The potential energy of nucleons decreases as the nuclear force increases, due to the strong attractive force that holds protons and neutrons together in the nucleus. A stronger nuclear force means that nucleons are more tightly bound, requiring more energy to separate them, which results in lower potential energy. Conversely, a weaker nuclear force leads to less binding, increasing potential energy as it takes less energy to separate the nucleons. This relationship is vital for understanding atomic stability, as a decrease in nuclear force can lead to increased potential energy and potential instability or radioactive decay. Overall, the interplay between nuclear force and potential energy is crucial for the stability and behavior of atoms.