The carbon14 decays with its halflife of 5,700 years, while the amount of carbon12 remains constant in the sample.By looking at the ratio of carbon12 to carbon14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent carbon14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (0.693) ] x 5,700 years t = [ (2.303) / (0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the halflife of carbon14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old. And maybe not carbon12, maybe we're talking about carbon14 or something. And then nothing happens for a long time, a long time, and all of a sudden two more guys decay. And the atomic number defines the carbon, because it has six protons. If they say that it's halflife is 5,740 years, that means that if on day one we start off with 10 grams of pure carbon14, after 5,740 years, half of this will have turned into nitrogen14, by beta decay. What happens over that 5,740 years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points. So if we go to another halflife, if we go another halflife from there, I had five grams of carbon14. So now we have seven and a half grams of nitrogen14. This exact atom, you just know that it had a 50% chance of turning into a nitrogen.
