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JEE Main202126 Feb 2021Evening ShiftPhysicsNuclear PhysicsActual

A radioactive sample is undergoing α decay, At any time t 1 , its activity is A and another time t 2 , the activity is A 5 . What is the average life time for the sample ?

Options

  1. Aln 5 t 2 - t 1
  2. Bln t 2 + t 1 2
  3. Ct 2 - t 1 ln 5
  4. Dt 1 - t 2 ln 5

Correct answer

C. t 2 - t 1 ln 5

Step-by-step solution

Let initial activity be A 0 A = A 0 e - λ t             . . . 1 A 5 = A 0 e - λ t 2           . . . 2 1 ÷ 2 5 = e λ t 2 - t 1 λ = ln 5 t 2 - t 1 = 1 τ τ = t 2 - t 1 ln 5

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