How does the photoelectric effect show that light can behave as particles?

The photoelectric effect demonstrates that light behaves as particles, or photons, because classical wave theory fails to explain several key experimental observations.12

In 1905, Albert Einstein proposed that light consists of discrete energy packets, where the energy of each photon is given by the relationship $E=h\nu$ (or $hf$), with $h$ being Planck’s constant and $\nu$ (or $f$) representing the frequency of the light. This particle model explains the following:312

• Frequency Dependence: The maximum kinetic energy of emitted electrons depends on the frequency of the light, not its intensity. A photon must have sufficient energy to overcome the work function of the metal; if the frequency is below a specific threshold, no electrons are emitted, regardless of how intense the light is.312
• Intensity and Electron Count: Increasing the light intensity increases the number of photons, which in turn increases the number of emitted electrons, but it does not change the energy of individual electrons.32
• Instantaneous Emission: Emission occurs immediately upon illumination because the interaction involves a discrete energy transfer from a single photon to an electron, rather than the gradual accumulation of energy expected from a continuous wave.12