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JEE MainPhysicsNuclear Physics

Two radioactive sources A and B initially have the same activity. The half-life of A is T and the half-life of B is 2T . After a time interval t = 4T , the ratio of the number of active nuclei of A to that of B is

Options

  1. A1 4
  2. B1 2
  3. C1 8
  4. D1 16

Correct answer

C. 1 8

Step-by-step solution

The activity of a radioactive source is given by A = N . Given that the initial activities are equal: A_ 0A = A_ 0B _A N_ 0A = _B N_ 0B The decay constant is related to half-life by = 2 T_ 1/2 . Since T_A = T and T_B = 2T , we have: _A = 2 T and _B = 2 2T This implies _A = 2 _B . Substituting this into the initial activity equation: 2 _B N_ 0A = _B N_ 0B N_ 0B = 2N_ 0A After time t = 4T , the number of active nuclei of A is: N_A = N_ 0A ( 1 2 )^ 4T T = N_ 0A 16 After time t = 4T , the number of active nuclei of B i

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