binding curve
/ BYND-ing kurv /
Imagine rolling a marble around inside a smooth bowl. It naturally settles at the lowest point and, if nudged, rolls back. A bond between two atoms has its own invisible bowl, drawn as a graph, and the binding curve is that picture: a plot of the pair's energy against how far apart the atoms are, with a dip marking their happiest spacing.
Read from right to left, the curve starts flat when the atoms are far apart and feel almost nothing, then dips downward as attraction pulls them together and lowers their energy. Pushed too close, their electron clouds repel and the curve shoots steeply upward. The bottom of the dip pins down two key numbers at once: the horizontal position of the lowest point is the equilibrium bond length, and the depth of the dip is the bond energy needed to climb back out and separate the atoms.
The binding curve matters because it captures, in one simple shape, everything about a bond's strength and size and even its stiffness — how sharply the bowl curves tells you how hard the bond resists stretching. A subtle point worth knowing is that the bowl is never perfectly symmetric: it climbs more steeply on the squeezed-in side than on the stretched-out side. That gentle lopsidedness is exactly why most materials expand a little when heated, as jittering atoms drift toward the shallower, wider side of the dip.
For two hydrogen atoms, the binding curve dips to its lowest point at a separation of about 0.74 angstroms — that is the bond length — and the dip is roughly 4.5 electron-volts deep, which is the energy you must supply to break the molecule back into two free atoms.
The dip in hydrogen's binding curve gives both its bond length and bond energy.
The dip in the curve points downward by convention, marking lower (more stable) energy. The deeper the well, the stronger the bond — so depth means strength, not weakness.