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 atmosphare which maintains the above equilibrium activity, ceases and its activity begins to drop. form 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 spacimen form Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus Vally Civilization.

Explanation

Here, normal activity, `R_0=15decays//min`
Present activity `R=9decay//min`, `T=5730yrs, age,t=?`
As activity is proportional to the number of radioactive atoms, therefore, `N/(N_0)=R/(R_0)=9/15`
But `N/(N_0)=e^(-lambdat) :. e^(-lambdat)=9/15=3/5 " " e^(+lambdat)=5/3`
`lambdat log_(e) e=log_(e). (5)/(3)=2.3026 log 1.6667`
`lambdat=2.3026xx0.2218=0.5109`
`t=0.5109/lambda`
But `lambda=0.693/T=0.693/5730Yr^(-1) :. t= 0.5109/lambda=(0.5109xx5730)/0.693=4224.3years`