14 carbon dating
The carbon-14 isotope would vanish from Earth's atmosphere in less than a million years were it not for the constant influx of cosmic rays interacting with molecules of nitrogen (NFigure 1: Diagram of the formation of carbon-14 (forward), the decay of carbon-14 (reverse).
Carbon-14 is constantly be generated in the atmosphere and cycled through the carbon and nitrogen cycles.
Or in other words, if we have a box, and we don't know how old it is but we know it started with 100 carbon 14 atoms, and we open it and find only 50 carbon 14 atoms and some other stuff, we could say, 'Aha!
It must be 1 carbon 14 half-life (or 5730 years) old.' This is the basic idea behind carbon dating. In the atmosphere, cosmic rays smash into normal carbon 12 atoms (in atmospheric carbon dioxide), and create carbon 14 isotopes.
Thus, the Turin Shroud was made over a thousand years after the death of Jesus.
It uses the naturally occurring radioisotope carbon-14 (14C) to estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.
Once an organism is decoupled from these cycles (i.e., death), then the carbon-14 decays until essentially gone.
The half-life of a radioactive isotope (usually denoted by \(t_\)) is a more familiar concept than \(k\) for radioactivity, so although Equation \(\ref\) is expressed in terms of \(k\), it is more usual to quote the value of \(t_\).
In 1960, Libby was awarded the Nobel Prize in chemistry for this work.
He demonstrated the accuracy of radiocarbon dating by accurately estimating the age of wood from a series of samples for which the age was known, including an ancient Egyptian royal barge dating from 1850 BCE.