How is radioactive decay used to date fossils?
All organic matter contains carbon. Upon death, Carbon 14 in the decomposing body undergoes its own "decomposition" or radioactive decay which is what radioactive carbon dating measures.
Carbon 14 (affectionately called C14) is not a stable isotope of Carbon and has to decay into the much stabler Nitrogen 17 (which can be found in the atmosphere). Therefore, once an organism dies, the C14 it holds in its body "wriggles free" in a radioactive decay process. The half-life of C14 is 5, 730 years and thus makes a pretty accurate factor for dating fossils which can be billions of years old.