proton radius
A proton is not a hard sphere with a sharp edge — it is a fuzzy ball of churning quarks and gluons. Still, you can sensibly ask how big it is, by measuring how its electric charge is spread out in space. The answer, the proton's charge radius, is roughly a quadrillionth of a meter — about 0.84 of a femtometer. It is one of the most basic numbers describing the particle that makes up most of visible matter.
There are two classic ways to measure it. You can fire electrons at protons and watch how they scatter, since the spread of the charge affects the bounce. Or you can study the energy levels of hydrogen, a single electron orbiting a single proton, since a bigger proton shifts those levels by a tiny amount. For years both methods agreed. Then, around 2010, a clever new measurement using muonic hydrogen — where a heavier muon replaces the electron and orbits much closer to the proton, making it far more sensitive to the proton's size — gave a noticeably smaller radius. The disagreement became known as the proton radius puzzle.
For a decade the discrepancy looked like it might point to new physics, perhaps an unknown force felt differently by muons and electrons. But improved hydrogen and scattering measurements gradually shifted toward the smaller muonic value, and the puzzle is now largely resolved as having come mostly from underestimated experimental difficulties rather than new physics. It remains a textbook example of how a single precise number can stress-test the whole framework, and of how science self-corrects.
The proton charge radius is about 0.84 femtometers. The earlier electron-based value of about 0.88 fm clashed with this for years before the smaller value won out.
The proton's charge radius — under a femtometer — became a famous puzzle when two methods briefly disagreed.
The proton has no crisp surface, so its "radius" is a defined measure of how its charge is distributed, not the edge of a solid ball. Different probes can weight that distribution slightly differently.