= Solution
Resolving a length requires <momentum transfer> $q$ of order $\hbar/\ell$. Taking a hard relativistic scale $qc\sim4\,\mathrm{TeV}$ gives
$$
\boxed{\ell\sim\frac{\hbar c}{E}\simeq4.9\times10^{-20}\,\mathrm m}.
$$
The full <de Broglie wavelength> convention gives $hc/E\simeq3.1\times10^{-19}\,\mathrm m$, 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.
Back to article page
