Final answer:
Fusing heavy nuclei costs energy as opposed to yielding it because elements heavier than iron require an input of energy for fusion, making the process endothermic rather than exothermic.
Step-by-step explanation:
When considering the fusion of heavy nuclei, such as two gold nuclei, the process actually costs energy rather than yielding it. This is because, as per the energy-mass curve referenced by nuclear physics, once the size of an atomic nucleus exceeds that of iron, the binding energy per nucleon starts to increase. Therefore, fusion reactions involving elements heavier than iron require an input of energy to occur. In contrast to light element fusion—like hydrogen, which powers the stars and yields a significant amount of energy—heavy element fusion is endothermic.
Thus, for gold nuclei to fuse, substantial energy must be added to overcome the electrostatic Coulomb force between the positively charged nuclei. The process of fusing heavy nuclei like gold does not release energy, unlike the fusion of lighter elements such as hydrogen or helium which are exothermic and fuel stars. Therefore, the correct answer to whether fusing heavy nuclei yields or costs energy is 'b) It costs energy'.