Radiocarbon dating is possible because

As the Earth's upper atmosphere is bombarded by cosmic radiation, atmospheric nitrogen is broken down into an unstable isotope of carbon - carbon 14 (C-14).

Libby in 1949, and has become an indispensable part of the archaeologist's tool kit since.Because it reacts identically to C-12 and C-13, C-14 becomes attached to complex organic molecules through photosynthesis in plants and becomes part of their molecular makeup.Animals eating those plants in turn absorb Carbon-14 as well as the stable isotopes.This predictability allows scientists to measure the age of an object if they can work out how many radioactive atoms were originally present.