Wavelength of Compton

The wavelength of Compton $\ lambda_C \$ of a Particule is given by

\ lambda_C = \ frac {H} {m C} = 2 \ pi \ frac {\ hbar} {m C} \

where

h \

is the Constante of Planck,

m \

the Masse of the particle,

c \

the Speed of light.

The value wavelength of Compton of the electron, of CODATA 2002 is 2.426310238×10^-12 m with a standard uncertainty of 0.000000016×10^-12 Mr. the other particles have different wavelengths of Compton.

The wavelength of Compton can be regarded as a fundamental limitation with the measure of location of a particle, taking account of the quantum Mécanique and the restricted Relativité. This depends on the mass $m \$ of the particle. To see that, let us note that one can measure the position of a particle by sending light above - but to measure the position with precision requires a light short wavelength. The light with a low wavelength is made up of Photon S of high energy. If the energy of these photons exceeds $mc^2 \$ , when one of them strikes the particle whose position is known, the collision can release enough from energy to create a new particle of the same type. This makes debatable the question about the initial position of the particle.

This demonstration also shows that the wavelength of Compton is the limit below which the Quantum theory the fields - which makes it possible to describe the creation and the annihilation of particles - becomes important.

Let us suppose that we wish to measure the position of a particle with a precision $\ Delta X \$ . Then the relation of uncertainty between the Position and the Quantité of movement says that

\ Delta X \, \ Delta p \ Ge \ hbar/2

thus uncertainty on the satisfied momentum of the particle

\ Delta p \ Ge \ frac {\ hbar} {2 \ Delta X}

By using the relativistic relation between the momentum and energy, when

\ Delta p

then exceeds

mc

uncertainty on energy is larger than

mc^2 \

, which is enough of energy to create another particle of the same type. Thus, with a little algebra, we see that there is a limitation fondamentale

\ Delta X \ Ge \ frac {\ hbar} {2mc}

Therefore, at least for same the Order of magnitude, the uncertainty of the position can be larger than the wavelength of Compton

h/mc \

The wavelength of Compton can be compared with the wavelength of Broglie, which depends on the momentum of the particle and determines the limit between the particle and the undulatory behavior in quantum Mécanique.

References

Sources

This article is entirely or partially translated English article.

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