Duane's hypothesis

In 1922 American physicist William Duane presented the hypothesis that the scattering of X-Ray photons by a crystal could be best explained by a mechanism of discrete quantized transactions between the crystal and the incident X-Ray photons, where the reaction of the crystal is constrained by a simple quantum rule, and the incident photons behave as free particles. Duane argued that the observed discrete scattering (i.e. one photon at a time) is not explainable in a simple manner by theories based on classical waves.

Duane applied his hypothesis to derive Bragg's Law for the scattering angles of X-Rays by a crystal. Subsequently, the principles that Duane advanced were also seen to provide the correct relationships for optical scattering at gratings, and the diffraction of electrons.

In 1905, Albert Einstein presented the hypothesis that the photoelectric effect could be explained if a beam of light was composed of a stream of discrete particles (photons), each with an energy (E = hf) the energy (E) of each photon being equal to the frequency (f) multiplied by Planck's constant (h). Later, in 1916 Einstein also showed that the recoil of molecules during the emission and absorption of photons was consistent with, and necessary for, a quantum description of thermal radiation processes. Each photon acts as if it imparts a momentum impulse p equal to its energy divided by the speed of light, (p = E/c).

In 1925, shortly before the development of the full mathematical description of quantum mechanics, Born drew Einstein's attention to the then new idea of "de Broglie's waves". He wrote "It seems to me that a connection of a completely formal kind exists between these and that other mystical explanation of reflection, diffraction and interference using 'spatial' quantisation which Compton and Duane proposed and which has been more closely studied by Epstein and Ehrenfest." Examining the hypothesis of Duane on quantized translational momentum transfer, as it accounted for X-ray diffraction by crystals, and its follow-up by Compton, Epstein and Ehrenfest had written "The phenomena of Fraunhofer diffraction can be treated as well on the basis of the wave theory of light as by a combination of concept of light quanta with Bohr's principle of correspondence." Later, Born and Biem wrote: "Every physicist must accept Duane's rule."

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