A) \[1.96\times {{10}^{8}}\]years
B) \[3.85\times {{10}^{9}}\]years
C) \[4.11\times {{10}^{9}}\]years
D) \[9.59\times {{10}^{9}}\]years
Correct Answer: C
Solution :
If in the rock there is no Y element, then the time taken by element X to reduce to \[\frac{1}{8}th\] the initial value will be equal to \[\frac{1}{8}={{\left( \frac{1}{2} \right)}^{n}}\]or n =3 Therefore, from the beginning three half life time is spent. Hence the age of the rock is \[=\lambda N=\lambda {{N}_{0}}{{\left( \frac{1}{2} \right)}^{\frac{9}{3}}}=\frac{\lambda {{N}_{0}}}{8}\].
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