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JEE Main202311 Apr 2023Morning ShiftPhysicsNuclear PhysicsActual

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B . If λ A and λ B are decay constants of A and B respectively, then choose the correct relation from the given options.

Options

  1. Aλ A ln 2 = λ B
  2. Bλ A = λ B
  3. Cλ A = λ B ln 2
  4. Dλ A = 2 λ B

Correct answer

C. λ A = λ B ln 2

Step-by-step solution

It is given that T 1 2 ( A ) = T a v ( B ) The half life of a substance is given by T 1 2 = ln 2 λ So, ln 2 λ A = 1 λ B ⇒ λ A = λ B ln 2

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