Final answer:
To produce gold-108 by beta decay, an isotope with 79 protons and 30 neutrons is required; none of the options given directly decay into gold-108.
Step-by-step explanation:
To produce gold-108 by beta radiation, we need an element with one more neutron and the same number of protons because beta decay involves a neutron in the nucleus decaying into a proton and emitting a beta particle (an electron).
Gold (Au) has an atomic number of 79, meaning it has 79 protons. Gold-108 would have 79 protons and 29 neutrons. To get gold-108 from beta decay, we would need an element with 79 protons and 30 neutrons. None of the options (Uranium-235, Plutonium-239, Mercury-202, Lead-208) directly undergo beta decay to form gold-108. However, if we examine these options, Mercury-202 is the closest to gold in terms of atomic number, and another isotope of mercury, specifically Mercury-197 (Hg-197), can beta decay into gold-197 (Au-197), but not directly into gold-108.