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NEET2014PhysicsNuclear PhysicsActual

A radio isotope ‘ X ’ with a half life 1.4 × 10 9 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

Options

  1. A1.96 × 10 9 years
  2. B3.92 × 10 9 years
  3. C4.20 × 10 9 years
  4. D8.40 × 10 9 years

Correct answer

C. 4.20 × 10 9 years

Step-by-step solution

Given a radioactive isotope decays into a stable element, X → Y At time t = 0 , x =   N 0 , y = 0 At time t = t , x = N 0 - x , y = x N 0 - x x = 1 7 ⇒ x = 7 N 0 8 So, remaining nuclei of X = N 0 - x = N 0 8 = N 0 2 3 So, three half-life periods would have been passed, ⇒ t = 3 t 1 2 = 3 × 1.4 × 10 9 = 4.2 × 10 9 years.

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