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Bottom line: Radiocarbon dating is a technique used by scientists to learn the ages of biological specimens from the distant past.

Carbon-14 has a half-life of 5,730 ± 40 years—, half the amount of the radioisotope present at any given time will undergo spontaneous disintegration during the succeeding 5,730 years. It has proved to be a versatile technique of dating fossils and archaeological specimens from 500 to 50,000 years old.

Most radiocarbon dating today is done using an accelerator mass spectrometer, an instrument that directly counts the numbers of carbon-14 and carbon-12 in a sample.

A detailed description of radiocarbon dating is available at the Wikipedia radiocarbon dating web page.

But when gas exchange is stopped, be it in a particular part of the body like in deposits in bones and teeth, or when the entire organism dies, the ratio of carbon-14 to carbon-12 begins to decrease.

The unstable carbon-14 gradually decays to carbon-12 at a steady rate. Scientists measure the ratio of carbon isotopes to be able to estimate how far back in time a biological sample was active or alive.

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