Compton Wavelength


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Compton wavelength

[′käm·tən ′wāv‚leŋkth]
(quantum mechanics)
A convenient unit of length that is characteristic of an elementary particle, equal to Planck's constant divided by the product of the particle's mass and the speed of light.

Compton Wavelength

 

a quantity with the dimension of length that is characteristic of relativistic quantum processes; it is expressed in terms of the particle’s mass m and the universal constants h and c (h is Planck’s constant and c is the speed of light): λo = h/mc. The term “Compton wavelength” arose because the quantity λo determines the change Δλ in the wave-length of electromagnetic radiation during Compton scattering (scattering by free electrons; seeCOMPTON EFFECT). The quantity λ̸ = h̸/mc (where h̸ = h/2π) is more often called the Compton wavelength. For the electron λ̸o = 3.86151 × 10˗14 cm, and for the proton λ̸ = 2.10308 X 10˗14 cm.

The Compton wavelength determines the scale of spatial nonuniformities of the field at which quantum relativistic processes become significant. In fact, if we consider a certain wave field—for example, an electromagnetic wave field—whose wavelength λ is less than the Compton wavelength λ0 of the electron, then the energy of the quanta of this fieldع = hv (where v = c/λ is the frequency) is found to be greater than the rest energy of the electron (ع › hc/λo), and consequently the production of electron-positron pairs in the field becomes possible and occurs. Such processes of particle production are described by relativistic quantum theory.

Since measurement of the coordinates of a particle is possible only with a precision of the order of the wavelength of the “light” that is “illuminating” it, it is clear that the position of a specific particle may be determined only with an accuracy of the order of the Compton wavelength of the particle. The Compton wavelength also determines the distance to which a virtual particle with mass m may move from the point of its production. Therefore, the radius of operation of nuclear forces (whose carriers are mainly virtual pi-mesons, the lightest of the strongly interacting particles) is of the order of the pi-meson’s Compton wavelength (λ0 ~ 1013 cm). Similarly, the polarization of a vacuum caused by the production of virtual electron-positron pairs appears at a distance of the order of the Compton wavelength of the electron.

V. I. GRIGOR’EV

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0], becomes equal to the reduced Compton wavelength of it, namely
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C] = h/2[pi]mc is the reduced Compton wavelength of the proton with the numerical value 2.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the reduced Compton wavelength of the electron with the numerical value 3.
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035999074 express the electron motion on the elliptic sphere of the radius of 3679 Compton wavelengths of the electron.
Bizouard discovered that the use of the reduced electron Compton wavelength is decisive for the compatibility of the Hubble-Lemaitre length with [2.
Another derivation involves the consideration of a body whose Compton wavelength equals its Schwarzschild or gravitational radius [1].
d) Why does the wavelength of the light observed by us not fit to the Compton wavelength of the electrons emitting the light?
The greatest finite elliptic radius is a half of the Compton wavelength of the electron:
F], a string of length equal to its Fermi wavelength, composed by unit cells having a length equal to the Compton wavelength of the electron.
C] the Compton wavelengths of the elementary particles involved and elt see below.