This difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay.
One effect is that there are few stable odd–odd nuclides, but another effect is to prevent beta decay of many even–even nuclei into another even–even nucleus of the same mass number but lower energy, because decay proceeding one step at a time would have to pass through an odd–odd nucleus of higher energy.
Double beta decay directly from even–even to even–even skipping over an odd–odd nuclide is only occasionally possible, and even then with a half-life greater than a billion times the age of the universe.
For example, the extreme stability of helium-4 due to a double pairing of two protons and two neutrons prevents any nuclides containing five or eight nucleons from existing for long enough to serve as platforms for the buildup of heavier elements via nuclear fusion in Big Bang nucleosynthesis; only in stars is there enough time for this (see triple-alpha process).
This is also the reason why 84Be decays so quickly into two alpha particles, making beryllium the only even-numbered element that is monoisotopic.
[1] 20882Pb is the final decay product of 23290Th,[2] a primordial radionuclide with an even proton and neutron number.
[4] All even–even nuclides have spin 0 in their ground state, due to the Pauli exclusion principle (See Pairing Effects for more details).
[5] Also, four long-lived radioactive odd–odd nuclides (4019K – the most common radioisotope in the human body,[6][7] 5023V,13857La,17671Lu with spins 4, 6, 5, 7, respectively) occur naturally.
This high-spin inhibition of decay is the cause of the five heavy stable or long-lived odd-proton, odd-neutron nuclides discussed above.
In some odd–odd radionuclides where the ratio of protons to neutrons is neither excessively large nor excessively small (i.e., falling too far from the ratio of maximal stability), this decay can proceed in either direction, turning a proton into a neutron, or vice versa.
There are another nine radioactive primordial nuclides (which by definition all have relatively long half lives, greater than 80 million years) with odd mass numbers.
Generally speaking, since odd-mass-number nuclides always have an even number of either neutrons or protons, the even-numbered particles usually form part of a "core" in the nucleus with a spin of zero.
The unpaired nucleon with the odd number (whether proton or neutron) is then responsible for the nuclear spin, which is the sum of the orbital angular momentum and spin angular momentum of the remaining nucleon.
[15][16] The last two were only recently found to undergo alpha decay, with half-lives greater than 1018 years.
These stable even-proton odd-neutron nuclides tend to be uncommon by abundance in nature, generally because in order to form and contribute to the primordial abundance, they must have escaped capturing neutrons to form yet other stable even–even isotopes, during both the s-process and r-process of neutron capture, during nucleosynthesis in stars.