Question

An electron microscope passes 1.00-pm-wavelength electrons through a circular aperture $2.00 \textrm{ }\mu\textrm{m}$ in diameter. What is the angle between two just-resolvable point sources for this microscope?

$ 6.1\times 10^{-7}\textrm{ rad} $

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Video Transcript

This is College Physics Answers with Shaun Dychko. This question is asking about the Rayleigh criterion which we encountered in chapter 27; this is equation number 25. So the angle between two just barely resolvable points is gonna be 1.22 times the wavelength of the wave being used to do the observation divided by the diameter of the aperture through which those waves have to travel. And the waves being used in this case are not light waves but rather electron waves with a de Broglie wavelength of 1 picometer. And they go through an aperture of diameter—2 micrometers. So we have 1.22 times 1 times 10 to the minus 12 meters—wavelength— divided by 2 times 10 to the minus 6 meters—aperture size— which gives 6.1 times 10 to the minus 7 radians.