AP® Chemistry · Unit 2 · Topic 2.2
Potential Energy and Internuclear Distance
As two atoms approach, their potential energy drops due to attraction then rises sharply due to repulsion, creating a curve with a minimum. That minimum fixes the bond length and its depth equals the bond energy.
Picture two hydrogen atoms far apart, each with a proton and an electron. Far away, they barely interact, so their potential energy is close to zero. As they move closer, the positive nucleus of one atom attracts the electron of the other, and that attraction lowers the system's potential energy — energy drops as r shrinks, similar to the -k(q1 q2)/r relationship for ions. But this drop can't continue forever. Once the atoms get close enough that their electron clouds and nuclei start crowding each other, repulsion kicks in and grows faster than the attraction does. Energy shoots back up. The result is a curve shaped like a well: energy falls, bottoms out, then climbs steeply.
That bottom point is the equilibrium bond length, the one separation where attraction and repulsion balance and potential energy is lowest. The depth of the well, measured from the bottom up to zero (atoms infinitely far apart), is the bond energy — how much energy you'd need to pull the atoms completely apart. A deep, narrow well means a strong bond; a shallow one means a weak bond. Pushing the atoms closer than that minimum doesn't help, because the short-range repulsion between nuclei and electron clouds overwhelms the attraction and the energy rises again.
This curve connects directly to bond length and bond strength trends elsewhere in the unit: smaller atoms or more shared electron pairs pull the minimum to shorter distances and deepen the well. Swapping in ions instead of neutral atoms, like a 2+ cation and a 2- anion, keeps the same well shape but drops the curve much lower, since the -k(q1 q2)/r attraction is stronger with larger charges.
Key terms
- Potential energy curve
- A graph of potential energy versus distance between two atoms or ions as they approach each other.
- Equilibrium bond length
- The internuclear distance at the minimum of the potential energy curve, where attraction and repulsion balance.
- Bond energy
- The energy needed to separate two bonded atoms completely, equal to the depth of the potential energy well.
- Electron-cloud repulsion
- The repulsive force between negatively charged electron clouds that dominates at very short internuclear distances.
Watch it explained
- How it worksWalk me through the shape of a potential energy curve as two atoms approach from far apart.
- How it worksHow does the depth of the well on that curve correspond to the bond energy?
- Common mistakeWhy doesn't pushing two bonded atoms closer together keep lowering their energy?
- Going furtherWhat happens to the curve when you put a plus-2 ion next to a minus-2 ion instead?
Check yourself
End of topic.