The work function of a material is crucial in the context of the photoelectric effect as it represents the minimum energy required to liberate an electron from the surface of that material. It’s material-specific, implying that different materials necessitate different minimum energy thresholds to initiate the photoelectric effect. Understanding the work function allows for a nuanced comprehension of why certain materials exhibit the photoelectric effect under specific light frequencies and intensities, while others do not. It's an intrinsic property that underscores the material's electronic structure and response to incident photon energy.

Materials with different work functions respond variably to the same incident light frequency due to their distinct energy thresholds needed to eject electrons. A material with a lower work function requires less photon energy to initiate the photoelectric effect, leading to the emission of photoelectrons at lower light frequencies. Conversely, a material with a higher work function necessitates higher photon energy, correlating to a higher threshold frequency. This disparity in work functions elucidates why certain materials are more responsive to photoelectric emission under given light conditions, influencing their applications in devices like photodetectors and solar cells.

The photoelectric effect provides compelling evidence supporting the particle theory of light. Key observations, such as the instantaneous emission of electrons and the existence of a threshold frequency, cannot be explained by classical wave theory. These phenomena align with the notion of light consisting of discrete energy packets, or photons, each possessing a quantised energy level dependent on its frequency. The direct proportionality of photon energy to frequency, and the requirement for this energy to exceed the material’s work function to emit photoelectrons, corroborates the particle nature of light, reinforcing the foundational principles of quantum mechanics.

The discovery of the photoelectric effect played a pivotal role in the development of quantum mechanics. The effect’s distinct characteristics, especially the existence of a threshold frequency and the instant emission of electrons, were incompatible with classical wave theory. These observations suggested a particle nature of light, leading to the concept of photons—quantised energy packets. Albert Einstein’s explanation of the photoelectric effect using photons provided critical experimental validation for the emerging quantum theory, bridging the gap between theory and experiment and laying foundational stones for modern quantum mechanics.

Experimental setups for studying the photoelectric effect often involve a photoelectric cell, which includes a photosensitive material to emit photoelectrons when illuminated by light. The cell is often connected to an external circuit and a device to measure the current produced by the emitted electrons. By varying the frequency and intensity of the incident light, and observing the resultant current, researchers can study the relationship between these variables and the energy and number of emitted photoelectrons, thus exploring key aspects of the photoelectric effect that are essential for validating theoretical propositions.