A certain radioactive nucleus X undergoes two successive α-decays followed immediately by one β−-decay to form a stable nuclide 83210Bi.
a. (i) Starting from the given final product, work backward to determine the mass number and atomic number of the original nucleus X.
b. (ii) For the nucleus X obtained in part (i), calculate the number of neutrons present.
c. (iii) The stable bismuth product exists as a singly ionised cation 83210Bi+. Determine the total number of electrons in this ion.
d. (iv) Compute the neutron–proton ratio for both nucleus X and the final bismuth nucleus. Using these values, comment on how the sequence of decays brings the nuclide closer to the region of stability.