10.3 Radioactive decay  (Page 3/15)

Radioactive dating

Radioactive dating is a technique that uses naturally occurring radioactivity to determine the age of a material, such as a rock or an ancient artifact. The basic approach is to estimate the original number of nuclei in a material and the present number of nuclei in the material (after decay), and then use the known value of the decay constant $\lambda$ and [link] to calculate the total time of the decay, t .

An important method of radioactive dating    is carbon-14 dating    . Carbon-14 nuclei are produced when high-energy solar radiation strikes ${}^{14}\text{N}$ nuclei in the upper atmosphere and subsequently decay with a half-life of 5730 years. Radioactive carbon has the same chemistry as stable carbon, so it combines with the ecosphere and eventually becomes part of every living organism. Carbon-14 has an abundance of 1.3 parts per trillion of normal carbon. Therefore, if you know the number of carbon nuclei in an object, you multiply that number by $1.3\times {10}^{\mathrm{-12}}$ to find the number of ${}^{14}\text{C}$ nuclei in that object. When an organism dies, carbon exchange with the environment ceases, and ${}^{14}\text{C}$ is not replenished as it decays.

By comparing the abundance of ${}^{14}\text{C}$ in an artifact, such as mummy wrappings, with the normal abundance in living tissue, it is possible to determine the mummy’s age (or the time since the person’s death). Carbon-14 dating can be used for biological tissues as old as 50,000 years, but is generally most accurate for younger samples, since the abundance of ${}^{14}\text{C}$ nuclei in them is greater. Very old biological materials contain no ${}^{14}\text{C}$ at all. The validity of carbon dating can be checked by other means, such as by historical knowledge or by tree-ring counting.