why does it take thousands or billions of years for some radioactive isotopes to fully decay?
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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.
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