1. Photoelectric effect: In the photoelectric effect, light incident on a metal surface can knock electrons out of the metal. The kinetic energy of the ejected electrons depends on the frequency of the incident light, not its intensity. This result cannot be explained by the wave theory of light, which predicts that the kinetic energy of the electrons should be proportional to the intensity of the light.

2. Compton scattering: In Compton scattering, X-rays or gamma rays are scattered by electrons. The scattered X-rays or gamma rays have a longer wavelength than the incident X-rays or gamma rays. This result cannot be explained by the wave theory of light, which predicts that the wavelength of the scattered light should be the same as the wavelength of the incident light.