Uranium-238 is converted into lead-206 through a long natural decay chain consisting only of alpha and beta-minus emissions.
(a) Let the number of alpha emissions be n and the number of beta-minus emissions be m. Establish two independent equations connecting n and m by comparing the mass numbers and atomic numbers of the initial and final nuclei.
(b) Solve the equations obtained in part (a) to find the values of n and m.
(c) Write the net balanced nuclear reaction representing this overall transmutation from 92238U to 82206Pb.