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## Compton wavelength
The - ,
## Additional recommended knowledgewhere - is the Planck constant,
- is the particle's mass,
- is the speed of light.
The CODATA 2002 value for the Compton wavelength of the electron is 2.4263102175×10 The Compton wavelength can be thought of as a fundamental limitation on measuring the position of a particle, taking quantum mechanics and special relativity into account. This depends on the mass of the particle. To see this, note that we can measure the position of a particle by bouncing light off it - but measuring the position accurately requires light of short wavelength. Light with a short wavelength consists of photons of high energy. If the energy of these photons exceeds , when one hits the particle whose position is being measured the collision may have enough energy to create a new particle of the same type. This renders moot the question of the original particle's location. This argument also shows that the Compton wavelength is the cutoff below which quantum field theory– which can describe particle creation and annihilation – becomes important. We can make the above argument a bit more precise as follows. Suppose we wish to measure the position of a particle to within an accuracy . Then the uncertainty relation for position and momentum says that
so the uncertainty in the particle's momentum satisfies
Using the relativistic relation between momentum and energy,
when Δ
So, at least to within an order of magnitude, the uncertainty in position must be greater than the Compton wavelength . The Compton wavelength can be contrasted with the de Broglie wavelength, which depends on the momentum of a particle and determines the cutoff between particle and wave behavior in quantum mechanics. For fermions, the Compton wavelength sets the cross-section of interactions. For example, the cross-section for Thomson scattering of a photon from an electron is equal to , where is the fine-structure constant and is the Compton wavelength of the electron. For gauge bosons, the Compton wavelength sets the effective range of the Yukawa interaction: since the photon is massless, electromagnetism has infinite range. The Compton wavelength of the electron is one of a trio of related units of length, the other two being the Bohr radius
## References**^**CODATA 2002 value for Compton wavelength for the electron from NIST
Categories: Atomic physics | Foundational quantum physics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Compton_wavelength". A list of authors is available in Wikipedia. |