Final answer:
The characteristic with the lowest rank order stability is the internuclear distance at very short ranges, where repulsive interactions cause instability. Systems in chemistry seek the lowest energy state, which is seen in cluster stability and reactions where lower activation energy signifies a more stable process.
Step-by-step explanation:
The characteristic that has the lowest rank order stability is the internuclear distance at very short ranges. At these distances, repulsive interactions dominate due to the positive charges of the nuclei being so close together, making the system less stable than when atoms are separated. This concept is rooted in the principle that systems tend to move toward the state with the lowest possible energy. Clusters of atoms or nuclei that are too close to one another will experience increased repulsion, which is destabilizing compared to configurations where atoms are appropriately spaced to balance attractive and repulsive forces.
When discussing the systematic characteristics of high-Z nuclei, such as those near Z = 114, the stability of these nuclei is a point of interest and active study. Another factor influencing stability is carbocation formation, which increases in stability from primary (RCH₂) to secondary (R₂CH) to tertiary (R₃C), due to the increasing availability of neighboring carbon atoms to help disperse the positive charge.
Overall, in chemical systems, whether discussing nuclear stability or molecular reactions, the general trend is for systems to favor configurations of lowest energy and highest stability. In the context of chemical reactions, the reaction with the smallest activation energy (Ea) will occur most rapidly, since lower energy barriers are easier for reactants to overcome, making such configurations more stable.