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Constructive resonances with minimum entropy are derived from measurements ofphotoelectric effect cross sections at atomic K-shell thresholds. A resonanceregion with optimal constructive interference is given by a principal wavelength {\lambda} of the order of Bohr atom radius. Our study shows that theproton shape is not a sphere but it has an elliptical volumetric shape with twoequal axes and the other different. Resonance waves allowed us the possibilityto measure both proton radius and shape through an interference term. Thislast, was a necessary condition in order to have an effective cross sectionmaximum at threshold. The minimum entropy means minimum shape deformation andit was found to be (0.830 +/- 0.015) fm and the average proton radius was foundto be (0.851 +/- 0.201) fm.

Measurements of minimum entropy at K-shell photoelectric effect provides the radius and shape of the proton