Not all atoms experience nuclear decay. The phenomenon of spontaneous atomic nuclear decay is called natural radioactivity. It has been reported that the stability or instability of the nucleus is connected with the pairing of spins of neutrons among neutrons, and pairing of spins of protons among protons. When all the non-radioactive isotopes of elements are considered it is found that nuclei with even number of protons and with even number of neutrons are most abundant. This is because even numbers lead to spin pairing and odd numbers confirm the presence of unpaired spins of the subatomic particles. Nuclei with either of the proton number or neutron number odd are slightly less stable than nuclei with both of them even-numbered. But the least stable isotopes are those with odd number of protons and odd number of neutrons.
Furthermore, the nuclear stability is also controlled by the relative numbers of protons and neutrons in it. A plot of number of neutrons vs. number of protons of the stable nuclei reveals that the (n/p) ratio is 1 for lower atoms, breaks off from 1 at around atomic number 20, and rises rather steeply thereafter. This indicates that as the number of protons increase inside the nucleus, more and more neutrons are needed to neutralize the proton-proton repulsion. An atomic nucleus falling below, above or beyond this zone of stability will undergo nuclear decay and stabilize thereby.
The way an unstable nucleus will disintegrate will be decided by its position vis a vis the actual n/p plot of stable nuclei. An isotope situated above this plot has too many neutrons and will stabilize itself by converting a neutron into a proton, and consequent beta-emission. A nucleus deficient in neutrons (n/p ratio too low) will tend to attain nuclear stability by converting one of its protons into neutron. This will be achieved either by emission of a positron (low atomic number isotopes) or by capture of a K-orbit electron (isotopes of higher atomic number side).