Compton effect wavelength

In modified scattering, the resulting increase in wavelength (Compton effect) is evidence that the x-ray photon acting as a corpuscle has been scattered by colliding with an electron to which it has lost momentum in the process. The Compton effect is not at present of practical importance in analytical chemistry. 

Compton effect. A small fraction of the primary X-ray excitation beam is scattered in the form of radiation whose wavelength depends on the angle of observation. This radiation is superimposed on the X-ray fluorescence spectrum. The shift in angstroms between the two wavelengths (excitation and Compton) is given by ... 

Thus, the wavelength-frequency relation (2.1) implies the Compton-effect formula (2.10). The best we can do is to describe the phenomena constituting the wave-particle duality. There is no widely accepted explanation in terms of everyday experience and common sense. Feynman referred to the experiment with two holes as the central mystery of quantum mechanics. It should be mentioned that a number of models have been proposed over the years to rationalize these quantum mysteries. Bohm proposed that there might exist hidden variables whieh would make the behavior of each photon deterministic, i.e., particle-like. Everett and Wheeler proposed the many worlds interpretation of quantum mechanics in which each random event causes the splitting of the entire universe into disconnected parallel universes in whieh eaeh possibility becomes the reality. 

Strongly influenced by the interpretation of the Compton effect, the French physicist Louis Victor, Prince de Broghe (1892-1987, 1929 Nobel laureate in Physics), suggested in his doctoral thesis in 1924 that the wave-particle duahty for photons could be extended to any particle of momentum p = mv which, somehow, would then have a wavelength - the de Broglie wavelength - associated with it and given by... 

As well as the coherent scattering, which has the same wavelength as the incident waves, an atom scatters waves of reduced wave-length. The intensity of these waves is not included in the formulae (I) and (2). For X-rays falling on a hydrogen atom, the total intensity scattered inelastically, due both to Raman effect and Compton effect, is given by the formula... 

Incoherent (or Compton) scattering, in which the wavelength of the scattered beam increases due to partial loss of photon energy in collisions with core electrons (the Compton effect). 

Fig. 8.—Compton Effect. A light quantum on colliding with an electron transfers part of its energy to the latter, and its wavelength becomes greater after the scattering.

The Compton effect, ejection of an electron without annihilation of the photon. Instead, the scattered photon has lost energy and thus has a higher wavelength. 

Compton wavalength The length below which a particle s quantum-mechanical properties become relevant in relativistic quantum mechanics. For a particle of rest mass m the Compton wavelength is ft/ me, where ft is the rationalized Planck constant and c is the speed of light. The Compton wavelength is so named because of its occurrence in the theory of the Compton effect, where its value for the electron is 3.8616 x 10" m. The Compton wavelength is sometimes defined as hi me, with h being the Planck constant, in which case the electron value is 2.4263 x lO" m. 

Figure 8.13 The Compton effect (incoherent scattering) showing the effect of the scattering angle on the magnitude of the energy (or wavelength) shift (AE or AA.).

Compton Effect n (Compton Recoil Effect) Elastic scattering of photons by electrons results in decrease infi e-quency and increase of wavelength of x-rays and gamma-rays when scattered by free electrons. 

The interaction of radiation with matter can take many forms. The photoelectric effect, the Compton effect, and pair generation-armihilation are processes that occur at wavelengths shorter than those encountered in the infrared. Infrared photons can excite rotational and vibrational modes of molecules, but they are insufficiently energetic to excite electronic transitions in atoms, which occur mostly in the visible and ultraviolet. Therefore, a discussion of the interaction of infrared radiation with matter in the gaseous phase needs to consider only rotational and vibrational transitions, while in the solid phase lattice vibrations in crystals must be included. 

The equation p = hjX also helps us understand the effect of a transfer of momentum in a collision of a photon with another particle, such as an electron. If a photon transfers some of its momentum to another particle, then the momentum, p, of the photon decreases and, as a consequence, its wavelength. A, increases. The change in wavelength that occurs when light is scattered by electrons in atoms in a crystal (the Compton effect) was first observed in 1923. The Compton effect provides additional confirmation that light consists of particle-like entities that can transfer momentum to other particles through collisions. 

At the same time, a diffraction grating with a period of about 1 A has the nature that the interatomic distances in crystals are about this size. As the interatomic distances are approximately 10 m and the size of even the smallest crystal is 10 m (repetition is 10 in the majority of cases), the crystal can be considered infinite. If a beam of X-rays falls on a crystal, under the action of an electromagnetic wave the atoms electrons begin to oscillate and scatter secondary radiation of the same wavelength in all directions (compare with Compton-effect, Section 6.6). As the atoms in a crystal are ordered, these secondary waves are coherent and interfere this defines the diffraction effect. 

Ti(acac)2 was rapidly and quantitatively analyzed by X-ray fluorescence (XRF) spectroscopy. Fe(acac)2 was similarly determined by XRF with correction for Compton scattering. An instrumental geometrical factor and an equivalent wavelength were obtained experimentally, while all the other factors were calculated with the mass absorption coefficients of Fe ". K and XRF spectra of Cr(acac)3 and other Cr compounds were measured with a Bragg spectrometer. The relative intensities of the 3, K 2, K / and K lines with respect to the K line confirm the chemical effect on the intensity... 

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