 Solution

The photon relation gives $\lambda =hc/E=2.4797\times 10^{-12}\mathrm{m}$. The diffraction-limited angular scale of an aperture of diameter $D$ is thereforeFor a uniformly illuminated circular aperture, the Rayleigh criterion instead gives $1.22\lambda /D=3.03\times 10^{-11}\mathrm{rad}$. Both express the same requested estimate. This is an ideal diffraction limit, conditional on the effective diameter behaving as a coherent imaging aperture; photon energy and diameter alone do not specify the performance of a practical gamma-ray telescope.