What explains the presence of photons with different frequencies in the scattered X-ray radiation?

Compton gave a theoretical explanation of the results obtained on the basis of the concept of X-ray quanta as particles with energy and momentum and capable of experiencing elastic collisions with other particles – photons. In an elastic collision with a free stationary electron, the photon transfers part of its momentum to it and changes the direction of motion. In this case, the photon energy decreases, therefore, its wavelength increases. The presence in the composition of the scattered radiation of photons with a constant frequency Compton explained by the fact that some of the photons are scattered not by the outer electrons, but by the electrons of the inner shells of atoms. These electrons are so tightly bound to atoms that when a photon is scattered, it interacts with the entire atom. Due to the large mass of the atom, a photon loses very little energy during elastic collision.