Answer to Question #227213 in Atomic and Nuclear Physics for BENSON

Question

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) (𝑒^𝜆1𝑡− 𝑒^𝜆2𝑡).

(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 t_m = 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

Answer 1

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