= Solution
For a <photon>, $E=hc/\lambda$. Using <Planck constant> $h=6.62607015\times10^{-34}\,\mathrm{J\,s}$, <speed of light> $c=2.99792458\times10^8\,\mathrm{m\,s^{-1}}$ and $1\,\mathrm{eV}=1.602176634\times10^{-19}\,\mathrm J$ gives
$$
\lambda=\frac{hc}{2.5\,\mathrm{eV}}=4.96\times10^{-7}\,\mathrm m.
$$
The <Rayleigh criterion> for a circular <aperture> of diameter $D$ is $\theta_R=1.22\lambda/D$, set by the first zero of its <Airy disk>. Thus the ideal <diffraction-limited resolution> is
$$
\boxed{\theta_R=2.52\times10^{-7}\,\mathrm{rad}},\qquad
\boxed{s=R\theta_R=5.04\times10^{10}\,\mathrm m}.
$$
The conversion to transverse separation uses the <small-angle approximation>. An order-of-magnitude estimate $\lambda/D$ instead gives $2.07\times10^{-7}\,\mathrm{rad}$ and $4.13\times10^{10}\,\mathrm m$; the distinction is the chosen resolution criterion. These are <aperture> limits, before instrumental aberrations and detector sampling.
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