Spatial resolution from momentum transfer ($\ell \sim \hslash /q$)

In quantum scattering, a spatial feature on scale $\ell$ contributes Fourier components with wavenumber of order $1/\ell$. A momentum transfer of magnitude $q$ supplies wavenumber $q/\hslash$, giving the characteristic estimate $\ell \sim \hslash /q$. With the energy-like quantity $Q=qc$, this becomes $\ell \sim \hslash c/Q$. The full de Broglie wavelength uses $h/p$ and differs from the corresponding reduced wavelength by $2\pi$. Beam energy only bounds accessible momentum transfer; it does not determine the resolution of every event.