Davies & Gribbin (1992: 196):
A French student, Louis de Broglie, came up with a bold idea. If light waves can behave like particles, perhaps electrons, which everyone then thought of as material particles, could also behave like waves? Developing this idea, de Broglie produced a simple formula showing how the wavelength of such a particle might be related to the momentum of the particle. Momentum is the product of mass and velocity; de Broglie suggested that converting momentum into wavelength involved, once again, Planck's constant.
Although de Broglie did not provide a detailed theory of matter waves (that was achieved by the Austrian physicist Erwin Schrödinger), his idea provided a graphic model for the way that electrons might occupy only certain energy levels around the nucleus of an atom. If an electron is in some sense a wave, then in order to make the wave "fit'' into an orbit around the nucleus, the size of the orbit must correspond to a whole number of wavelengths, so that when the wave is wrapped around the nucleus it will join together smoothly. Only certain discrete energy levels are allowed because only at certain distances from the nucleus will the wave patterns join up consistently.
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From the perspective of Systemic Functional Linguistic Theory, wave-particle duality is the duality of potential and instance. The wave of an electron is, for example, a measure of the probable locations of electrons, and wavelength is the distance between equiprobable locations.
On this basis, the discrete energy levels at certain distances from the nucleus of an atom correspond to those orbits that accommodate a whole number of equiprobable locations of electrons.
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