An introduction to wave mechanics

The wave-nature of electrons

The quantum theory of radiation introduced by Max Planck and Albert Einstein implies a particle theory of light, in addition to the wave theory of light required by the phenomena of interference and diffraction. In 1924, Louis

de Broglie argued that if light were composed of particles and yet showed wave-like properties, the same should be true of electrons and other particles. This phenomenon is referred to as wave–particle duality. The de Broglie relationship (equation 1.11) combines the concepts of classical mechanics with the idea of wave-like properties by showing that a particle with momentum mv (m = mass and v =velocity of the particle) possesses an associated wave of wavelength λ.

An important physical observation which is a consequence of the de Broglie relationship is that electrons accelerated to a velocity of 6 × 10⁶ ms^-1 (by a potential of 100 V) have an associated wavelength of ≈ 120pm and such electrons are diffracted as they pass through a crystal. This phenomenon is the basis of electron diffraction techniques used to determine structures of chemical compounds.