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NTA Abhyas JEE Main2020PhysicsNuclear PhysicsPractice

The activity of a radioactive sample decreases to 1 3 rd of its original value in 3 days. Then, in 9 days its activity will become

Options

  1. A1 27 of the original value
  2. B1 9 of the original value
  3. C1 8 of the original value
  4. D1 3 of the original value

Correct answer

A. 1 27 of the original value

Step-by-step solution

R = R 0 e - λ t ⇒ 1 3 = e - λ × 3 = e - 3 λ … ( i ) Again R ' R 0 = e - λ × 9 = e - 9 λ = ( e - 3 λ ) 3 = 1 3 3 [ F r o m E q . i ] = 1 27 ⇒ R ’ = R 0 27 Hence, in 9 days activity will become 1 27 of the original value.

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