why does it take thousands or billions of years for some radioactive isotopes to fully decay?
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Because neutrons. When neutrons and protons are at the right balance,they tend to stick longer. Iron 56, with 26 protons and 30 neutrons is very very stable and therefore sticks around for a very long time.You could count all the atoms in the universe many many many many times over and yet Iron 56 wouldn’t have decayed. Other elements like Francium have a life of less than 2 decades and the longest lived isotope of Francium, Francium 223 has a half life of only 23 years,for comparison,Tellurium (or more specifically Tellurium 128) has a half life of 100 yottaseconds which is 160 trillion times the age of the current universe roughly 2,206,506,000,000,000,000,000,000 years.
If you had a atomic nucleus just made of protons it would fly apart because they are all positively charged. Having neutrons in the nucleus tends to glue everything together. But you need them to be in the right numerical ratio to get the best stability. Carbon-12 with 6 protons and six neutrons is very stable, so is carbon-13 with 6:7. They are probably not going to break apart spontaneously in the lifetime of the universe. Get to 6:8 in carbon-14 and it’s not so stable, theres a chance of it breaking apart sometime in a few thousand years, on average half will in 5,700 years
So something that takes billions of years to decay just means that that particular combination of protons and neutrons has a high level of stability and vice versa for a rapidly decaying isotope. Really its just statistical likelihood coupled to an average stability for a particular combination.
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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