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

 

Answers (1)
V Vakul

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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