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The Compton wavelength of a particle is given by
Additional recommended knowledge
The CODATA 2002 value for the Compton wavelength of the electron is 2.4263102175×10-12 meter with a standard uncertainty of 0.0000000033×10-12 m. Other particles have different Compton wavelengths.
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 Δp exceeds mc then the uncertainty in energy is greater than , which is enough energy to create another particle of the same type. So, with a little algebra, we see there is a fundamental limitation
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.
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 a0 and the classical electron radius re. The Compton wavelength is built from the electron mass me, Planck's constant h and the speed of light c. The Bohr radius is built from me, h and the electron charge e. The classical electron radius is built from me, c and e. Any one of these three lengths can be written in terms of any other using the fine structure constant α:
|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.|