A given radioactive parent has decay constant 𝜆1 and at time t = 0 there are 𝑁10 parent nuclei and the number of radioactive daughter nuclei is 𝑁20 = 0. The daughter has decay constant 𝜆2. Show;
(i) that the number of daughter nuclei 𝑁2 at time t > 0 is N2 = 𝑁20 (𝜆1/𝜆2 − 𝜆1) (𝑒𝜆1𝑡− 𝑒𝜆2𝑡).
(ii) The value of N2 is zero at t = 0 and at t = ∞ . It therefore passes through a maximum at some time tm. Show that tm is given by tm = 𝜏2(𝑇1/𝑇1 − 𝑇2) In[𝑇1/𝑇2] where T1 and T2 are the half – lives of the parent and the daughter respectively, and 𝜏2 is the mean life of the daughter
Comments