Short answers, pulled from the story.
Arthur Holly Compton discovered that the wavelength of scattered light was longer than the incoming light when he directed a beam of photons with energy around 17 keV toward a graphite target. This shift proved that classical wave theory could not explain the interaction and convinced physicists that light behaves as a stream of particle-like objects called quanta.
The quantity known as the Compton wavelength of the electron equals approximately 0.00243 nanometers. The maximum shift occurs when the photon scatters backward at an angle of 180 degrees, which is twice the Compton wavelength of the electron.
Compton scattering is the most probable interaction of high-energy X-rays with atoms inside human bodies because it allows doctors to target tumors while sparing surrounding healthy cells. It occurs when photons strike loosely bound electrons in outer valence shells and transfers energy to the recoiling particle known as a Compton recoil electron.
Electrons in hot gas surrounding galaxy clusters scatter cosmic microwave background photons to higher energies resulting in the Sunyaev-Zel'dovich effect. Observations of this effect provide nearly redshift-independent means of detecting distant galaxy clusters.
Researchers magnetize a crystal sample hit with high energy circularly polarized photons and measure the scattered photon's energy while reversing the magnetization direction of the sample. Taking the difference between these profiles yields the magnetic Compton profile as a one-dimensional projection that represents bulk properties of the sample and serves as a probe of ground state magnetism.