How does the photoelectric effect demonstrate that light has particle-like behavior?

The photoelectric effect demonstrates the particle-like behavior of light by showing that electromagnetic radiation interacts with matter as discrete packets of energy, or photons, rather than as a continuous wave.12

Classical wave theory could not explain several key observations, which Albert Einstein resolved in 1905 by proposing that light is quantized. The particle-like nature is evidenced by the following:32

• Frequency Dependence: The kinetic energy of ejected electrons depends on the frequency of the incident light, not its intensity. If light were purely a wave, intensity should dictate the energy of the electrons.312
• Threshold Frequency: For any given material, there is a minimum frequency below which no electrons are emitted, regardless of how intense the light is. This confirms that a single photon must possess enough energy to overcome the work function of the material to eject an electron.312
• Instantaneous Emission: There is virtually no time lag between the arrival of radiation and the emission of electrons, suggesting a direct, particle-like collision between a photon and an electron.12

Einstein’s equation, ${ϵ}_{max}=h\nu -\psi$, where $h\nu$ is the photon energy and $\psi$ is the work function, mathematically describes this discrete energy transfer.12