The “springiness” in our atomic models of tension, the normal force, and thermal energy comes from molecular bonds. The molecular bond that holds two atoms together is an electric interaction between the atoms’ negative electrons and positive nuclei. Fortunately, we don’t need to know any details about electric potential energy to understand the energy diagram of a molecular bond.

FIGURE 10.23 shows the energy diagram of the oxygen molecule $\text{O}{}_2$. Distance $x$ is the atomic separation, the distance between the two atoms. Note the very small distances: $1\text{nm}={10}^{-9}\text{m}$. You can see that the molecule has a stable equilibrium—a minimum in the PE curve—when the atoms are separated by $0.13\text{nm}$. This is the bond length of $\text{O}{}_2$. If the atoms have no kinetic energy—no molecular vibration—they will form a molecule with an atomic separation of 0.13 nm.

FIGURE 10.23 The energy diagram of molecular oxygen $\text{O}{}_2$.

If you try to push the atoms closer together, the potential energy rises very rapidly. Physically, this is an electric repulsion between the electrons orbiting each atom, but it’s analogous to the increasingly strong repulsive force you get when you compress a spring. There is also an attractive force between two atoms. This can be the force between two oppositely charged ions or the force of covalent bonds when electrons are shared. The attractive force resists if you try to pull the atoms apart—analogous to stretching a spring—and thus potential energy increases to the right.

The repulsive force gets stronger as you push the atoms closer together, but the attractive force gets weaker as you pull them farther apart. If you pull too hard, the bond breaks and the atoms come apart. Consequently, the PE curve becomes less steep as $x$ increases, eventually leveling out when the atoms are so far apart that they cease interacting with each other. This difference between the attractive and repulsive forces explains why the PE curve in Figure 10.23 is asymmetric.

It turns out, for quantum physics reasons, that a molecule cannot have $E=0$ and thus cannot simply rest at the equilibrium position. By requiring the molecule to have some energy, such as $E_1$, we see that the atoms oscillate back and forth between two turning points. This is a molecular vibration, and atoms held together by a molecular bond are constantly vibrating. For an $\text{O}{}_2$ molecule with energy $E_1=2\times {10}^{-19}\text{J,}$ as illustrated, the bond length oscillates between roughly 0.10 nm and 0.16 nm.

Suppose the molecule’s energy is increased to $E_2=12\times {10}^{-19}\text{J}$. This could happen, for example, if the molecule absorbs some light. You can see from the energy diagram that the molecules will keep moving apart. By raising the molecule’s energy to $E_2$, we’ve broken the molecular bond. The breaking of molecular bonds by the absorption of light is called photodissociation. It is an important process in making integrated circuits.