Radiocarbon Dating Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, ¹⁴C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates ¹⁴C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of ¹⁴C present begins to decrease through radioactive decay. Therefore the level of radioactivity must also decay exponentially.

Dinosaur fossils are often dated by using an element other than carbon, such as potassium-40, that has a longer half-life (in this case, approximately 1.25 billion years). Suppose the minimum detectable mass is 0.1% and a dinosaur is dated with ⁴⁰K to be 68 million years old. Is such a dating possible? In other words, what is the maximum age of a fossil that could be dated using ⁴⁰K?