The wave theory of light does not explain photoelectricity because

Analyze the question: It asks why classical wave theory fails to explain the photoelectric effect. We need the observation that wave theory could not account for.

Concept: In the photoelectric effect, light shining on a metal surface ejects electrons. Experiments show:

1. Threshold frequency (f₀): Below a certain frequency, no electrons are emitted, however bright the light is or however long it shines. Equivalently, there is a maximum (threshold) wavelength λ₀ beyond which no emission occurs.
2. Kinetic energy depends on frequency, not intensity: Brighter light gives more electrons, not faster ones.
3. Instantaneous emission: There is no time delay, even with very dim light.

Wave theory predicts that energy is spread continuously over the wavefront. So any frequency, if intense enough or applied long enough, should eventually eject electrons. It also predicts that a more intense beam should give electrons greater kinetic energy. Neither prediction matches experiment.

Einstein explained it with the photon (particle) theory: E = hf, and

hf = φ + ½mv²max

where φ = hf₀ is the work function. If hf < φ, no emission occurs. This is the threshold effect.

Check the options:

• A. Wrong. Light's energy content is not the issue; the frequency matters.
• B. Waves can transfer energy to particles, and this is not the stated reason. It is not the key experimental finding.
• C. Wrong. High frequency actually helps emission.
• D. Correct. The existence of a threshold wavelength (or frequency) cannot be explained by wave theory, which predicts that any wavelength could eject electrons given enough intensity or time.
• E. Wrong. Short wavelength means high energy photons, which favours emission.

Answer: D

Tip: Remember the three failures of wave theory in photoelectricity: threshold frequency, no dependence of KE on intensity, and no time delay. In NECO and JAMB, "threshold" is the keyword linked to photon theory.