PhysicsThe half life of a radioactive nucleus is 50 days. The time interval (t2-t1)  between the time t2  when 23 of it has decayed and the time t1 when of it had decayed 13  is:

The half life of a radioactive nucleus is 50 days. The time interval (t2-t1)  between the time t2  when 23 of it has decayed and the time t1 when of it had decayed 13  is:


  1. A
    60 days
  2. B
    15 days
  3. C
    30 days
  4. D
    50 days 

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    Solution:

    Concept: From radioactive decay law, N = N0-λt where N0 be the amount of nuclei at t = 0 and N be the left nuclei under decay at any time t.
    At t2N=N0-2N03  = N03
    And at t1 N=N0-N03 = 2N03
    Now,  N03= N0-λt2………(1)
    And 2N03= N0-λt1………(2)
    (1) (2)  λ(t2-t1)  = 2
       t2-t1= lnln 2 λ= t12 = 50 days
    Hence, the correct option is 4.
     
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