-N nuclide and count how many unpaired nucleons result.

• Assuming the unpaired proton and unpaired neutron somehow pair with each other, which the chapter's own pairing model explicitly rules out.
• Not connecting the explanation back to the very small observed count (4) of stable odd-odd nuclides.