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Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.Natasha Glydon Exponential decay is a particular form of a very rapid decrease in some quantity. So what we do is we come up with terms that help us get our head around this. So I wrote a decay reaction right here, where you have carbon-14. So now you have, after one half-life-- So let's ignore this. I don't know which half, but half of them will turn into it. And then let's say we go into a time machine and we look back at our sample, and let's say we only have 10 grams of our sample left. 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? Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.

The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.

In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 years.

This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.

Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: C ratio of 0.795 times that found in plants living today. Solution The half-life of carbon-14 is known to be 5720 years.​ Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation: is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay.

The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists.

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