Wave nature of particles

   This is one of the most misinterpreted phenomena which mislead the scientific community since its introduction in 1924 by de Broglie. Einstein explained photoelectric effect considering light as particle. This proposal influenced de Broglie to develop his matter wave concept. He believed that, if light has both wave like and particle like behaviour simultaneously, a particle like electron must also have wave-particle duality. The Davisson-Germer experiment and G.P. Thomson experiment conducted in 1927 demonstrated that fast moving electrons exhibit wave like behaviour.
   Now, we have two questions. 1) Both the experiments are conducted with artificially accelerated electrons (they applied potential difference between the anode and cathode in the experimental setup to provide the electrons with sufficient kinetic energy); but what makes the electrons in an atom in motion? 2) Why electrons in motion act as wave?
   Today we know that, in an atom there are two types of forces acting on its electrons. They are attraction from the nucleus and repulsion between electrons (in hydrogen atom attraction from the nucleus only) but these forces cannot cause any kind of motion of electrons in an atom (see structure of atom). Since the electrons are not in motion, there is no matter wave of electrons in atoms.
   Recent studies indicate that electron (charged particle) has a standing electric field and magnetic field at right angle simultaneously (see structure of electron). In fact electrons are not merely tiny "spherical balls" of matter to travel in a straight line when it is accelerated. So, fast moving electrons make oscillations in its path. Uncharged particle neutron has a standing magnetic field, so accelerated neutrons make oscillations. Because of the presence of electrons protons and neutrons, fast moving atoms and molecules also demonstrate wave like behaviour.

See wikipedia articles: De broglies Matter wave concept, Gavission-Germer experiment and G.P Thomson Experiment