How did the photoelectric effect challenge the classical wave theory of light?

The classical wave theory of light, which successfully explained phenomena like interference and diffraction, failed to account for several key observations of the photoelectric effect. These discrepancies challenged the prevailing view of light as a continuous electromagnetic wave.12

The primary contradictions included:

• Energy Independence from Intensity: Classical theory predicted that the kinetic energy of emitted electrons should increase with the intensity of the light. Instead, experiments showed that kinetic energy depends solely on the frequency of the light, while intensity only affects the number of electrons released.132
• Threshold Frequency: Classical theory suggested that any light, if sufficiently intense, should eventually eject electrons. In reality, no emission occurs below a specific threshold frequency, regardless of how intense the light is.13
• Lack of Time Lag: Classical wave theory implied that energy would need time to accumulate before an electron could be ejected. Observations revealed that electron emission occurs with virtually no time delay, suggesting a discrete, particle-like interaction.32

Albert Einstein resolved these issues in 1905 by proposing that light consists of quanta of energy, later called photons, where energy is proportional to frequency ($E=h\nu$).132