The Compton Effect
Making researches on X-rays (discovered in 1896) scientists discovered an interesting fact. That was when they were doing their research on the effect of the rays dissipation on a graphite block. The source of rays was the X-ray tube sending monochromatic X-rays. The beam went then through two narrow slots and fell on the graphite block. The dissipation proceeded, and the scientists studied the wavelengths of the falling, and the dissipated rays. And the interesting fact they noticed was that the dissipated X-rays consisted of two different wavelengths. One of them was the same as the wavelength of the falling rays, and the second one was longer. The effect occurred even if the block was built of the material different than graphite. And another interesting fact was that the increase of the length of the dissipated wave depended on the dissipation angle.
In 1923 Arthur Holly Compton developed a theory explaining these phenomena. He assumed that photons of X-radiation, just like it was with other particles, were carrying also some momentum, besides the energy. And so the process of dissipation is just the series of elastic collisions between the falling photons of the radiation and the electrons or atoms.
The momentum of each photon is inversely proportional to its wavelength. The momentum is given by the formula:
(1)
A photon going through a graphite block can get dissipated on the electrons inside. In the world of atoms, just like in the world of ordinary sizes, there are some quantities that are always conserved. Among others these are the momentum and the energy. At the moment of dissipation the electron, on which it proceeds, achieves some velocity, and also some energy. The photon must lose some of its energy, because the absolute energy of the system (electron and photon) remains the same. On the other hand the momentum of the system before and after the dissipation must also stay unchanged. Compton took the both conservation laws into consideration. The formula he achieved describes the dependence of the wavelength of the dissipated photon upon the wavelength before the dissipation, and the angle of dissipation:
(2)
m means here the mass of the electron.
As you see, the bigger the angle of dissipation (the smaller cosine), the longer the wave of the dissipated photon.
We have said before that except for the photons having their wavelength hanged there were also some having their wavelength the same as before the dissipation. That is because some of the photons are dissipated not on free electrons but on whole atoms. Replacing the mass of an electron with the mass of an atom (which is a few thousand times bigger than this of an electron) in the formula above we see that the second element of the right side of the equation has no influencing power now. And so:
(3)
That is how Compton, basing on the theory of the photons, explained the experimental facts.
