No, it is not possible for photons with energy less than the work function to cause the emission of photoelectrons. The work function is the energy barrier that must be overcome to release an electron from the surface of a material. If the energy of incident photons is less than the work function, electrons cannot absorb enough energy to be freed. This is evidenced in the threshold frequency, the minimum light frequency at which photons possess sufficient energy to overcome the work function, underscoring the frequency-dependent nature of the photoelectric effect.

Planck’s constant plays a critical role in Einstein’s equation for the maximum kinetic energy of photoelectrons (Emax = hν - Φ). It represents the proportionality factor between the energy of a photon and its frequency. This concept underscores the quantised nature of energy transfer in the photoelectric effect, and it establishes the linear relationship between photon energy and frequency. As such, Planck’s constant is instrumental in calculating the energy of emitted photoelectrons and underscores the shift from the continuous energy paradigm of classical physics to the quantised energy perspective of quantum physics.

Einstein’s explanation of the photoelectric effect significantly bolstered the development and acceptance of quantum theory. By introducing the concept of photons and quantised energy transfer, Einstein resolved anomalies unexplainable by classical wave theory. His explanation, substantiated by empirical evidence, endorsed the existence of quantised energy levels and the particle nature of light. This bolstered the credibility and acceptance of quantum theory, positioning it as a valid and essential framework to explain various physical phenomena at atomic and subatomic scales, fostering advancements in theoretical and applied physics alike.

According to Einstein’s explanation, increasing the intensity of light does not increase the energy of emitted photoelectrons. This contradicts the classical wave theory and is a fundamental aspect of the quantum explanation of the photoelectric effect. The energy of photoelectrons is determined by the frequency of the incident photons, not their intensity. Increasing light intensity increases the number of photons (and therefore potentially the number of emitted photoelectrons), but not the energy each photon carries, which is inherently tied to the frequency of light according to the equation E = hν.

The work function aligns with the experimental observations of the photoelectric effect by explaining the energy threshold necessary for the emission of photoelectrons. Experimentally, it's observed that not all frequencies of light can cause electron emission. The work function quantitatively describes this threshold as the minimum energy required to free an electron from a material. Photons with energy equal to or exceeding the work function can release electrons, validating the observed frequency-dependent nature of the photoelectric effect, a departure from classical wave theory’s intensity dependence.