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 146C present with the stable carbon isotope 126C. 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 146C, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of 146C 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 civilization.

Let N be a number of radioactive carbon found in normal carbon and N0 be the number of radioactive carbon found in the specimen. The half-life of C-14 is 5730 yrs.

Decay rate of living carbon-containing matter = D = 15 decay/min-gm

Decay rate of the specimen at Mohenjo-Daro = D0 = 9 decays/min-gm

From the exponential decay rate law, we get,

Hence,

So, -λt = ln(3/5) = -0.5108

t =

or, t =

Approximate age of Indus-Valley-Civilization is 4223.5 years.

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