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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 ""_6^14C 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. |
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Answer» SOLUTION :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 . |
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