At what separation distance is the force zero between two atoms?

You can work it out this way: find the minimum of the potential energy curve.

How does temperature affect bond formation?

Higher temperature means more kinetic energy to overcome attraction.

Why do atoms never overlap completely?

The repulsive r⁻¹² term grows much faster than the attractive r⁻⁶ term.

Pro 🔒~20 min

Atomic Interactions

Explore the forces between atoms at the molecular scale

How it works

The Lennard-Jones potential models the interaction between a pair of neutral atoms. The r⁻¹² term represents Pauli repulsion at short range, while the r⁻⁶ term represents van der Waals attraction at longer range. The equilibrium distance is where the force is zero, corresponding to the minimum potential energy. This model explains bonding, phase transitions, and molecular structure.

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Step-by-step

Place atoms on the canvas and observe how they interact.
The potential energy graph updates in real time.
Cool atoms to form stable bonds; heat them to break bonds and observe phase-like transitions.

Key formulas

$U(r) = 4\epsilon\left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6\right]$ Lennard-Jones potential
$F = -\frac{dU}{dr}$ Force from potential

Frequently asked questions

At what separation distance is the force zero between two atoms?: You can work it out this way: find the minimum of the potential energy curve.
How does temperature affect bond formation?: Higher temperature means more kinetic energy to overcome attraction.
Why do atoms never overlap completely?: The repulsive r⁻¹² term grows much faster than the attractive r⁻⁶ term.