Some comments on the matter wave-light wave hypothesis - Bucknum, Michael J. (2007)
From the de Broglie matter wave hypothesis and Planck’s energy quantization law, and assuming conservation of energy in the absorption of a photon and its consequent conversion to kinetic energy of motion by a material particle initially at rest, one can deduce a simple mathematical relationship between the wavelength λ (or frequency ν), of the photon absorbed by the particle at rest, and the resulting de Broglie matter wave length, λD, of the particle with kinetic energy of motion of mv²/2. The relationship so deduced, λD ∝ √λ, suggests that visible wavelengths of light, from about 4000 Å, in the violet, to beyond about 7000 Å, in the red, on absorption by an electron at rest, lead to material electron wavelengths, λD, of the order of the size of the electron transfer proteins seen in the photosynthetic reaction centers of photosynthesizing organisms, at about a size of 50–100 Å. In addition to understanding the mechanism of photosynthesis as a material wave mediated phenomenon, further areas of importance of the relations pointed out in this paper are in the design of experiments to gain a deeper understanding of the basic tenets of wave mechanics, and in the use of tunable lasers to probe various properties of material waves, and to precisely control their properties for applications including lithography.