An unknown radioactive nuclide X decays to the stable nuclide 82208Pb after experiencing exactly six α-decays and three β⁻-decays (β⁺ emission does not occur).
a. (i) Determine the atomic number Z and mass number A of the original nuclide X.
b. (ii) Write a single balanced nuclear equation that summarises the overall transformation from X to lead-208.
c. (iii) Show, by explicit calculation of A and Z at each stage, that the total number of nucleons is conserved in the process.