# Dual Nature of Radiation and Matter

### ABSTRACT

This blog lays down the important concepts associated with Dual Nature of Radiation and Matter and gives the students insights of its application for problem solving.

1. Introduction
2. Electron Emission
3. Photoelectric Effect
4. Experimental Study of Photoelectric effect
5. Photoelectric Effect and wave theory of Light
6. Einstein’s Photoelectric Equation: Energy Quantum of Radiation
7. Particle Nature of Light: The Photon
8. Wave Nature of Matter
9. De Broglie Relation
10. Davisson and Germer Experiment
11. Applications
12. Summary

### 1. Introduction

The Dual Nature of Radiation and Matter also known as the wave particle duality states that every particle has a wave nature and particle nature associated with it. The most common example is light it exhibits the wave nature of light in the Young’s Double slit Experiment and particle nature in photoelectric Experiment.

### 2. Electron Emission

The phenomenon of escaping of electrons from the metal surface is known as electron emission. Electrons can be emitted from the metal surface with the help of heat energy, electric field or light wave.

### 3. PHOTOELECTRIC EFFECT

When a light wave greater than or equal to a certain frequency strikes a certain metal surface then electrons escape from the surface of that metal, this is known as electron emission. The minimum frequency light wave which needs to be applied to emit electrons from the metal surface is known as the threshold frequency of the metal.

### 4. EXPERIMENTAL EFFECT OF PHOTOELECTRIC EFFECT

In this experiment the light waves were made incident on a metal plate inside a vacuum tube and the electrons emitted from that plate were collected at the plate at the other end of the tube. The two plates are connected to a power supply so that the emitter plate is negatively charged and the collector plate is positively charged. It was observed that when the intensity of light falling on the plate was increased then the number of electrons emitted from the metal surface increased. It was also observed that increasing the frequency of the incident light resulted in the increase of the energy of electrons emitted from the metal surface. The energy required to stop the emission of electrons for a particular frequency of light is known as the stopping potential of the metal for that particular frequency.

### 5. PHOTOELECTRIC EFFECT AND WAVE THEORY OF LIGHT

The photoelectric effect depicts the particle nature of light and the wave theory of light depicts the wave nature of light. In the photoelectric effect the light wave is considered to be a wave of photons and in wave theory light is considered a De-Broglie wave.

### 6. EINSTEIN’S PHOTOELECTRIC EQUATION

According to Einstein, the energy carried by each photon is given by:
E = h𝝂.
The energy of a photon goes into emitting the electron and the kinetic energy of the electron. Mathematically,
E = W + K.E.

### 7. PARTICLE NATURE OF LIGHT

Light wave is considered to be a stream of photons which are particles. Photons are discrete energy packets known as Quanta. Photons are electrically neutral. The energy of a photon is given by E = h𝝂. It is a massless particle.

### 8. WAVE NATURE OF MATTER

As we have discussed above that light has a dual nature, i.e. wave nature as well as particle nature but what about matter does it only have particle nature. The answer is no matter also has a wave nature as particle nature. Now the question arises how do we know that matter has a wave associated with it. We can prove it using the mass energy equivalence relation of the Einstein’s equation $E=m c^{2}$ and Einstein Planck relation E = h𝝂.  When we equate the two equations for a particle we get $\lambda=\frac{h}{p}$, where p is the momentum of the particle. This relation is known as the De Broglie relation.

### 9. DAVISSON AND GERMER EXPERIMENT

The basic thought behind the Davisson and Germer experiment was that the waves reflected from two different atomic layers of a Ni crystal will have a fixed phase difference. After reflection, these waves will interfere either constructively or destructively.

Hence producing a diffraction pattern. In the Davisson and Germer experiment waves were used in place of electrons. These electrons formed a diffraction pattern. The dual nature of matter was thus verified. From the Davisson and Germer experiment, we get a value for the scattering angle θ and a corresponding value of the potential difference V at which the scattering of electrons is maximum. Thus the de-broglie equation was verified.

The experimental setup for the Davisson and Germer experiment is enclosed within a vacuum chamber. Thus the deflection and scattering of electrons by the medium are prevented. The main parts of the experimental setup are as follows:

● Electron gun: An electron gun is a Tungsten filament that emits electrons via thermionic emission i.e. it emits electrons when heated to a particular temperature.
● Electrostatic particle accelerator: Two opposite charged plates (positive and negative plate) are used to accelerate the electrons at a known potential.
● Collimator: The accelerator is enclosed within a cylinder that has a narrow passage for the electrons along its axis. Its function is to render a narrow and straight (collimated) beam of electrons ready for acceleration.
● Target: The target is a Nickel crystal. The electron beam is fired normally on the Nickel crystal. The crystal is placed such that it can be rotated about a fixed axis.
● Detector: A detector is used to capture the scattered electrons from the Ni crystal. The detector can be moved in a semicircular arc as shown in the diagram above.

### 10. APPLICATIONS

Used to generate electricity in Solar Panels. These panels contain metal combinations that allow electricity generation from a wide range of wavelengths.

Motion and Position Sensors: In this case, a photoelectric material is placed in front of a UV or IR LED. When an object is placed in between the LED and sensor, light is cut off and the electronic circuit registers a change in potential difference

Lighting sensors such as the ones used in smartphone enable automatic adjustment of screen brightness according to the lighting. This is because the amount of current generated via the photoelectric effect is dependent on the intensity of light hitting the sensor.

Digital cameras can detect and record light because they have photoelectric sensors that respond to different colors of light.

X-Ray Photoelectron Spectroscopy (XPS): This technique uses x-rays to irradiate a surface and measure the kinetic energies of the emitted electrons. Important aspects of the chemistry of a surface can be obtained such as elemental composition, chemical composition, the empirical formula of compounds and chemical state.

### CHEAT SHEET:

Einstein’s Photoelectric equation: E = h𝝂.
De-Broglie’s relation,  $\lambda=\frac{h}{p}$.

### 11. SUMMARY

In this blog we have seen that light is not only a wave but it also has a particle nature. Also we have seen about the hypothesis and experiments which were used to prove the dual nature of radiation. We have seen about photoelectric effect which is a phenomenon associated with the dual nature of light and also Einstein’s photoelectric equation.