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Question

A radio isotope X has a half-life of 1.4×109 yr and Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is:

A
1.96×109
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B
3.92×109
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C
4.2×109yr
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D
8.4×109yr
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Solution

The correct option is C 4.2×109yr

XY=17
In such question always add numerator and denominator to get initial number of atoms. X+Y=8=N0 before decay.
NN0=(12)n18=(12)n(12)=(12)nn=3n=Tt13T=n×t12
T=3×1.4×109
T=4.2×109 year

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