Consider a nuclide ZAX that undergoes a chain of k successive alpha decays.
(i) Derive expressions for the mass number and atomic number of the final nuclide in terms of A, Z, and k.
(ii) Thorium-232 (90232Th) undergoes four successive alpha decays. Using your result from part (i), determine the symbol (element and mass number) of the resulting nuclide.
(iii) For the sequence described in part (ii), calculate the total number of protons and neutrons lost by the nucleus in all four decays combined.