Step 1: Examine the photoelectric effect. This phenomenon, where electrons are ejected from a material by incident light, presented anomalies like a threshold frequency and immediate electron emission that classical wave theory couldn't explain. Albert Einstein resolved this by proposing light exists as discrete energy packets, or photons. Consequently, the photoelectric effect serves as crucial evidence for light's particle nature. Statement A is incorrect; statement C is correct.
Step 2: Examine the Compton effect. This involves the scattering of X-rays or gamma rays by electrons. The observed shift in the radiation's wavelength is explicable by modeling the interaction as a collision between a photon and an electron, where both energy and momentum are conserved. This interaction, analogous to billiard balls colliding, definitively demonstrates light's particle nature. Therefore, the Compton effect illustrates light's particle characteristics. Statement B is incorrect; statement D is correct.
Step 3: Determine the correct statements. Statements C and D are both accurate. They both describe phenomena that support the particulate (photon) model of light.