Description of The Phenomenon
See also: Klein-Nishina formulaBy the early 20th century, research into the interaction of X-rays with matter was well underway. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle and emerge at a different wavelength related to . Although Classical electromagnetism predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.
In 1923, Compton published a paper in the Physical Review which explained the X-ray shift by attributing particle-like momentum to “photons” which Einstein had invoked the use of for his Nobel prize winning explanation of the photo-electric effect. However, first postulated (unenthusiastically) by Planck, these "particles" conceptualized as elements of light “quantized” as containing a specific amount of energy depending only on the frequency of the light. In his paper, Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments which verified his derived relation:
where
- is the initial wavelength,
- is the wavelength after scattering,
- is the Planck constant,
- is the Electron rest mass,
- is the speed of light, and
- is the scattering angle.
The quantity h⁄mec is known as the Compton wavelength of the electron; it is equal to 2.43×10−12 m. The wavelength shift λ′ − λ is at least zero (for θ = 0°) and at most twice the Compton wavelength of the electron (for θ = 180°).
Compton found that some X-rays experienced no wavelength shift despite being scattered through large angles; in each of these cases the photon failed to eject an electron. Thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10 000 times smaller.
Read more about this topic: Compton Scattering
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