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A radioactive isotope X with a half-life of 1.37 \times {10^9}  years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y which were in the ratio of 1 : 7. The age of the rock is

a
b
c
d

detailed solution

Correct option is C

If in the rock there is no Y element intially, then the time taken by element X to reduce to 18th the initial value will be equal to or n =3Therefore, from the beginning three half life time is spent. Hence the age of the rock is = 3x1.37x109 = 4.11x109 years

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