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JEE Main201910 Apr 2019Morning ShiftPhysicsNuclear PhysicsActual

Two radioactive materials A and B have decay constants 10 λ and λ , respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1 / e after a time:

Options

  1. A1 10 λ
  2. B1 9 λ
  3. C1 11 λ
  4. D11 10 λ

Correct answer

B. 1 9 λ

Step-by-step solution

N A = N 0 e - 10 λ t N B = N 0 e - λ t N A N B = 1 e = e - 10 λ t + λ t = e - 9 λ t 1 = 9 λ t t = 1 9 λ

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