Question

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 ${}_6^{14}C$ present with the stable carbon isotope ${}_6^{12}C$. 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 ${}_6^{14}C$, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of ${}_6^{14}C$ 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 civilisation.

Answer 1

Decay rate $R=15decay/min$
Let, $N$ be number of radioactive atoms present.
Half-life of carbon, $T=5730years$
Decay rate of specimen, $R^{{}^{\prime }}=9decay/min$
Let $N^{{}^{\prime }}$ be bumber of radioactive present in specimen.
as, $\frac{N}{N^{{}^{\prime }}}=\frac{R}{R^{{}^{\prime }}}=e^{-\lambda t}$
So, $t=0.5108/\lambda$ or $\lambda =0.693/T$
i.e., $t=4223.5$ years