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Let's say I have a bunch of, let's say these are all atoms. And let's say we're talking about the type of decay where an atom turns into another atom. Or maybe positron emission turning protons into neutrons. And we've talked about moles and, you know, one gram of carbon-12-- I'm sorry, 12 grams-- 12 grams of carbon-12 has one mole of carbon-12 in it.

So you might get a question like, I start with, oh I don't know, let's say I start with 80 grams of something with, let's just call it x, and it has a half-life of two years.

The changing ratio of C-12 to C-14 indicates the length of time since the tree stopped absorbing carbon, i.e., the time of its death.

Obviously, if half the C-14 decays in 5,730 years, and half more decays in another 5,730 years, by ten half-lives (57,300 years) there would be essentially no C-14 left.

One of the most frequent uses of radiocarbon dating is to estimate the age of organic remains from archaeological sites.

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? Radiocarbon decays slowly in a living organism, and the amount lost is continually replenished as long as the organism takes in air or food.Once the organism dies, however, it ceases to absorb carbon-14, so that the amount of the radiocarbon in its tissues steadily decreases.The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample.By looking at the ratio of carbon-12 to carbon-14 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 carbon-14 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 half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.