Question

Write three characteristic features in photoelectric effect which cannot be explained on the basis of wave theory of light, but can be explained using Einstein’s equation.

Answer 1

Hint: Photoelectric effect is observed when conduction is caused as light is incident on an electrode kept in an evacuated chamber. The electrons emitted by light (with frequency higher than threshold) are called photoelectrons.

Complete step by step answer:
Before Einstein, Sir Isaac Newton proposed a corpuscular nature of light in the ${17}^{th}$ century. The wave nature came to be recognized after its verification by Young's double slit experiment. Huygens was the one who gave the basic principles on wave nature of light first. After Maxwell's work, light was firmly believed to be an electromagnetic wave.
Max Plank towards the end of the ${19}^{th}$ century gave a hint towards the particle natured absorption and emission of light in Black body radiation. Einstein in 1905 gave a formula given by:
$E=h\nu$
that established the frequency dependence of the energy.

The photoelectric effect established the particle nature of light firmly and established Einstein's formula. The experiment consists of a sealed vacuum chamber containing cathode and anode at some separation. When light of appropriate frequency is incident on the cathode electrons get ejected out of it and current flows in the circuit. The features of the experiment that wave nature couldn't explain were:

1. In a wave model, the energy depends on the amplitude or intensity of the wave. In photoelectric effect, the electrons did not get ejected by increasing the intensity but rather by increasing the frequency. The higher is the frequency of the light incidenting, more will be the energy the photoelectrons emitted. Although, if we provide more intensity, more photoelectrons get ejected.

2. It was observed that there was no time lapse in the emission of the electrons after the arrival of light on the surface. The emission is an instantaneous process. However, because in an em wave, energy has to spread across the wave front, it takes some time for an atom to absorb such continuous energy and attain sufficient energy so that it can emit an electron.

3. No current will flow in the circuit if the frequency of incident light is lower than the threshold frequency no matter how bright the incident light is. There is the presence of a cutoff energy which could not be predicted by the wave model. At any frequency above the threshold, the number of electrons ejected increases with intensity of light and does not depend on the light’s frequency.

Note: Wave nature of light corresponds to continuous energy and particle nature of light corresponds to discrete emission and absorption of energies. The key is continuous and discrete behaviors which help us in differentiating the two models.