Relativity Science Calculator - Compton Effect

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 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.png - components 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.png - components is set to zero because gamma.png - photon has no y - direction.

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§ Compton Momentum Scattering - Analysis:

(1). Conservation of Momentum:

scattered_electron_momentum.png


(2). Conservation of Energies:

conservation_energies.png

(3). Combiningp.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: 1). The NIST Reference on Constants, Units, and Uncertainty

2). National Institute of Standards and Technology

§ Compton Wavelength and Heisenberg's Uncertainty Principle:

Compton_Heisenberg.png

§ 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