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The Compton Effect

The Compton Effect is whenever an incoming gamma.png- 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 gamma_primed.png- 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

Planck's_relationship.png.

[ 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 gamma.png- 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: 


wave_diagram.png

Energy and Momentum Conservation Laws:

conservation_lawspng.png

where

definitions.png

Deconstructing Compton Effect Momenta ( abstracting from above ):

deconstructed_wave.png

deconstructed_equations.png                           

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

law.png

directions.png

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

The total composition of y-direction for momentum_gamma.pngcomponents is set to zero because gamma.png- photon has no y-direction.

dingbat.gif

Compton Momentum Scattering - Analysis:

(1). Conservation of Momentum:

scattered_electron_momentum.png

(2). Conservation of Energies:


conservation_energies.png

(2). Combining p.png from both conservation laws:

compton_wavelength.png

trig_identities.png

remember.png

dingbat.gif


Compton Energy Scattering - Analysis:

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

Compton_energy_scattering.png.

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

dingbat.gif

More about Compton Wavelength:

compton_wavelength_1.png

Other Compton Wavelengths are

other_comptons.png

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

National Institute of Standards and Technology

Compton Wavelength and Heisenberg's Uncertainty Principle:

Compton_Heisenberg.png




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