How is the Compton Effect similar to the Photoelectric Effect?
Both Compton and Photoelectric effect are quantum effects. Both effects takes places when a photon collides with an electron (although the Compton effect can involve also a nucleon and a photon). Both effects involve that all or only a part of the energy of the incoming photon is absorbed by the electron (considered in most cases initially at rest). Here there is a difference. Whereas only a part of the energy of the incoming photon is transferred to the electron in the Compton effect (hence the emerging photon has a lower energy and a higher wavelength), in the photoelectric effect all the energy of the photon is transferred to the electron. Another similarity between the two effects is that they have demonstrated that light can not be considered only a wave but by its nature is composed out of particles (quanta named photons) which carry a well defined quantity of energy. Both effects are examples of the conservation law of energy and of total momentum.