What determines isotope stability?
The neutron/proton ratio and the total number of nucleons determine isotope stability.
The principal factor is the neutron to proton ratio.
At close distances, a strong nuclear force exists between nucleons. This attractive force comes from the neutrons. More protons in the nucleus need more neutrons to bind the nucleus together.
The graph below is a plot of the number of neutrons versus the number of protons in various stable isotopes.
The stable nuclei are in the pink band known as the belt of stability They have a neutron/proton ratio between 1:1 and 1.5:1.
NUMBER OF NUCLEONS
As the nucleus gets bigger, the electrostatic repulsions between the protons gets weaker. The nuclear strong force is about 100 times as strong as the electrostatic repulsions. It operates over only short distances. After a certain size, the strong force is not able to hold the nucleus together.
Adding extra neutrons increases the space between the protons. This decreases their repulsions but, if there are too many neutrons, then the nucleus is again out of balance and decays.