femtometer

Nuclear physics runs on a one-line rule in this unit: the radius of a nucleus is roughly $R = 1.2\,A^{1/3}$ fm, with $A$ the mass number, which is how the 7 fm quoted for uranium follows from $A = 238$. The formula works because nuclear matter is nearly incompressible, so nuclear volume grows in proportion to the number of nucleons packed in. The strong force itself reaches only 1 to 3 fm, and the field's cross-section unit, the barn, is 10⁻²⁸ m², which is exactly the area of a square 10 fm on a side.

The unit's famous argument is the proton radius puzzle. In 2010 a measurement using muonic hydrogen, where a muon orbits the proton about two hundred times closer than an electron would, gave a proton charge radius near 0.84 fm while the accepted electron-based value stood near 0.88 fm. A 4% disagreement between careful experiments was a genuine crisis at this scale, and it took most of a decade of remeasurement before the community converged on the smaller number, which is the 0.84 fm in the definition above. In conversation the field still says fermi, as the origin note records, and the femtometre is one of the scales the site's unit converters cover without ever appearing on a physical ruler: no instrument is graduated in it, and every value in it is inferred from scattering.