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It seems as though the equation here ($d\sinθ=1.22\lambda$) is more or less the same as the equation for diffraction gratings ($d\sinθ=n\lambda$). However, in the equation for the gratings, d is the grating spacing, not the thickness of one of the gratings, which is how I'm assuming the nuclei would act in this set up (as the gratings). So how is it that the electron diffraction equation can tell us the diameter/radius of the nucleus, and not the distance between nuclei i.e. the grating spacing?

Also if anyone know why we use 1.22 that'd be great, I know it's something to do with the Rayleigh criterion but haven't been able to find a suitable explanation for it in this context.

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A better analogy for the equation you're using is not the equation giving the intensity maximums for a multiple-slit grating, $$ d\sin \theta =n\lambda $$ but rather the diffraction pattern from a single slit of width $a$, which has intensity minimums when $$ a \sin \theta = n \lambda \qquad (n \neq 0). $$ This means that the central bright spot from a single slit subtends an angle $\theta \approx \lambda/a$ in either direction from the "forward direction", assuming that $\theta$ is small.

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Image from Wikimedia Commons

When you then go to a circular aperture of diameter $a$, the angular radius of the resulting diffraction pattern becomes $\theta \approx 1.22 \lambda/a$ instead. The reasons for this factor of 1.22 are explained in this related question (hat tip to @ThomasFritsch for linking this in the comments.)

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