. In the future you will receive a little piece of software to bring up Relativity Science Calculator directly from within this web pageRelativity Science Calculator
rssxml

Google
 



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.


dingbat.gif


§ Compton Momentum Scattering - Analysis:

(1). Conservation of Momentum:

scattered_electron_momentum.png


(2). Conservation of Energies:

conservation_energies.png

(3). 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: 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




[ Mail this page to a friend ]



 
The best browser for this site is Firefox for our Windows friends and Safari or Firefox for Mac folks
Your ip address is: 54.205.95.9
This document was last modified on: Sunday, 22-Dec-2013 13:10:02 PST
Your browser is: CCBot/2.0 (http://commoncrawl.org/faq/)
relativitycalculator.com

.

.

.

.

.

.

.

.

.

.

.

.