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The half –life of a radioactive isotopes X is 20 years. It decays to another element Y which is stable .The two elements X and Y were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be in years is

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answer is 60.

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Detailed Solution

$\begin{array}{l} N_{x} = N . . . (1) \\ N_{y} = N_{0} - N \dots . . (2) \\ Let as N_{x} + N_{y} = N_{0} \dots (3) \\ But N = N_{0} e^{- λ t} \dots . . (4) \end{array}$

Solving above $t = \frac{3 l n 2}{λ} = 60 year$

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