Dual Nature of Radiation And Matter - Notes, Topics, Formulas, Books, FAQs

Edited By Vishal kumar | Updated on Sep 26, 2024 04:30 PM IST

The dual nature of matter and radiation is a pivotal concept in physics that defines the relationship between light and matter. It states that both light and matter can exhibit properties of waves as well as particles. This idea emerged from key experiments like the photoelectric effect and the double-slit experiment. In this article, we will explore about dual nature of matter and radiation.

Dual Nature Of Matter And Radiation - Overview

As the name suggests Dual Nature of Matter and Radiation chapter deals with the duality in the nature of matter, namely particle nature and wave nature. Various experiments by various scientists were done to prove it. For example, light behaves both as a wave and as a particle. If you are observing phenomena like interference, diffraction, or reflection, you will find that light behaves as a wave. However, if you are looking at phenomena like the photoelectric effect, you will find that light behaves as a particle.

You must have heard about solar energy in your earlier classes and how it can be a good alternative to non-renewable sources of energy. We can use solar energy as a source of electricity using solar panels. The solar panel has solar cells (semiconductors like Si and Ge) and when photons hit the solar cells the electrons get excited and due to their movement electric current is produced. So here we got to know that light consists of photons or in other words light contains particles which are a packet of energy.

But light does not only show particle nature it also shows wave nature and you will get to know about it through various experiments.

Dual Nature of Matter and Radiation is one of the most important chapters from modern physics while preparing for all competitive exams because it helps you to understand the dual nature of matter. With the help of either wave nature or particle nature, we can explain the various phenomena that we will study in physics. This is easy to understand and a high-scoring topic. The Concept of the Dual Behaviour of Matter and Radiation and other chapters of physics are mixed in miscellaneous questions that are asked in various competitive exams.

So we will discuss step by step about important topics from this chapter followed by an overview of this chapter. Then we will understand important formulas from this chapter. Remembering these formulas will increase your speed while question-solving.

Dual Nature of Radiation and Matter Class 12 Topics

The dual nature of radiation,
Photoelectric effect,
Hertz and Lenard's observations,
Einstein’s photoelectric equation- the particle nature of light
Experimental study of the photoelectric effect
Matter-wave: the wave nature of particles
De Broglie relation, Davisson and Germer experiment.

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Dual Nature of Matter and Radiation Notes

In this chapter, we will study the dual nature of matter which will be explained by Wave-particle duality postulates. According to this postulate, all particles exhibit both wave properties and particle properties.
Then we will study the particle nature of the light wave. For this, we will consider light as particles or light consisting of photons.
Then we will study various characteristics of photons, like their mass, energy, momentum, etc. Various scientific experiments will explain the particle nature of light and the Photoelectric Effect experiment is one of them.
In the photoelectric Effect experiment, the emission of electrons (photoelectrons) takes place when light strikes a surface. We will understand all the procedures and results of this experiment. We will understand various terminology regarding this experiment and how they depend on each other. And based on their dependence on each other we can get different results if we change the input quantity of experiments. Einstein's Photoelectric Equation gives the relation between input and output quantity of experiments. This experiment also follows the Conservation of energy.
After studying the particle nature of matter we will learn about the wave nature of matter. So we will learn about De - Broglie wave which is nothing but a wave associated with moving material particles. To understand the wave nature of matter it is very important to study its associated De - Broglie wavelength. So we will study various characteristics of De - Broglie wavelength. We will study how De - Broglie wavelength of matter depends on various factors like its mass, frequency of the wave, etc. With the help of the formula, we can also calculate values of De - Broglie wavelength for particles like electrons, Deuteron, Alpha particles, etc.
There are various scientific experiments like the Davisson Germer Experiment, Frank Hertz Experiment, etc which will explain the wave nature of matter.

1. Dual Nature Of Radiation

Electron Emission

Free electrons in the metals are responsible for their electrical conductivity. But, the free electrons normally, can not escape from metal. A certain energy is required for the emission of electrons. The minimum energy required to escape an electron from a metal surface is called the work function $\phi_0$ of that metal and is expressed in $eV$ (electron volt).

The minimum energy required for the electron emission can be supplied by one of the following methods:

(i) By heating(thermionic emission)

(ii) By applying a very strong electric field of the order of 10⁸V m^-1 (field emission)

(iii) By irradiating the surface with light rays of suitable frequencies (photoelectric emission)

Particle nature of radiation

According to Planck, light consists of tiny packets of energy called quanta or photons of energy value $h \nu$ and momentum $\frac{\mathrm{h}}{\lambda}$.

Momentum of photon $$P=mc$$

$$P=\frac{\mathrm{h}}{\lambda}$$

or $$\lambda=\frac{h}{m c}$$

where,

$\lambda$ is the attribute of a wave

$mc$ is an attribute of the particle

This shows the dual nature of radiation

2. Photoelectric Effect

Discovered by Hertz. The phenomenon of emission of electrons from the surface of the metals when irradiated with $\gamma$ rays, $X$- rays, $U.V$ rays, or visible rays is called the photoelectric effect. Electrons are only emitted if the incident light has a frequency greater than a certain threshold frequency specific to the material. Below this frequency, no electrons are emitted, regardless of the light's intensity.

3. Hertz's Observations

The phenomenon of photoelectric emission was discovered in 1887 by Heinrich Hertz (1857-1894), during his electromagnetic wave experiments. In his experimental investigation on the production of electromagnetic waves through a spark discharge, Hertz observed that high voltage sparks across the detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp.

4. Lenard's observations

Lenard conducted experiments on the photoelectric effect after Hertz, further exploring how light interacts with metals. He observed that when ultraviolet light was shone on a metal surface, it resulted in the emission of electrons, confirming that light could impart energy to electrons. Lenard noted that the emitted electrons were more energetic with higher-frequency light. He also discovered that the number of emitted electrons increased with the intensity of the light, while their maximum kinetic energy remained constant.

5. Einstein’s photoelectric equation- the particle nature of light

Einstein's photoelectric equation describes the relationship between the energy of incident photons and the kinetic energy of emitted electrons. The equation is given by

$$E_k=h f-\phi$$

where,

$E_k$ is the kinetic energy of the emitted electrons

$h f$ is the energy of the incoming photons

$\phi$ is the work function of the material

6. Matter-wave: the wave nature of particles

From the particle nature of radiation, Louis de Broglie argued that what is true for radiation must be true for particles also. ie, for a particle of mass m moving with a velocity $v$, a wave must be associated with it. This wave is called de Broglie wave or matter wave. The wavelength of the de Broglie wave,

$$\lambda=\frac{h}{m v}$$

7. De Broglie wavelength of an accelerated motion

The velocity of the electron accelerated through a p.d of V volts. $v=\sqrt{\frac{2 e V}{m}}$

De Broglie wavelength of the electrons $\lambda=\frac{h}{m v} = \frac{h}{\sqrt{2 m e V}}=\frac{12.27}{\sqrt{V}}$ Å

For V =100 vlts , $\lambda$ = 1.227Å

This was verified by Davisson and Germer.

Davisson and Germer Experiment

Davisson and Germer allowed the electron beam accelerated through 54 volts to fall on a nickel crystal. They measured the maximum intensity of the diffracted electron beam at an angle $\theta$ = $50^{\circ}$. Then the glancing angle $\phi=\frac{180-\theta}{2} = 65^{\circ}$. Using this value in Bragg's equation for x-ray diffraction we get $\lambda$ as 1.65 Å. This is a close agreement with the theoretical value of 1.66 Å.

8. Experimental study of the photoelectric effect

An evacuated glass or quartz tube contains a photosensitive cathode (C) and a collector plate (A). A battery connects to the cathode to help evacuate photoelectrons. A quartz window allows light to pass through and hit the cathode. A microammeter measures the photocurrent that's produced when the emitted photoelectrons hit the anode.

(i) Effect of intensity of light

The photoelectric current emitted is directly proportional to the intensity of light.

(ii) Effect of P.D between A and B

Saturation current value increases with the intensity of incident light
Cut-off potential V₀ is independent of intensity.

(iii) Effect of Frequency

Formulas Of Dual Nature of Radiation And Matter

The energy of a photon-

$$E=h \nu=\frac{h c}{\lambda}$$

Kinetic mass of the photon=

$$m=\frac{E}{c^2}=\frac{h}{c \lambda}$$

3.The momentum of photon=

$$P=\frac{E}{C}=\frac{h}{\lambda}$$

4. Work function-

$$w=h \nu_0=\frac{h c}{\lambda_0}$$

5. Einstein's Photoelectric Equation=

$$h \nu=w+\frac{1}{2} m v_{\max }^2$$

6. De - Broglie wavelength-

$$\lambda=\frac{h}{p}=\frac{h}{m v}=\frac{h}{\sqrt{2 m E}}$$

NCERT Notes Subject Wise Link:

How to prepare Dual Nature of Matter and Radiation

First, you should have good command over the concepts of the Dual Nature of Matter and Radiation and you should also know how to apply them well at the time of the entrance exam or while solving questions.
Please try to understand each concept from this chapter, with the help of theory, questions with solutions, and video lectures on each important concept. For each concept practice enough problems so that you have a thorough understanding of the concept.
Solve all the questions at home with proper concentration and try to do all calculations by yourself without seeing the solution first.
While solving questions of Photoelectric Effect first find out the relation between work function and the energy of the incident wave and then solve for the result.
Please have a thorough knowledge of the Effect of intensity, potential, and frequency on photoelectric current.
Remember all the formulas for calculating De - Broglie wavelength. This will help you solve questions.

Dual Nature of Matter and Radiation Tips

Make a proper plan to prepare for this chapter and Stick to it.
Study the concept first and then start solving questions. Don't go through the question directly without knowing the concept.
Formulas from this chapter are very important from the point of view of competitive exams. So please remember them and solve lots of questions based on these formulas.
Solve previous year's questions of various exams from this chapter.
Use smart methods to solve questions.

Dual Nature of Matter and Radiation Books

For Dual Nature of Matter and Radiation, chapter concepts in NCERT are enough but you will have to practice lots of questions including previous year questions and you can follow other standard books available for competitive exam preparation like Concepts of Physics (H. C. Verma) and Understanding Physics by D. C. Pandey (Arihant Publications).

NCERT Solutions Subject-wise link:

Summary

The dual behaviour of matter and radiation refers to the concept that both exhibit properties of particles and waves. We have discussed the dual nature of radiation and matter class 12 topics, the photoelectric effect, Einstein’s equation, the Davisson and Germer experiment, Hertz and Lender’s observations, and de Broglie's relation in this article. We have covered almost all the topics included in the syllabus.

NCERT Exemplar Solutions Subject-wise link: