λ=h(2mE)2, where me is the mass of the electron and h is the constant introduced by Max Planck and Albert einstein in the early 1900s to relate a photon s energy e to its frequency v via e hv. These amazing findings were among the earliest to suggest that electrons, which had always been viewed as particles, might have some properties usually ascribed to waves That is, as de broglie has suggested in 1925, an electron seems to have a wavelength inversely related to its momentum, and to display wave-type diffraction. I should mention that analogous diffraction was also observed when other small light particles(e.g protons, neutrons, nuclei, and small atomic ions) were scattered from crystal planes. In all such cases, Bragg -like diffraction is observed and the Bragg equation is found to govern the scattering angles if one assigns a wavelength to the scattering particle according to 入=h(2mE where m is the mass of the scattered particle and h is Plancks constant(6.62 x10-erg sec) The observation that electrons and other small light particles display wave like behavior was important because these particles are what all atoms and molecules are made of. So, if we want to fully understand the motions and behavior of molecules, we must be sure that we can adequately describe such properties for their constituents Because the classical Newtonian equations do not contain factors that suggest wave properties for electrons or nuclei moving freely in space, the above behaviors presented significant challenges4 l = h/(2me E)1/2 , where me is the mass of the electron and h is the constant introduced by Max Planck and Albert Einstein in the early 1900s to relate a photon’s energy E to its frequency n via E = hn. These amazing findings were among the earliest to suggest that electrons, which had always been viewed as particles, might have some properties usually ascribed to waves. That is, as de Broglie has suggested in 1925, an electron seems to have a wavelength inversely related to its momentum, and to display wave-type diffraction. I should mention that analogous diffraction was also observed when other small light particles (e.g., protons, neutrons, nuclei, and small atomic ions) were scattered from crystal planes. In all such cases, Bragg-like diffraction is observed and the Bragg equation is found to govern the scattering angles if one assigns a wavelength to the scattering particle according to l = h/(2 m E)1/2 where m is the mass of the scattered particle and h is Planck’s constant (6.62 x10-27 erg sec). The observation that electrons and other small light particles display wave like behavior was important because these particles are what all atoms and molecules are made of. So, if we want to fully understand the motions and behavior of molecules, we must be sure that we can adequately describe such properties for their constituents. Because the classical Newtonian equations do not contain factors that suggest wave properties for electrons or nuclei moving freely in space, the above behaviors presented significant challenges