Dual Nature of Matter and Radiation Chapter - Physics JEE Main

Dual nature of matter chapter of Physics is significant for JEE and is based on the knowledge about the 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 their 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's 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 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 behavior of the matter.

JEE Main Physics Chapters 2024 

Important Topics of Dual Nature of Matter Chapter

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

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.

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

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 overcome 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 that is required to eject an electron from a metal’s surface.

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

• Threshold Wavelength: It is the maximum wavelength of light that 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 the 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. The 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:

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

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

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

• The process of photoelectric emission is an instantaneous process.

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

Hertz and Lenard's Observations

Heinrich Hertz and Philipp Lenard conducted a series of experiments on the photoelectric effect. They found that:

• The energy of the ejected electrons is proportional to the frequency of the incident light.

• There is a minimum frequency of light, called the threshold frequency, below which no electrons are ejected.

• The intensity of the incident light has no effect on the energy of the ejected electrons, but it does affect the number of electrons ejected.

Hertz and Lenard's observations regarding the phenomena in question were groundbreaking.

Einstein's Photoelectric Equation

Albert Einstein explained the photoelectric effect by proposing that light is made up of individual particles, called photons. He also proposed that the energy of a photon is proportional to its frequency.

Einstein's photoelectric equation is given by:

E_k = hν - Φ

where:

E_k is the kinetic energy of the ejected electron

h is Planck's constant

ν is the frequency of the incident light

Φ is the work function of the metal

The work function is the minimum energy required to eject an electron from the metal surface.

Particle Nature of Light

The photoelectric effect provides strong evidence for the particle nature of light. It shows that light can interact with matter in a way that is consistent with it being made up of individual particles.

Matter Waves

Louis de Broglie proposed that matter can also exhibit wave-like properties. This hypothesis is known as the wave-particle duality of matter.

Various theories on the Dual Nature of the Matter?

De Broglie Hypothesis

• Heisenberg’s Uncertainty principle

• Bohr's model is based on angular momentum from the DeBrigile equation.

• Davison and Germer's experiment

• Thompson experiment.

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 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's theory explains wave behavior 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/mcif c = v

 then ƛ = h/mv

We also know the momentum of a particle

 P = mvThus, 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 the emission of thermal radiation with different wavelengths or frequencies. 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 the 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.

The above theories are based on the dual nature of matter and it suggests that sometimes the particle behaves like a wave rather than a particle.It also further describes the difference between electromagnetic waves and matter waves.

Study of Dual Matter-Quantum Mechanics

Quantum physics is a branch of science that deals with the study of matter which we cannot see. Quantum mechanics is really very difficult to understand for students. Quantum mechanics is related to the physical properties of nature at the scale of atoms and subatomic elements. Quantum physics helps students to understand the properties of nature and due to this, it is difficult to make a decision because it does not follow any kind of rules of Physics. It also depends on controversial features whether they are observed or not. 

Under proper circumstances, particles can behave as waves While Waves may behave as particles. Thus dual nature,i.e.particle, and the wave was established and a fascinating branch of physics, called quantum mechanics came into existence. In quantum mechanics, some of the classically inspired notions of the distinction between particles and waves are discarded. Quantum mechanics involves concepts that are often strange and counter to our intention.

Students at higher levels of education learn about quantum physics in detail.

Below are the few topics that are taught to students regarding quantum physics.

• The domain of quantum mechanics

• key concepts in quantum mechanics

• a review of complex numbers 

• probability in quantum mechanics

• wave function

• position, velocity, and Momentum from the wave 

• separation of variables and many more.

Hertz and Lenard's Observations: Pioneers of Photoelectric Effect

Before Einstein's groundbreaking work on the photoelectric effect, scientists Heinrich Hertz and Philipp Lenard made significant contributions to this field. Hertz's experiments with cathode rays laid the foundation for understanding the release of electrons under the influence of electromagnetic radiation.

Lenard, on the other hand, investigated the photoelectric effect and discovered that the kinetic energy of emitted electrons increased linearly with the frequency of incident light. This observation, in conjunction with Einstein's theory, offered crucial support for the particle nature of light.

Applications of the Dual Nature of Matter and Radiation

The dual nature of matter and radiation has a wide range of applications, including:

• Lasers: Lasers produce a beam of coherent light. This means that all of the photons in the beam have the same frequency and phase. Lasers are used in a variety of applications, including medicine, communication, and manufacturing.

• Electron microscopes: Electron microscopes use electrons to magnify objects. Electrons have a very small wavelength, which allows electron microscopes to achieve very high magnifications. Electron microscopes are used in a variety of fields, including biology, materials science, and nanotechnology.

• X-ray diffraction: X-ray diffraction is a technique that uses X-rays to study the structure of crystals. X-ray diffraction is used in a variety of fields, including materials science, chemistry, and biology.

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