# Dual Nature of Radiation and Matter Class 12 notes Physics Chapter 11

Introduction, Electron Emission, Photoelectric Effect, Einstein’s Photoelectric Equation, Particle and Wave Nature of Matter, Compton Effect

## Introduction

Various phenomena like interference, diffraction, and polarization of light were explained by the wave nature of light. The wave nature of light is further supported by Maxwell’s equations of electromagnetism and the production and detection of electromagnetic waves in 1986 by Hertz.

The photoelectric effect by Hertz, Compton effect by Compton, and Stark effect by Stark were discovered in the 20th century and were explained by the quantum theory of light. According to which, the light consists of packets of energy. Each packet of energy is called a photon or quantum of light (= hυ) where h is Planck’s constant, υ is the frequency of light, c is the velocity of light and these packets of energy travel in straight line with the speed of light.

Hence, it was concluded that light is of dual nature as some phenomena were explained by the wave theory of light and some by particle nature of light, In this unit, we shall study the dual nature of radiation and matter.

## Electron Emission

In metal, electrons are quite free to move easily within the metal. These electrons are responsible for the conductivity of metals. These electrons in the outer shell of the atoms are loosely bound. These loosely bound electrons are called free electrons.

If it has got sufficient energy to overcome the attractive pull then only the electron can come out of the metal surface. This phenomenon of emission of electrons from the metal surface is called electron emission.

### Work Function

To pull out electrons from the surface of the metal, a certain minimum amount of energy is required. This minimum energy required by the electron is called the work function of the metal. Work function is generally denoted by 'w' and measured in eV (electron volt).

Read also: Atoms Class 12 Physics Notes Chapter 12

### Threshold Frequency

The minimum frequency of light that can emit photoelectrons from a material is called threshold frequency or cut-off frequency of that material.

### Threshold Wavelength

The maximum wavelength of light which can emit photoelectrons from a material is called the threshold wavelength or cut-off wavelength of that material.

### Electron Volt

One electron volt is the energy acquired by an electron when it has been accelerated by a 1-volt potential difference. (1 eV = 1.602 × 10–19 J)

### Process of Electron Emission

#### (i). Thermionic emission

The process of emission of electrons when a metal is heated is known as thermionic emission. The emitted electrons are called thermions. Emitted number of thermions depends on the temperature of the metal surface.

#### (ii). Field emission

The process of emission of free electrons when a strong electric field (108 V/m) is applied across the metal surface is known as field emission. Field emission is also known as cold emission or cold cathode emission. One of the examples of cold emission is the spark plug.

#### (iii). Photoelectric emission

The process of emission of electrons when the light of suitable frequency is incident on a metal surface is known as photoelectric emission. These photo-generated electrons are called photoelectrons. The number of photoelectrons emitted depends on the intensity of the incident light.

## Photoelectric Effect

The phenomenon of emission of electrons from (preferably) metal surface exposed to light energy of suitable frequency is known as the photoelectric effect. The emitted electrons are called photoelectrons and the current so produced is called photoelectric current. Alkali metals (lithium, sodium, potassium, cesium, etc.) show a photoelectric effect with visible light.

### Hertz’s Observations

The phenomenon of photoelectric emission was discovered in 1887 by Heinrich Hertz while studying experimentally the production of electromagnetic waves by means of spark discharge. He found that when the emitter plate was illuminated by ultraviolet light, high-voltage sparks across the detector loop were enhanced. This observation led him to conclude that light facilitated the emission of some electrons.

From this, it was concluded that when suitable radiation falls on a metal surface, some electrons near the surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions in the material of the surface.

### Lenard’s Observation

Lenard observed that when ultraviolet radiation was allowed to fall on the emitter plate of an evacuated glass tube enclosing two electrodes, current flows. As soon as, the ultraviolet radiations were stopped, the current flows also stopped. These observations indicate that when ultraviolet radiations fall on the emitter plate, electrons are ejected from it which are attracted towards the positive plate by the electric field.

## Experimental Study of Photoelectric Effect

It consists of an evacuated glass or quartz tube having two electrodes. Electrode ‘C’ is a photosensitive plate, which emits photoelectrons when exposed to ultraviolet radiation. The electrode ‘A’ is a charge-collecting plate. The tube has a side window, which will allow the light of a particular wavelength to pass through it and falls on the photosensitive plate ‘C’.

The window is made of quartz covered with a filter. The electrons collected by plate A (collector), are emitted by the plate C. Battery creates the electrical field between collector and emitter. The potential difference between plates C and A is maintained by the battery, which can be varied.

From a commutator, the polarity of the plates C and A can be reversed. Thus with respect to emitter C, plate A can be maintained at a desired positive or negative potential. The electrons are attracted, when the collector plate A is positive with respect to the emitter plate C. Electron emission causes the flow of electric current in the circuit.

Voltameter (V) measures the potential difference between the emitter and collector plates. Microammeter (μA) measures the resulting photocurrent flowing in the circuit. The current flowing in the circuit can be increased or decreased by varying the potential between collector plate A and emitter plate C. We can also vary the intensity and frequency of the incident light.

### (i). Effect of Intensity

According to this, Photoelectric current for a fixed frequency of incident radiation, the photoelectric current increases linearly with an increase in the intensity of incident light.

### (ii). Effect of Potential

According to this, photoelectric current for a fixed frequency increases with an increase in the potential applied to the collector.

### (iii). Effect of Frequency

According to this, the energy of the emitted electrons depends on the frequency of the incident radiations. The stopping potential is more negative for higher frequencies of incident radiation.

## Laws of photoelectric emission

1. The photoelectric current is directly proportional to the intensity of incident radiation.

2. Saturation current is found to be proportional to the intensity of incident radiation whereas the stopping potential is independent of its intensity.

3. The maximum kinetic energy or equivalently stopping potential above the threshold frequency of the emitted photoelectrons increases linearly with the frequency of the incident radiation but is not a function of intensity.

4. The photoelectric emission is an instantaneous process. The time lag is very small between the incidence of radiation and emission of photoelectrons (~10–9 s or less), even when the incident radiation is extremely dim.

## Einstein’s Photoelectric Equation

To explain the photoelectric effect in 1905, Albert Einstein proposed a completely different picture of electromagnetic radiation. In this picture radiation energy is built up of discrete units and photoelectric emission does not take place by continuous absorption of energy from radiation. These discrete units are called quanta of energy of radiation. Each quantum of energy is hν, where v is the frequency of light and h is Planck’s constant.

In the photoelectric effect, an electron absorbs a quantum of energy (hv) of radiation. If this absorbed energy exceeds the minimum energy (work function 'w' of the metal), the most loosely bound electron will emerge with maximum kinetic energy, more tightly bound electron will emerge with kinetic energies less than the maximum value.

Einstein’s photoelectric equation

E_{k}=h\nu-w

E_{k}=h\nu-h\nu_{0}

E_{k}=h(\nu-\nu_{0})

## Particle Nature of Light

The photoelectric effect thus gave evidence to the strange fact that light in interaction with matter behaved as if it was made of quanta or packets of energy, each of energy hv. A definite value of energy, as well as momentum, is associated with a particle. This particle was later named photon.

We can summarise the photon picture of electromagnetic radiation as follows:

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

2. Each photon has energy E (=hv) and momentum p (= hv/c), and speed c, the speed of light.

3. All photons of light of a particular frequency v, or wavelength λ, have the same energy E (=hv = hc/λ) and momentum p (= hv/c = h/λ). Photons are electrically neutral and are not deflected by electric and magnetic fields.

4. In a photon-particle collision (such as a photon-electron collision), the total energy and total momentum are conserved.

## Wave Nature of Matter

The wave nature of light shows up in the phenomena of interference, diffraction, and polarisation. De Broglie proposed that the wavelength λ associated with a particle of momentum p is given as

λ=\frac{h}{p}=\frac{h}{mv}

## Davisson and Germer Experiment

The wave nature of electrons was first experimentally verified independently by C. J. Davisson and L. H. Germer in 1927 and by G. P. Thomson in 1928 while observing diffraction effects with beams of electrons scattered by crystals. The experimental arrangement is schematically shown in the figure.

It has an electron gun made up of a tungsten filament F, heated by a low voltage battery and the filament is coated with barium oxide. Emitted electrons from filament are accelerated to a desired velocity by applying the required potential/voltage from a high-voltage power supply. C is a hollow metallic cylinder with a hole along the axis and is kept at a negative potential to get a convergent beam of electrons emitted from the filament. It acts as a cathode. A is a cylinder with a fine hole along its axis acting as an anode.

The cathode and anode form an electron gun by which a fine beam of electrons can be obtained at different velocities by applying different accelerating potentials. N is a nickel crystal cut along a cubical diagonal, and D is an electron detector that can be rotated on a circular scale and is connected to a sensitive galvanometer that records the current.

Working: From the electron gun a fine beam of accelerated electrons is made to fall normally on the surface of the nickel crystal. The atoms of the crystal scatter the incident electrons in different directions. The detector detects the intensity of the electron beam scattered in a particular direction by rotating the electron detector on the circular scale at different positions.

According to de Broglie's hypothesis, the wavelength of the wave associated with the electron is given by

\lambda=\frac{12.27}{sqrt{V}}\dot{A}

## Summary

• Photon: The rest mass of the photon is zero. Its momentum is h / λ. These are packets of energy that travel in a straight line.

• Velocity in different media is different but the frequency of photons in different media is the same.

• Dual nature of light and matter: Light exhibits particle aspects in certain phenomena (e.g., photoelectric effect, emission, and absorption of radiation), while wave aspects in other phenomena (e.g., interference, diffraction, and polarisation) i.e., light has dual nature.

• de Broglie concluded that matter also possesses dual nature. Light and matter both possess properties of wave and matter.

• Work function: Minimum energy required by a free electron to just come out of the metal surface (with KE = 0) is called the work function of the metal. Work function is expressed in eV.

1 eV = 1.6 × 10–19 J.

• Photoelectric effect: The phenomenon of emission of electrons from a metallic surface by the use of light (or radiant) energy is called the photoelectric effect. For photo-electric emission, the metal must have a low work function.

• Alkali metals have a low value of work function. Cesium is the best metal for the photoelectric effect.

• The photoelectric current depends on

(i) the intensity of incident light
(ii) the potential difference applied between the two electrodes, and
(iii) the nature of the emitter material.
• Threshold frequency: The minimum frequency of incident light that is just capable of ejecting electrons from metal is called the threshold frequency. It is denoted by υ0. The corresponding wavelength of light is called threshold wavelength0). If there will be no photo-electric emission.

• Stopping potential: The minimum retarding potential applied to the anode of a photoelectric tube that is just capable of stopping the photoelectric current is called the stopping potential. It is denoted by V0 (or Vs). Stopping potential depends upon the frequency of incident light.

• de Broglie hypothesis: A wave is associated with a moving material particle that controls the particle in all respect. The wavelength associated with a moving particle is given by

λ = h / mv

where m is the mass of the particle moving with velocity v and h is Planck's constant. This wave is called the de Broglie wave.

• Photoelectric cell: It is a device used to convert light energy into electrical energy. Photoelectric cells are of three types:

(i) Photoemissive cell

(ii) Photovoltaic cell

(iii) Photoconductive cell

• The photoelectric effect has established the particle nature of light.

• Einstein’s photoelectric equation was experimentally verified by Millikan for radiations of lower frequencies and de Broglie for higher frequency radiations.