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Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.
The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.
This was a giant leap forward in that it offered far more accurate dates for a far smaller sample (9); this made destruction of samples a far less delicate issue to researchers, especially on artefacts such as The Shroud of Turin for which accurate dates were now possible without damaging a significant part of the artefact.
AMS counts the quantity of C isotope is constantly formed in the upper atmosphere thanks to the effects of cosmic rays on nitrogen-14 atoms.
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.
For example, say a fossil is found that has 35% carbon 14 compared to the living sample. We can use a formula for carbon 14 dating to find the answer.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.After 5,730 years, the amount of carbon 14 left in the body is half of the original amount.If the amount of carbon 14 is halved every 5,730 years, it will not take very long to reach an amount that is too small to analyze.