Final answer:
U-238 is the isotope that undergoes radioactive decay to eventually produce the stable nuclide Pb-206, through a series of alpha and beta decays. The conservation of atomic numbers and mass numbers is essential in balancing the nuclear equations for these decay processes.
Step-by-step explanation:
The isotope that undergoes radioactive decay to produce the stable nuclide Pb-206 is U-238. This isotope of uranium has an atomic number of 92 and a mass number of 238, represented by the atomic symbol 23892U. Uranium-238 undergoes a radioactive decay series which consists of multiple alpha and beta decays. Over this series of decay steps, the atomic number gradually decreases until it reaches 82 (the atomic number for lead), at which point the stable isotope Pb-206 is produced.
When considering the nuclear equation for alpha decay, one must remember that it results in a decrease of 2 in the atomic number and a decrease of 4 in the mass number. For instance, the decay of U-238 to Th-234 involves the loss of an alpha particle (represented as 42He). This is expressed in a balanced nuclear equation where the sum of atomic numbers and mass numbers are conserved on both sides of the equation.