Dual Nature of Matter

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Introduction

Dual nature of matter chapter of Physics is significant for JEE and is based on the knowledge about different nature of matter. Various theories and experiments have come up to prove that a matter can either display or possess a particle or wave nature. 

Earlier, the properties of light and matter were explained in terms of its particle nature. Some of the primitive steps supported that it was the corpuscular theory. Later on, it was found through various experiments that matter possesses the properties of a wave. Therefore, it’s concluded that matter has dual nature; it means that it has both the properties of a particle as well as a wave.

Strong establishments were done with the help of Maxwell’s equation of electromagnetism and Hertz experiments on the generation and detection of electromagnetic waves in 1887. These theories support the wave nature of light. Thus, the concept of the wave-particle duality of the matter is important in quantum mechanics. It describes that every particle or quantum entity may be expressed in terms of a particle or a wave. Further, the concept helps in modifying the inability of the classical mechanic approach or theories to totally describe the behaviour of the matter.


Important Concepts for Dual Nature of Matter

Let’s explore some of the important topics related to this topic as follows:

  1. Electronic Emission

For emitting an electron from a metal’s surface, minimum energy is required which is supplied to the free electrons with the following methods:

  • Thermionic emission where suitable heating enables electrons to come out of the metal.

  • Field emission where a strong electric field influences electron emission out of the metal.

  • Photo-electric emission where an appropriate frequency of the light helps in the emission of electrons by illuminating the metal’s surface. The photo-generated emitted electrons are called photoelectrons.

  1. Photoelectric Effect

It is a phenomenon involving electrons that escape from the material’s surface. We know the surface of the material comprises both positive and negative ions. When light hits the metal surface, some of the electrons present near the surface absorb enough energy from the incident radiation and then overcomes the attraction of the positive ions. Then, the electrons gain sufficient energy to escape out of the metal’s surface into the surrounding. This is called the photoelectric effect.

Given below are some of the related terms and facts related to the photoelectric effect:

  • Work Function: It is the minimum energy which is required to eject an electron from a metal’s surface.

  • Threshold Frequency: It is the minimum frequency of light which can force an electron to emit from a metal surface.

  • Threshold Wavelength: It is the maximum wavelength of light which can eject a photoelectron from the metal’s surface. 

  • The work function is denoted by the symbol Ɵ, threshold frequency by f, threshold wavelength by ƛ (lambda) and the formula is represented as Ɵ = hf = hc/ ƛ, where h is Planck’s constant and E=hf.

  • The cut-off potential is the minimum negative or retarding potential denoted by V0 given to a plate for which photoelectric current becomes zero. It is also called the stopping potential.

  • The effect of the incident light intensity falling is linear with the photoelectric current for a fixed incident frequency.

  • Photoelectric current increases with an increase in potential applied to the collector for a fixed frequency and the intensity of the light falling. Maximum current attained is termed as saturated current.


Laws of Photoelectric Effect

Some of the major points to understand about the laws of photoelectric effect are as follows:

  1. The photoelectric current is directly proportional to the light’s intensity incident on the surface of a given metal and frequency of the incident light.

  2. Threshold frequency exists for a given metal which is a certain minimum frequency below which there is an absence of photo-electric emission.

  3. The maximum kinetic energy of photoelectrons (above a threshold frequency) depends upon the frequency of incident light.

  4. The process of photoelectric emission is an instantaneous process.

  5. The minimum negative potential energy applied to anode plate at which photoelectric current becomes zero is known as stopping potential, denoted by V0.


De Broglie Hypothesis

De Broglie defined the relationship between momentum and wavelength. According to the mathematical representation, wavelength ƛ = h/P where P is the momentum of the particle under study and h is the Planck’s constant.


De Broglie-Bohm Theory and Derivation of Equation

According to the theory of De-Broglie-Bohm, which is also known as Bohmian Mechanics, it considers the wave nature of matter and hence it predominates and particle-wave duality somewhere vanishes. De-Broglie-Bohm theory explains wave behaviour as a scattering wave-like appearance and the particle’s expression is subjected to a gilding equation or quantum potential.

hf = mc²

we know that the frequency f = c/ ƛ

it implies that hc/ ƛ = mc² or ƛ = h/mc

if c = v; then ƛ = h/mv

We also know the momentum of a particle, P = mv

Thus, ƛ = h/P


Heisenberg’s Uncertainty Principle

According to Heisenberg’s uncertainty principle, it is not possible to simultaneously determine both the momentum and position of the particle.

Mathematically, it is expressed as  ∆ x ∆P ≥ (h / 4π) where ∆x denotes the Uncertainty in position and ∆P denotes the Uncertainty in Momentum.


Planck’s Quantum Theory

According to Planck’s quantum theory, if we apply heat to a black body, it leads to emission of thermal radiations with different wavelengths or frequency. Some of the top points to remember for this theory are as follows:

  • Substances radiate or absorb energy in a discontinuous manner and it takes place in the form of small packets.

  • This process takes place in the whole-number form in the multiples of quantum such as hf, 2hf, 3hf, 4hf,......nhf where n=positive integer.

  • Quantum is the smallest packet of energy and is referred to as a photon in case of light.

  • The quantum energy is directly proportional to the radiation frequency.


Davisson and Germer Experiment

This experiment proves the wave nature of electrons and verifies the de Broglie equation. The result thus establishes the first experimental proof of quantum mechanics. 

The Davisson and Germer experiment is set up enclosing within a vacuum chamber Therefore, the electron deflections and scattering by the medium are prevented. The various parts involved in the experiment are:

  • Electron Gun: It is a Tungsten filament emitting electrons via thermionic emission.

  • Electrostatic Particle Accelerator: Two plates, that are oppositely charged, are employed to accelerate the electrons at a known potential.

  • Collimator: The accelerator is enclosed within a cylinder having a narrow beam for the electrons along its axis.

  • Target: It is a Ni crystal where the electron beam is fired over.

  • Detector: It is used to capture the scattered electrons from the Ni crystal.

FAQ (Frequently Asked Questions)

Q1. What is the Photoelectric Effect?

Ans: It was proposed by J.J. Thomson and he observed that when the light of certain frequency strikes the metal’s surface, electrons eject from the metal. The phenomenon is called photoelectric effect and the ejected electrons are known as photoelectrons.

Metals having low ionization energy such as Cesium display this effect under the action of visible light but many others show it under the action of highly energetic UV light.

Q2. What is the dual Nature of Matter?

Ans: As the name suggests, the matter has both kinds of nature i.e. it acts as a particle as well as a wave. Various experiments were conducted to prove this theory. It is supported by an example of light that behaves as a wave and a particle. This is an important concept of quantum mechanics.