54 V, giving the electrons a kinetic energy of . As Max von Laue proved in 1912, the periodic crystal structure serves as a type of three-dimensional diffraction grating. The angles of maximum reflection are given by Bragg's condition for constructive interference from an array, Bragg's law for , , and for the spacing of the crystalline planes of nickel () obtained from previous X-ray scattering experiments on crystalline nickel. According to the de Broglie relation, electrons with kinetic energy of have a wavelength of . The experimental outcome was via Bragg's law, which closely matched the predictions. As Davisson and Germer state in their 1928 follow-up paper to their Nobel prize winning paper, "These results, including the failure of the data to satisfy the Bragg formula, are in accord with those previously obtained in our experiments on electron diffraction. The reflection data fail to satisfy the Bragg relation for the same reason that the electron diffraction beams fail to coincide with their Laue beam analogues." However, they add, "The calculated wave-lengths are in excellent agreement with the theoretical values of h/mv as shown in the accompanying table." So although electron energy diffraction does not follow the Bragg law, it did confirm de Broglie's theory that particles behave like waves. However, the experiments did not follow the de Broglie calculations which led to attempts by Carl Eckart, A.L. Patterson, and Fritz Zwicky to make an examination of the possible ways of interpreting the systematic differences between observed and de Broglie calculated electron wavelengths by a contraction factor or index of contraction. Davisson and Germer's accidental discovery of the diffraction of electrons was the first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well. Davisson's attention to detail, his resources for conducting basic research, the expertise of colleagues, and luck all contributed to the experimental success. Practical applications It wasn't until the 1960s that vacuum tubes were adequately made reliable and available to expand on the electron diffraction technique, but since that time, scientists have used LEED diffraction to explore the surfaces of crystallized elements and the spacing between atoms. References External links Foundational quantum physics Physics experiments 1927 in science