Parent nuclide P (half-life 20y) decays to daughter D (half-life 30d), which further decays negligibly slowly compared with laboratory timescales. Initially only NP0 atoms of P are present.
(i) Starting from the decay law, derive an expression for the ratio of the activities AD(t)/AP(t).
(ii) Show that for t≫T1/2(D) the activities of P and D become almost equal.
(iii) Calculate the minimum time (in years, correct to one decimal place) after which AD reaches 99% of AP.
(iv) Explain why the situation in this system is described as secular equilibrium.