And that one actually often finds more Carbon-14 in coal than might be otherwise expected due to radioactive in nearby rocks. While you may find some carbon 14 in a 500 million year old coal deposit, it would be exceptionally scarce, beyond our ability to read. And the fraction of the original concentration is now 1/(2 10000) Which is about 5.012372749×10 -3011 Needless to say, that is a lot of zeros. That would mean that it has gone through 10,000 half lives. But, say we have a coal deposit that is 570 million years old. The Carbon 14 on the surface of the Earth is almost all generated in the sun and stars and arrives here via solar wind and cosmic rays. These then could potentially be considered separate from the background. However, there are also some elements that are only found as synthetic nuclear reactor byproducts. We consider a radioactive isotope to have decayed to zero when it reaches background. There is a certain amount of radiation that is considered 'background radiation'. Except that one is truly dealing with discrete atoms, so eventually the last one could possibly decay away. It never completely goes away, although over time the concentration will become so low that it may be undetectable.
