The idea that a particle can act like a wave follows from Planck and Einstein's conclusion that a wave (light) can act like a particle. DeBroglie proposed that the dichotomy between waves and particles affects all matter. Electrons, protons, neutrons, alpha-particles, ions, etc. can act as waves according to this hypothesis. So can a basketball, but its wavelength is so short relative to any macroscopic object it comes into contact with that it does not affect the player at the free throw line. For the small particles, the wavelength can affect the interaction of the particle with matter. This is shown above for an aluminum foil. We see that electrons can give rise tot a diffraction pattern, just as X-rays can.

Implications for electron microscopy

Electron microscopy is a powerful analystical techique used to detect structures with nanometer accuracy. One can tune the wavelength of the electrons by accelerating them through charged plates. The DeBroglie equation can then be used to calculate the wavelength of the electron. For example, in a 200 kV (kilovolt) electron microscope we can calculate the energy of the electron based on the electron charge (1.602 x 10^-19 Coulombs) and the voltage (2 x 10⁵ volts). Note that Joules = Coulombs x Volts. Thus, the energy of the electron is 3.2 x 10^-14 J. This sounds like a small number, but the mass of the electron is very small as well (9.1 x 10^-31 kg, so this corresponds to a velocity of 2.65 x 10⁸ m/s! The wavelength calculated from the DeBroglie relation is 2.74 picometers..