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 `""_6^14C` present with the stable carbon isotope `""_6^12C`. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) cases and its activity begins to drop. From the known half-life (5/30 years) of `""_6^14C`, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of `""_6^(14)C` dating used in archacology. Suppose a specimen from Mohenjodaro gives as activity of 9 decyas per minute per gram of carbon. Estimate the approximate age of the Indus-Vally civillisation.

Explanation

Normal activity , `R_0 = 15` decays per min.
Present activity , R = 9 decays per min.
`T_(1//2) = 5730` days
`N = N_0 e^(-lambda t)`
`R prop N and R_0 prop N_0`
`(R )/(R_0) = N/(N_0) = e^(-lambda t)`
`e^(-lambda t) = R/(R_0) = 9/15`
`lambda t = log_e 15/9 = 2.303 log_(10) (5/9) = 0.511`
`t = (0.511)/(lambda) = (0.511)/(0.693) xx T_(1//2) = (0.511)/(0.693) xx 5730 = 4225` years .