The normal activity of living carbon -containing matter is found to be about 15 decay per minute for every gram of carbon. This activity arises form the small proportion of radioactive `._6C^(14)` present with the ordinary `._6C^(12)` isotope. 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 (=5730years) of `._6C^(14)`, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of `._6C^(14)` dating used in archaeology. Suppose a specimen from Mohenjo - daro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus Valley Civilization.

Explanation

Decay rate of living carbon-containing matter,`R = 15 decay/min`
Let N be the number of radioactive atoms present in a normal carbon- containing matter.
Half life of `_(6)^(14)C,T_(1/2)=5730" "years`
The decay rate of the specimen obtained from the Mohenjodaro site:
`R' = 9 decays//min`
Let N’ be the number of radioactive atoms present in the specimen during the Mohenjodaro period.
Therefore, we can relate the decay constant, λand time, t as:
`(N)/(N')=(R)/(R')=e^(-lambdat)`
`e^(-lambdat)=9/15=3/5`
`-lambdat=log_(e)""(3)/(5)=-0.5108`
`therefore t=0.5108/lambda`
But `lambda =0.693/T_(1/2)=(0.693)/(5730)`
`therefore t=(0.5108)/((0.693)/(5730))=4223.5" "`years
Hence, the approximate age of the Indus-Valley civilisation is 4223.5 years.