e-book Change in Wave-length by Scattering

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Compton effect , increase in wavelength of X-rays and other energetic electromagnetic radiations that have been elastically scattered by electrons; it is a principal way in which radiant energy is absorbed in matter. The effect has proved to be one of the cornerstones of quantum mechanics , which accounts for both wave and particle properties of radiation as well as of matter.

What is Raman Scattering?

See also light: Early particle and wave theories. The American physicist Arthur Holly Compton explained ; published the wavelength increase by considering X-rays as composed of discrete pulses, or quanta , of electromagnetic energy. The American chemist Gilbert Lewis later coined the term photon for light quanta. Photons have energy and momentum just as material particles do; they also have wave characteristics, such as wavelength and frequency.

quantum mechanics - Why wavelength does not change in scattering? - Physics Stack Exchange

The energy of photons is directly proportional to their frequency and inversely proportional to their wavelength, so lower-energy photons have lower frequencies and longer wavelengths. In the Compton effect, individual photons collide with single electrons that are free or quite loosely bound in the atoms of matter.

Colliding photons transfer some of their energy and momentum to the electrons, which in turn recoil. In the instant of the collision, new photons of less energy and momentum are produced that scatter at angles the size of which depends on the amount of energy lost to the recoiling electrons. Because of the relation between energy and wavelength, the scattered photons have a longer wavelength that also depends on the size of the angle through which the X-rays were diverted.

In this "normal" scattering model in contrast to the anomalous case in which those frequencies are comparable the scattered wave is in opposition of phase with the incident radiation.

Rayleigh scattering

The factor of the geometric "difference of phase". With regard to the phenomenon of diffraction and interference, it is important to consider the phase relationship between two waves due to their different geometric paths. Scattering by an atom. An atom that can be considered as a set of Z electrons its atomic number can be expected to scatter Z times that which an electron does.

But the distances between the electrons of an atom are of the order of the X-rays wavelength, and therefore we can also expect some type of partial destructive interferences among the scattered waves. If this distribution is considered spherically symmetric, it will just depend on the distance to the nucleus, so that, with:.

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By quantum-mechanics calculations we can obtain the values for the atomic scattering factors, and we can derive analytical estimates of the type:. Scattering by a set of atoms.

X-rays scattered by a set atoms produce X-ray radiation in all directions, leading to interferences due to the coherent phase differences between the interatomic vectors that describe the relative position of atoms. In a molecule or in an aggregate of atoms, this effect is known as the effect of internal interference , while we refer to an external interference as the effect that occurs between molecules or aggregates.

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The scattering diagrams below show the relative intensity of each of these effects:. The figures mainly represent the effect of the external interference , while the internal interference in this case due to a single atom only is simply reflected by the relative intensity of the maxima. In the case of monoatomic liquids some effects appear at short distances, due to correlations between atomic positions.

No matter the possible complexity with which the phenomenon of X-ray scattering is presented. Scattering by a monoatomic lattice: Diffraction. When the set of atoms is structured as a regular three-dimensional lattice so that the atoms are nodes of the lattice , the precise geometric relationships between the atoms give rise to particular phase differences. Note that the figures show a direct unit cell and a reciprocal unit cell only, corresponding to the diffraction patterns shown on the left side of the page.

See also direct and reciprocal lattices. Structured in a lattice, any atom can be defined by a vector, referred to a common origin:. And calculating this sum we have:. M3 around 10 15 in crystals of an average thickness of 0.

6.3: The Compton Effect

Due to the finite size of the samples, the small chromatic differences of the incident radiation, the mosaic of the sample, etc. Diffraction by a crystal. When the material is not structured in terms of a monoatomic lattice, but is formed by a group of atoms of the same or of different types, the position of every atom with respect to a common origin is given by:. This internal structural effect is:. As a consequence of the complex representation of waves, mentioned at the beginning, the square of a complex magnitude is obtained by multiplying the complex by its conjugate.

This means that if we change the origin, the phase differences will be produced according to the geometric changes, in such a way that as the exponential parts of the intensity functions are conjugate complexes, they will affect the intensities in terms of a proportionality constant only. Thus, a change of origin is not relevant to the phenomenon. To clarify what has been said above, the reader can analyse further objects and their corresponding diffraction patterns through this link. Additionally we suggest you to watch the video prepared by the Royal Institution to demonstrate optically the basis of diffraction using a wire coil representing a molecule and a laser representing an X-ray beam.

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Compton effect, Compton shift simple derivation step by step

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