Certain isotopes are more stable than others.
Their stability is determined by the ratio of the number of neutrons to the number of protons in the nucleus. At low atomic masses, the stable ratio is approximately 1:1. At about an atomic mass number of 20 this starts to increase until it is around 1.5:1 for the very heavy elements. This is due to the fact that with higher numbers of protons more neutrons are needed due to the repulsion of the protons from electrostatics. The details of this are a matter of high energy physics and there are many "rules" for predicting stability. Here is it useful to know that 1:1 is stable only below Z=20 and that after that the stable nuclei become neutron rich.
This ratio is not exact but represents a "band of stability" around which unstable isotopes cluster. There are a large number of unstable isotopes both above the band (too high a number of neutrons) and below the band (too high a number of protons).
At some point there are no longer any stable isotopes regardless of the neutron to proton ratio. This can be seen at very high atomic numbers. Above mass 208 there are no stable isotopes.
The graph below shows a number of isotopes along with a line with the 1:1 ratio. The stable isotopes are plotted as black dots. The unstable isotopes are plotted with a color coding based on their most prominent decay route. Note that isotopes that are closest to the stable isotopes in the center are "more stable" than isotopes that are father away. This "band" of isotropes running down the center of the plot is the "band of stability".
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