During the photoelectric process, photons are absorbed and electrons are ejected. In Compton scattering, photons are scattered rather than absorbed. My textbook (Quantum Physics of Atoms,Molecules,Solids,Nuclei, and Particles) explains that absorption occurs in the photoelectric process because the electrons are bound to atoms and a truly free electron cannot absorb a photon and conserve energy. So far so good. No questions. However, during compton scattering, there are two peaks of intensity. One peak (shifted wavelength) corresponds to the photons which struck free electrons and lost a bit of energy. The other peak (unshifted wavelength) corresponds to photons which actually hit more tightly bound inner electrons. So these photons are hitting BOUND electrons just as in the photoelectric effect and yet they are being scattered. So to summarize, I was told that photons in the photoelectric process are absorbed not scattered because the electrons are bound not free and yet here is this example of a photon hitting a bound electron and being scattered not absorbed?