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The radioactivity isotope X with a half-life of 10 9 year decays to Y which is stable. A sample of rocks was found to contain both the elements X and Y in the ratio 1 : 7 . If initially the no. of nuclei of Y were zero then the age of rock is

Options

  1. A2 × 10 9 y r
  2. B3 × 10 9 y r
  3. C6 × 10 9 y r
  4. D7 × 1 9 y r

Correct answer

B. 3 × 10 9 y r

Step-by-step solution

In radioactive decay N = N o 2 n N N 0 = 1 1 + 7 = 1 8 N N 0 = 1 2 n = 1 8 ∴ n = 3 t = n T = 3 × 10 9 y r

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