In chain analysis of a rock , the mass ratio of two radioactive isotope is found to be $\;100 \%\;$ . The mean lives of two isotopes are $\;4 \times 10^{9}\;$years and $\;2\times10^{9}\;$years respectively . If it is assumed that at time of formation of rock , both isotopes were in equal proportion . Then calculate age of rock . Ratio of atomic weights of two isotope is $\;1.02 \%\;(log_{10}^{1.02}=0.0086)$

Question

$(a)\;18.3 \times 10^{9} \;years\qquad(b)\;19.2 \times 10^{10} \;years\qquad(c)\;20.2 \times 10^{11} \;years\qquad(d)\;11.6 \times 10^{8} \;years$