Failure of Wave Theory in Explaining Photoelectric Emission Effect

Description of failure of wave theory in explaining photoelectric effect:

Although reflection, refraction, interference, diffraction and polarisation etc. are explained on the basis of wave theory but the laws of photoelectric effect cannot be explained on the basis of the wave theory of light. There are three main reasons for failure:

1.) According to wave theory, as the intensity of incident light increases, incident energy also increases. Therefore, greater is the intensity, greater will be the energy absorbed by the electrons of metal and therefore greater should be the kinetic energy of photoelectrons. From experimental observations, it is clear that the maximum kinetic energy of photoelectrons does not depend on the intensity of incident light.

2.) According to wave theory, photoelectric emission should occur for all the frequencies provided that it has enough energy to emit the electrons from the metal. Although from experimental observation it is clear that if the frequency of incident light is less than the threshold frequency, photoelectrons are not emitted.

3.) The energy carried by the light waves is absorbed by all the electrons and not by a single electron. Therefore, if the intensity of light is less, for the emission of electrons, there should be some time to collect sufficient energy. Although it is clear from experimental observation, the electrons are emitted instantaneously, whatever small be the intensity of light.

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Einstein Photoelectric Emission Effect Law

Description of the Light:

According to the Albert Einstein

The light is consist of small packets or bundles of energy. These packets are called photon. The energy of each photon is $h \nu$.

Theory of Photoelectric Effect:

When the photon of ultraviolet ray is incident on the metal then this energy is used in two parts:

1.) To emit the electron from a metal surface i.e. Work Function. The electron emitted from a metal surface is called the photoelectron.

2.) Remaining energy increases the kinetic energy of the emitted photoelectron. This is the maximum kinetic energy of the photoelectron.

Let us consider

The energy of incident Ultraviolet Photon $E=h\nu$

The work function $W= h \nu_{\circ}$

The maximum kinetic energy of photo electron $K_{max}= \frac{1}{2}mv^{2}_{max}$

According to Einstein's photoelectric effect theory

$E=W+K_{max}$

$h \nu = h \nu_{\circ} + \frac{1}{2}m v^{2}_{max}$

$h \nu - h \nu_{\circ} = \frac{1}{2}m v^{2}_{max}$

$h \left( \nu - \nu_{\circ} \right) = \frac{1}{2}m v^{2}_{max}$

Where
$\nu \rightarrow$ Frequency of incident Ultraviolet ray photon
$\nu_{\circ} \rightarrow$ Threshold frequency to emit the photoelectron from the metal surface
$ v_{max} \rightarrow$ Maximum velocity of emitted photoelectron from the metal surface

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Laws of photoelectric emission

There are the following laws of photoelectric emission:

1.) The rate of emission of photoelectrons from the metal surface is directly proportional to the intensity of the incident light on the metal surface.

2.) The maximum kinetic energy of photoelectrons does not depend on the intensity of incident light.

3.) If the frequency of incident light is less than the threshold frequency then no photoelectrons will come out of the surface.

4.) If the frequency of incident light is equal to the threshold frequency then electrons will come out of the surface but the kinetic energy of emitted photoelectrons will be zero.

5.) As the frequency of incident light increases greater than the threshold frequency, the maximum kinetic energy $K_{max}$ of photoelectrons emitted from the metal surface also increases.

6.) The value of threshold frequency depends upon the nature of the metal surface and its value is different for different metals.

7.) There is no time lag in the emission of photoelectrons to the metal surface i.e., as the light of proper from frequency is made to the incident on the metal surface, photoelectrons immediately come out of the surface within no time.

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