Unit – II |

## Explanation of Photoelectric Effect

### Planck’s quantum theory

1. The quantum theory was proposed by Max Planck.

2. According to this theory, radiation from a source is not emitted continuously, but it is emitted in packets or bundles of energy. These packets are called quanta or photons.

3. If the radiation is of frequency ν, each quantum has energy hν where h is Planck’s constant.

4. Thus energy is emitted in a discontinuous manner. This is contrary to the classical theory which assumes that emission of energy is a continuous process.

### Characteristics of photon | Particle nature of electromagnetic radiations

1. In the interaction of radiation with matter, the radiation behaves as if it is made up of particles. These particles are called photons.

2. Each photon has energy which is given by

3. All photons of light of particular frequency (Wavelength) has the same amount of energy associated with them.

4. The increase in intensity of light increases the number of photons per second through given area, but the energy of each photon will be the same.

5. Photons are electrically neutral and are unaffected by electric or magnetic field.

6. Photons travel in a straight line with the speed of light ‘c’ but show diffraction in certain conditions.

7. Momentum of each photon is given by

8. The wavelength of photon changes with the media, hence they have different velocities in different media.

9. The rest mass of a photon is zero. Its kinetic mass is given by

10.In photon particle collision (such as photon-electron collision) the total energy and momentum is conserved. However, number of photons may not be conserved in a collision. The photon may be absorbed or new photon may be created.

### Einstein’s photoelectric equation

1. On the basis of Planck’s quantum theory, Einstein derived an equation for the photoelectric effect known as Einstein photoelectric equation.

2. Einstein assumed that

a) light consists of photons or quanta of energy, energy in each photon is hn. Where h is the Planck’s constant and n is the frequency of light

b) each incident photon collides with an electron inside an atom and gives all its energy to the electron.

3. Part of this energy is used by the electron to come out of the surface of the metal and the remaining part is the kinetic energy with which the electron is emitted.

4. The minimum energy required by an electron to come out of the surface of the metal is called photoelectric work function (Φ_{0}) of the

metal.

5. The remaining energy (hυ – Φ_{0}) is the maximum kinetic energy of the electron with which a photoelectron will be ejected.

Thus, Maximum kinetic energy of electron

= energy of photon – work function

Let m be the mass of electron and v max be the maximum velocity of photo-electron by which it will be ejected

This equation is known as Einstein’s photoelectric equation

This is another form of Einstein’s photoelectric equation.

### Concept of photoelectric work function.

1. In photoelectric effect, the most loosely attached electron of an atom of photosensitive material is removed.

2. The minimum energy required to free an electron from the given surface is called photoelectric work function (Φ_{0} ) of the material of the surface.

3. Mathematically work function is given by

4. The work function is a characteristic property of the metal surface.

### Einstein’s photoelectric equation & terms involved in it.

### Existence of threshold frequency on the basis of Einstein’s photoelectric equation

1. For a given metallic surface, photoelectrons are emitted only when the frequency of incident light is greater than or equal to a certain minimum frequency (υ_{0}) known as the threshold frequency. The threshold frequency is different for different Substances,

υ = frequency of incident radiation

By the Einstein’s photoelectric equation

Where =υ_{0} Threshold frequency.

The kinetic energy is always nonnegative quantity i.e. it may either be positive or zero thus

Which indicates that for photoelectric effect, the frequency of incident radiation or incident photon should be equal to or greater than the threshold frequency.

3. Similarly, the attractive force acting on probable photoelectrons in different atoms is different. Therefore the threshold frequency is different for a different substance.

### Effect of intensity on the photoelectric effect on the basis of Einstein’s photoelectric equation

1. If the frequency of incident light is less than the threshold frequency, photoelectrons are not emitted, however large the intensity of incident light may be

Kinetic energy is always nonnegative quantity i.e. it may either be positive or zero thus the R.H.S. of the equation can not be negative. Thus the quantity (υ-υ_{0}) can not be negative.

Which indicates that the value of the frequency of incident radiation should be always greater than the threshold frequency. Thus if the value of incident radiation is less than threshold frequency no photoelectric effect is possible.

3. The number of photo-electrons emitted per second is directly proportional to the intensity of incident light. Thus photo- electric current is directly proportional to the intensity of incident light. If the intensity of light is more, the number of incident photons on the surface are more. Due to increased number of photoelectron the rate of photoemission increases, hence the strength of photoelectric current increases.

Thus we can conclude that the photoelectric effect (current) is directly proportional to the intensity of incident radiation.

### Why the maximum K.E. of the photo-electron increases with increase in the frequency of incident light.

1. By the Einstein’s photoelectric equation

Where = υ_{0} Threshold frequency

This equation does not contain the term of intensity, thus we can say that the maximum kinetic energy of photoelectron is independent of the intensity of incident radiation but depends upon the frequency of incident radiation.

2. This equation indicates that the maximum kinetic energy of an electron depends upon the frequency of incident radiation. And if the frequency of incident radiation is increased kinetic energy of photoelectron also gets increased.

### Why Photo-electric effect is an instantaneous process.

1. The photo-electric effect is an instantaneous process. There is no time lag between the incidence of light and the emission of the photo-electrons in other words, the surface begins to emit photoelectrons as soon as light falls on it. Also the emission of photoelectrons stop the moment incident light is cut off.

2. When radiation is incident on the photo-emitting surface at that instant, the whole energy of a photon is transferred to a single electron in one go. Thus the electron gets emitted without any time lag and the photoelectric effect is an instantaneous process.