The Compton Effect

"Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune intoned in the distance by an invisible player" - Albert Einstein ( 1879 - 1955 )

The Compton Effect is whenever an incoming - photon ( monochromatic beam of x - rays or gamma rays ) hits a stationary electron, part of the photon's energy is transferred to the released electron with the consequent result of the scattered - photon having a lower energy level as well as concomitant lower frequency and longer ( increased ) wavelength. The collision will have enough energy to make a new wave-particle of the same type, in this case another electron. This is all summarized by Planck's relationship:

.

[ note: The Inverse Compton Effect occurs whenever a photon gains energy from an incoming high velocity, high energy electron and thereby achieves a higher energy level as well as a shorter ( decreased ) wavelength and a higher frequency of radiation. ]

Gamma ray - photons are the most energetic form of light [ shortest electromagnetic wavelengths, highest energy ] having energies in excess of 100+ KeV and are the source of Gamma - Ray Bursts ( GRBs ), lasting from milli-fractions of a second to several minutes and shining a million trillion times brighter than the Sun at the heart of supernovae in other distant galaxies.

source: http://imagine.gsfc.nasa.gov/Videos/news/GRBstar2.mov

§ Compton Effect:

§ Energy and Momentum Conservation Laws:

where

§ Deconstructing Compton Effect Momenta ( abstracting from above ):

                           

In the x - and y - directions, the deconstructed components of total momentum are: 

The total composition of x - direction for components are additive and positive because - photon is traveling completely in x - direction along an orthogonal x - axis.

The total composition of y - direction for components is set to zero because - photon has no y - direction.

§ Compton Momentum Scattering - Analysis:

(1). Conservation of Momentum:

(2). Conservation of Energies:

(3). Combining from both conservation laws:

§ Compton Energy Scattering - Analysis:

We know from our earlier momentum scattering analysis when an - photon ( x - ray or gamma ray ) hits a free atomic electron that the following deconstructed components of total momentum and energies are true:

.

In other words, - photons which scatter off free atomic electrons will experience changes in both direction and energy ( frequency ) levels.

§ More about Compton Wavelength:

Other Compton Wavelengths are

sources: The NIST Reference on Constants, Units, and Uncertainty

National Institute of Standards and Technology

§ Compton Wavelength and Heisenberg's Uncertainty Principle:

§ References:

 "A Quantum Theory of the Scattering of X - rays by Light Elements", by Arthur H. Compton, The Physical Review, Second Series, May, 1923, Vol. 21, No. 5, pgs. 483 - 502

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