Final answer:
The relationship between internuclear distance and potential energy involves the balance of attractive and repulsive forces, with a minimum potential energy at the bond length. For hydrogen, bond length is 74 pm with a bond energy of 104 kcal/mol.
Step-by-step explanation:
The relationship between internuclear distance and potential energy in molecular physics is characterized by the interplay of attractive and repulsive forces as atoms come closer together. A plot of potential energy versus internuclear distance for two interacting hydrogen atoms reveals that as they approach each other from a long distance, the system's potential energy decreases. This is due to the attractive forces between the protons and electrons. However, as the atoms get too close, repulsive forces between like charges (electron-electron and proton-proton) increase, leading to a rapid rise in potential energy. There is an optimal internuclear distance, known as the bond length, where the potential energy is at a minimum, indicating the balance between attraction and repulsion.
For example, in the H₂ molecule, the bond length is 74 pm (74 x 10-12 meters), and this distance corresponds to the point where the potential energy graph reaches its minimum. The difference in potential energy between this lowest state and the state where the atoms are completely separated is called the bond energy, which in the case of hydrogen is about 104 kcal/mol.
Furthermore, if two light nuclei are considered, they must overcome the Coulomb repulsion between them to combine and release energy, as indicated by a decrease in potential energy after clearing a 'hump' in the energy plot. This description encapsulates the essential aspects of potential energy changes as a function of internuclear distance.