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 14 6 C present with the stable carbon isotope 12 6 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 14 6 C, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of 14 6 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 civilization.

Question

Philoid · Accepted Answer

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.