Here’s an analogy:
Imagine you have a dog in your yard, but your dog wants to be outside your yard. If you have no fence, the dog will leave your yard instantly.
A completely unstable nucleus is like that – physics “prefers” the nucleus to be broken up, so it breaks up.
You can keep the dog in your yard by building a fence. Well, you can keep it there for a while – at some random time, the dog might decide that it’s worth the effort to get over the fence, and out he goes. Maybe with a low fence, your dog scarpers within an hour, 50% of the time, but with a high fence, it takes a full day before there’s a 50% chance of him escaping.
A radioactive nucleus is like that. In this case, the “fence” is the very short-range “strong nuclear force” that holds the nucleus together. Once (say) an alpha particle spends the energy it needs to get past that fence, it gains it all back as the charged nucleus pushes the charged alpha particle away.
Different nuclei have different sized “fences”, so though the nuclei decay randomly, some decay much more slowly than others. Like the dog – it *will* escape eventually, but with a high enough fence, it might be many many years. Unlike dogs and fences, nuclei can hang around forever, so sometimes “many many years” means many billion s(or even trillions) of years.
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