= Solution
The <protons> at the <Large Hadron Collider> are ultrarelativistic: their <energy> is much greater than their <rest energy>, about $0.938\,\mathrm{GeV}$. The <relativistic energy-momentum relation> therefore gives $pc\simeq E$. Using the <de Broglie wavelength>,
$$
\lambda=\frac hp\simeq\frac{hc}{E}
=\frac{1.240\times10^{-6}\,\mathrm{eV\,m}}{6.5\times10^{12}\,\mathrm{eV}}
=1.91\times10^{-19}\,\mathrm m.
$$
Thus the conventional <de Broglie wavelength> estimate is \b[a distance of order $10^{-19}\,\mathrm m$].
There is a conventional factor of $2\pi$ in interpreting this estimate. <Spatial resolution from momentum transfer> is often expressed as $\ell\sim\hbar c/Q$, where $Q$ is the transferred <momentum> multiplied by the <speed of light>. Taking $Q$ of order the beam <energy> gives
$$
\ell\sim\frac{197.3\,\mathrm{MeV\,fm}}{6.5\times10^6\,\mathrm{MeV}}
=3.0\times10^{-20}\,\mathrm m.
$$
Both conventions describe the same characteristic scale up to $2\pi$. The beam <energy> alone does not give an exact experimental <spatial resolution>: a particular collision probes a scale set by its actual <momentum transfer>.
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