A given radioactive parent has decay constant π1 and at time t = 0 there are π10 parent nuclei and the number of radioactive daughter nuclei is π20 = 0. The daughter has decay constant π2. Show;
(i) that the number of daughter nuclei π2 at time t > 0 is N2 = π20 (π1/π2 β π1) (ππ1π‘β ππ2π‘).
(ii) The value of N2 is zero at t = 0 and at t = β . It therefore passes through a maximum at some time tm. Show that tm is given by tm = π2(π1/π1 β π2) In[π1/π2] where T1 and T2 are the half β lives of the parent and the daughter respectively, and π2 is the mean life of the daughter
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