The technique of comparing the abundance ratio of a radioactive isotope to a reference isotope to determine the age of a material is called radioactive dating.
Many isotopes have been studied, probing a wide range of time scales.
The best estimate from this dating technique says the man lived between 33 BC. From the ratio, the time since the formation of the rock can be calculated. Now you could say, OK, what's the probability of any given molecule reacting in one second? But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So I have a description, and we're going to hopefully get an intuition of what half-life means. And how does this half know that it must stay as carbon? So if you go back after a half-life, half of the atoms will now be nitrogen. Then all of a sudden you can use the law of large numbers and say, OK, on average, if each of those atoms must have had a 50% chance, and if I have gazillions of them, half of them will have turned into nitrogen. How much time, you know, x is decaying the whole time, how much time has passed? I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting. And it does that by releasing an electron, which is also call a beta particle. And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? So that after 5,740 years, the half-life of carbon, a 50% chance that any of the guys that are carbon will turn to nitrogen. But we'll always have an infinitesimal amount of carbon. Let's say I'm just staring at one carbon atom. You know, I've got its nucleus, with its c-14. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. After two years, how much are we going to have left? And then after two more years, I'll only have half of that left again. Radiocarbon dating is one of the most widely used scientific dating methods in archaeology and environmental science.It can be applied to most organic materials and spans dates from a few hundred years ago right back to about 50,000 years ago - about when modern humans were first entering Europe.
The dating process is always designed to try to extract the carbon from a sample which is most representative of the original organism.