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Q.

A radio isotope 'X' with a half life 1.4 × 109 years decays to '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

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a

3.92 × 109 years

b

4.20 × 109 years

c

8.40 × 109 years

d

1.96 × 109 years

answer is B.

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Detailed Solution

Half life period t12=1.4×109yr
NN0=12n=NxNx+Ny=11+7=18
12n=123⇒n=No.of half lives=3
total time taken , t=nt1/2
=3×t12=3×1.4×109=4.2×109yr

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