How is the behavior of an electron like a particle and wave?

If we use the mass of the electron traveling at 1 x 105 meters per second, we get a wavelength of about 7.3 x 10-9m, which is about the same size as the radius of an atom. At this speed, the electron can "orbit" the hydrogen nucleus over 3 million times in one second! It would appear that the electron is everywhere at once! Treating the electron as a wave just might be the right way to handle this problem.