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Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Nucleus

A radioactive sample has a decay constant . The half-life and average-life of the sample are respectively

Options

  1. A2 and 1
  2. B2 and 1
  3. C1 and 2
  4. D( 2) and 1

Correct answer

B. 2 and 1

Step-by-step solution

The radioactive decay law is given by N = N₀ e^ - t For half-life T_ 1/2 , the number of active nuclei becomes half of its initial value, so N = N₀ 2 N₀ 2 = N₀ e^ - T_ 1/2 e^ T_ 1/2 = 2 T_ 1/2 = 2 The average life or mean life T_ avg is defined as the sum of the lifetimes of all individual nuclei divided by the total number of nuclei, which is the reciprocal of the decay constant. T_ avg = 1 Thus, the half-life and average-life are 2 and 1 respectively.

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