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:


[ 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.


§ Compton Effect:


§ Energy and Momentum Conservation Laws:




§ 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 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.


§ Compton Momentum Scattering - Analysis:

(1). Conservation of Momentum:


(2). Conservation of Energies:


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





§ 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:


In other words, gamma.png - photons which scatter off free atomic electrons electron.png 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