The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive 614C present with the stable carbon isotope 612C. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life ( 5730 years) of 614C, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of 614C dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.
Solution: Suppose that the number of C−14 atoms per gram where N0 at t=0 (initially) when its activity was 15 decays per minute per gram. Today ie., after time t (Age of once living organism), the number of C-14 atom per gram left is N and shows an activity of 9 decays per minute per gram. Now, activity of a radioactive substance is given by R=R0e−λt R0=15decaysm−1;R=9decaysm−1 ∴9=15×e−λt⇒e−λt=915=1.6667 ⇒λt=loge1.6667=2.303log101.6667=2.303×0.2219=0.5110⇒t=λ0.5110 Now decay constant λ=T0.693=5,7300.693year−1 ∴t=0.6930.5110×5730=4225.15years