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 \({ }_{6}^{14} \mathrm{C}\) present with the
stable carbon isotope \({ }_{6}^{12} \mathrm{C}\). 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
\((5730 \mathrm{yr})\) of \({ }_{6}^{14} \mathrm{C}\) and the measured activity,
the age of the specimen can be approximately estimated. This is the principle
of \({ }_{6}^{14} \mathrm{C}\) 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.
(a) \(5224 \mathrm{yr}\)
(b) \(4224 \mathrm{yr}\)
(c) \(8264 \mathrm{yr}\)
(d) \(6268 \mathrm{yr}\)