Introduction:
The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when it is exposed to light of a certain frequency or higher. This effect cannot be explained by the wave nature of light alone.

Wave nature of light:
The wave nature of light suggests that light travels as a wave and has properties such as wavelength, frequency, and amplitude. According to this theory, the energy of light is proportional to its amplitude and the intensity of light is proportional to the square of its amplitude.

Limitations of wave theory:
The wave theory of light fails to explain the photoelectric effect because it cannot explain why electrons are emitted from a metal surface when it is exposed to light of a certain frequency or higher. According to the wave theory, the energy of the wave should be proportional to the intensity of the light, not its frequency. However, the photoelectric effect shows that it is the frequency of the light that determines the energy of the emitted electrons.

Quantum theory of light:
The photoelectric effect can only be explained by the quantum theory of light. This theory suggests that light travels as both a wave and a particle, known as a photon. According to this theory, the energy of a photon is proportional to its frequency, not its amplitude. This means that higher frequency light has more energy than lower frequency light, which explains why electrons are emitted from a metal surface when it is exposed to light of a certain frequency or higher.

Conclusion:
In conclusion, the photoelectric effect cannot be explained by the wave nature of light alone. The quantum theory of light, which suggests that light travels as both a wave and a particle, is necessary to explain this phenomenon.