Under which conditions is a nucleus unstable?

Answer 1

When certain combinations of protons and neutrons form an atomic nucleus, there is the possibility that the nucleus may be unstable. There may be too few or too many protons for the number of neutrons present, or there may be too few or too many neutrons for the number of protons present. In any case, if the nucleus is unstable, that nucleus is said to be radioactive. There is another case in which a nucleus can be unstable, and that is that it is simply too large to be able to stay together. Recall that nuclear binding energy holds atomic nuclei together, and it overcomes the electromagnetic repulsion of the positively charged protons to do this. But when atoms become "really big" as we see them at the top end of the Periodic Table, they are uniformly unstable. They are all radioactive and will eventually undergo nuclear decay of some kind. In a radioactive substance, the instability of the nuclei of the atoms will eventually "win out" over the binding energy holding the nuclei together, and the nucleus will "fall apart" or even "split" in some cases. Is there a "magic number" associated with the disproportionality that will tell us if a given atom is unstable? No, there isn't. We have to look at things on a case by case basis. Recall that atoms of the same element that have differing numbers of neutrons in them are isotopes of that element. And for a given element, some unstable isotopes exist. They may appear in nature, or we may see them in the physics lab. In addition to the existence natural or synthesized radioactive isotopes of the elements, some elements have no stable isotopes whatsoever. That means all isotopes of those elements are radioisotopes, and are radioactive. You probably recall the element technetium, which has no stable isotopes. That's an example, and we see more examples at the "top end" of the periodic table where the nuclei of the elements are huge. The binding energy or nuclear glue holding the nuclei together is losing ground to the repulsive forces of all the positively charged protons. Eventually we'll reach a point where a massive nucleus won't stay together, no matter what.