> I wish a physicist could explain here how the very notion of "diameter" has any meaning for an object whose size (IIUC) belong entirely to the quantum realm.

> I wish a physicist could explain here how the very notion of "diameter" has any meaning for an object whose size (IIUC) belong entirely to the quantum realm. Usually these are describing expectation values of radial positions. For the well-understood example of the hydrogen electronic orbit, the Bohr radius is the expectation value of the radial position of the electron. The electron has a wavefunction Ψ; When you calculate the expectation value of the radius r using Ψ (= \int_0^\infinity Ψ* r Ψ dr ) you find a value of about 0.5 nm. People will drop the subtlety of the "expectation value" and just say "the hydrogen atom has a radius of about 0.5 nm". The issue for the proton radius that the article did not delve into: There is currently more than one way to measure the proton radius. One is scattering (pitch another particle at the proton, look at how it "bounces" off), and another is spectroscopically (look at the energy levels of the electron, deduce the proton radius from the interaction of the electron orbit and the proton.) These methods do not give the same answer.