[UPSC CSE 2023] Nuclear Physics (Q27, 10M)

What is the age of a fossil that contains 6\text{ g} of carbon {}^{14}\text{C} and has a decay rate of 27\text{ decays per minute} ? Given : Ratio \frac{{}^{14}\text{C}}{{}^{12}\text{C}} = 1\cdot 3 \times 10^{-13}, Half life (T_{1/2}) of {}^{14}\text{C} = 5730\text{ yrs}.