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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 \(_6^{14}C\) present with the stable carbon isotope \(_6^{12}C\). 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 \(_6^{14}C\) and the measured activity, the age of the specimen can be approximately estimated. This is the principle of \(_6^{14}C\) 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.

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Suppose that the number of C-14 atoms per gram were N0 at t = 0 (initially) when its activity was 15 decays per minute per gram. Today, i.e. after time t (age of once-living organism), the number of C-14 atom per gram left is N and it shows an activity of 9 decays per minute per gram. Now, activity of a radioactive substance is given by,

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