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Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0 , a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become 1 e 2 will be

Options

  1. A1 λ
  2. B1 2 λ
  3. C2 λ
  4. D1 4 λ

Correct answer

B. 1 2 λ

Step-by-step solution

N = N 0 e - λ t N 1 = N 0 e - 5 λ t ...........(i) N 2 = N 0 e - λ t ............(ii) From equation (i) and (ii) N 1 N 2 = e - 5 λ t e - λ t 1 e 2 = e - 4 λ t 4 λ t = 2 t = 1 2 λ

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