A radio isotope 'X' with a half life 1.4 x 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 : Option 1) 1.96 x 109 years Option 2) 3.92 x 109 years Option 3) 4.20 x 109 years Option 4) 8.40 x 109 years

Since Y forms due to decay of X.

at t =t, suppose number of X=N

then number of Y =7N

Total number =8N =No.

$\therefore N=\frac{No}{8}=\frac{No}{2^{t/t1/2}}$

$\therefore t=3\frac{t_{1}}{2}=3\times 1.4\times 10^{9} years$

$\therefore t=4.2\times 10^{9} years$

Option 1)

1.96 x 109 years

This option is incorrect.

Option 2)

3.92 x 109 years

This option is incorrect.

Option 3)

4.20 x 109 years

This option is correct.

Option 4)

8.40 x 109 years

This option is incorrect.

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