According to the wave theory, light is an electromagnetic wave in which energy is spread continuously over the entire wavefront.

When light falls on a metal surface, electrons should absorb this energy gradually.

Predictions of Wave Theory

1. Kinetic energy should increase with intensity ❌

• Higher intensity means larger wave amplitude.
• Therefore, each electron should absorb more energy.
• Hence, the maximum kinetic energy (K.E.) of photoelectrons should increase.

Experimental observation:
The maximum kinetic energy depends on the frequency of light, not on intensity.

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2. No threshold frequency should exist ❌

According to wave theory:

• Every frequency carries energy.
• If light is sufficiently intense or allowed to fall for a long time, electrons should eventually receive enough energy to escape.

Therefore, photoelectric emission should occur at every frequency.

Experimental observation:
A threshold frequency (ν0\nu_0ν0​) exists. Below this frequency, no photoelectric emission occurs, regardless of intensity or exposure time.

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3. Intensity alone should produce emission ❌

Wave theory predicts:

• Increasing intensity should eventually eject electrons even if frequency is low.

Experimental observation:
Increasing intensity below the threshold frequency does not produce any photoelectrons.

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4. There should be a time delay ❌

According to wave theory:

• Energy is absorbed gradually.
• Each electron receives only a tiny fraction of the wave’s energy at a time.
• It should take seconds, minutes, or even hours for an electron to accumulate enough energy to escape.

Experimental observation:
Photoelectric emission is instantaneous (within about $10^{-9}$10−9 s or less).

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Why Wave Theory Fails

Wave Theory Prediction	Experimental Observation
K.E. increases with intensity	K.E. depends on frequency
No threshold frequency	Threshold frequency exists
Low-frequency intense light should eject electrons	No emission below threshold frequency
Time delay expected	Emission is instantaneous

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Conclusion

The wave theory of light could not explain the photoelectric effect because its predictions contradicted experimental observations. These failures led Albert Einstein to propose the photon (quantum) theory of light, according to which light consists of packets of energy called photons, each having energy:$$E = h\nu$$E=hν

This theory successfully explained all the observations of the photoelectric effect.

NEET One-Line Revision

Wave theory fails because it cannot explain:

1. Threshold frequency
2. Dependence of K.E. on frequency
3. Independence of K.E. from intensity
4. Instantaneous emission of photoelectrons