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

Normal activity, `A_(0)=15` decays/min
present activity, A = 9 decays/min
Half-life of `""_(9)C^(14),T_(1//2)=5,730` years
We know that, `A = A_(0)e^(-lambdat)`
where `lambda` is the decay constant and
t=time of disintegration = Age of Indus Valley Civilisation.
`e^(-lambdat) = A/A_(0)=9/15 = 3/5`
or `t=1/lambda log_(e)(5/3)`
`lambda` is related to half-life `T_(1//2)` by the relation.
`lambda =(log_(e)2)/(t_(1//2)`
Thus, `t=(log_(10)(5/3))/(log_(e)2) xx T_(1//2)`
`=4224.2` years.