Relativity Calculator
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:
(2). 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:
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