Step 1: Analyze the photoelectric effect.
The photoelectric effect involves the emission of electrons from a material when light shines on it. Key observations, such as the existence of a threshold frequency and the instantaneous emission of electrons, could not be explained by the wave theory of light. Albert Einstein explained it by postulating that light consists of discrete packets of energy called photons (particles). Therefore, the photoelectric effect is a primary evidence for the particle nature of light. Statement A is incorrect, and statement C is correct.
Step 2: Analyze the Compton effect.
The Compton effect describes the scattering of X-rays or gamma rays by electrons. The observed change in wavelength of the scattered radiation is explained by treating the interaction as a collision between a photon and an electron, conserving both energy and momentum. This billiard-ball-like interaction is a clear demonstration of the particle nature of light. Therefore, the Compton effect exhibits the particle nature of light. Statement B is incorrect, and statement D is correct.
Step 3: Conclude which statements are correct.
Both statements C and D are correct. They both point to phenomena that support the particle (photon) model of light.