The half life of #""^14C# is approximately #5730# years #+-40# years.
That means that in #5730# years, half of a sample of #""^14C# decays by beta emission into #""^14N#, electrons and electron antineutrinos.
A small proportion of the nitrogen in our upper atmosphere is continuously being converted into #""^14C# by cosmic rays. This is then included in the carbon compounds in living plants and animals. When they die, they stop absorbing carbon from the atmosphere, so the proportion of #""^14C# to #""^12C# starts to decrease, in accordance with the #5730# year half life. So the proportion of #""^14C# to #""^12C# can be used to calculate the approximate time since a living organism died.
This assumes we have a good estimate for the proportion at the time the plant or animal was living. This has to be calibrated in order to give good estimates, but radiocarbon dating can provide useful dating for organic artefacts up to about #70,000# years old.
