Past exam of the physics A course of the University of Cambridge / 2012 / Paper 1 / Section A / 3 / Solution

Resolving a length requires momentum transfer $q$ of order $\hslash /\ell$. Taking a hard relativistic scale $qc\sim 4\mathrm{TeV}$ givesThe full de Broglie wavelength convention gives $hc/E\simeq 3.1\times 10^{-19}\mathrm{m}$, differing by $2\pi$; the intended scale is roughly $10^{-19}\mathrm{m}$, far below a proton radius. Two opposing beams have a larger total collision energy, but proton energy is shared among partons: the actual resolution depends on the hard scattering momentum transfer, not simply on beam energy alone.