Dual Nature of Matter

Dual Nature of Matter states that a matter exhibits both Particle Nature and Wave Nature. It means that when a matter is at rest it behaves like a particle and when it is moving it behaves like wave. Different Experiments have been performed to prove this by the science community.

In this article, we will look into this theory and understand the dual nature of matter. We will also learn the experiments that proved the dual nature of matter.

What is Dual Nature of Matter

Dual Nature of matter states that a particles exhibit both wave and particle properties. It is the basic concept of Physics that explains various properties of matter, i.e. Compton Effect, Photoelectric Effect, etc.

Dual Nature of Matter Important Concepts

Some essential topics related to the dual nature of matter are:

• Electronic Emission
• Photoelectric Effect
• Particle Nature of Light
• Davisson Germer Experiment
• Crompton’s Effect
• Wave Nature of Light
• De-Broglie Hypothesis

Electronic Emission

Electron emission refers to the ejection of an electron from the surface of matter. This phenomenon can be stimulated by various factors such as temperature elevation, radiation, or applying a strong electric field. There are different types of electron emission, including thermionic emission, field emission, and photoelectric effect.

• Thermionic Emission is the liberation of electrons from an electrode due to its temperature.

• Photoelectric Emission is the emission of electrons when electromagnetic radiation (such as light) falls on a material surface.

• Field Emission is an emission of electrons from the surface of a conductor into a vacuum under the influence of a strong electric field

Photoelectric Effect

Photoelectric effect is the phenomenon in which electrons are ejected from the surface of a material when it absorbs electromagnetic radiation, such as light. This effect is described by the equation:

E = hf – ϕ

where,

• E is the Kinetic Energy of Emitted Electron
• h is Planck’s Constant
• f is Frequency of Incident Light
• ϕ is Work Function of Material

Kinetic energy of the emitted photoelectrons is directly proportional to the frequency of the incident light.

Terms Related to Photoelectric Effect

• Threshold Frequency: The minimum frequency of light required to cause the ejection of electrons from a material. Below this frequency, no photoelectrons are emitted, regardless of the intensity of the incident light.

• Photoelectrons: Electrons emitted from a material due to the photoelectric effect are called photoelectrons. These electrons are indistinguishable from other electrons and are distinguished because they have been ejected from a material by incident light.

• Work Function: The minimum amount of energy required to remove an electron from the surface of a material. It is a crucial parameter in the photoelectric effect, as it determines the minimum photon energy required to liberate an electron from the material.

• Stopping Potential: The potential difference at which the photocurrent stops flowing in a photoelectric setup. This potential difference is directly proportional to the frequency of the incident light, and the process of stopping the photocurrent is instantaneous.

Laws of Photoelectric Effect

The laws governing the photoelectric effect are,

• This law, also known as the first law of photoeffect, establishes the direct proportionality between the intensity of electromagnetic radiation acting on a metallic surface and the photocurrent induced by this radiation. It was discovered by Aleksandr Stoletov in 1888.

• For any given material, there is a certain minimum (energy) frequency, called the threshold frequency, below which the emission of photoelectrons stops completely, no matter how high the intensity of the incident light. This law was introduced by Albert Einstein in 1905.

• For a light of any given frequency, the photoelectric current is directly proportional to the intensity of light as long as the light’s frequency is above the threshold frequency. This relationship was discovered by Henri Poincaré in 1905.

• Kinetic energy of the photoelectrons is directly proportional to the light frequency. This relationship was discovered by Albert Einstein in 1905.

Hertz and Lenard’s Observations

Heinrich Hertz and Philipp Lenard made significant observations related to the photoelectric effect, which played a crucial role in the development of quantum theory. Hertz’s observations in 1887, while attempting to validate Maxwell’s electromagnetic theory of light, led to the unexpected discovery of the photoelectric effect.

He noticed that the spark length in a spark gap placed in a dark box decreased. However, when he replaced the dark box with a glass one, the spark length increased, and it grew even further when he used a quartz box. This was the pioneering observation of the photoelectric effect.

Subsequently, Lenard observed that the kinetic energy of the emitted electrons increased with the incident radiation frequency, contrary to the predictions of classical electromagnetic theory.

Particle Nature of Light

Photoelectric effect gives solid evidence of the particle nature of light. It tells that light can interact with matter in a way that is consistent with it being made of individual particles.

Compton Scattering

Compton scattering is a phenomenon in which a photon collides with a charged particle, typically an electron, and transfers some of its energy to the electron, causing it to recoil.

• The scattered photon has a longer wavelength and lower power than the incident photon, and the scattering angle depends on the incidence angle and the incident photon’s energy.
• Compton scattering is a fundamental process in X-ray and gamma-ray spectroscopy and is used to determine the structure of materials and the universe’s composition.
• The phenomenon was first observed by Arthur Compton in 1923. It provided evidence for the particle nature of electromagnetic radiation, as the scattering could only be explained by treating the photon as a particle with momentum and energy.

Davisson and Germer Experiement

Davisson and Germer experiment involved the following steps:

• A beam of electrons was produced and directed at a crystalline nickel target.
• The atoms of the nickel crystal scattered the electrons, and the angular dependence of the scattered electron intensity was measured.
• The electron beam was moved on a circular scale, and the intensity of the scattered electrons was measured at different angles.
• By changing the accelerating potential difference, the accelerated voltage was varied from 44V to 68V

The observations made during the experiment showed that the electrons exhibited wave-like behavior, as the nickel crystal scattered them in a manner similar to the diffraction of light by crystals. The experiment confirmed the de Broglie hypothesis. This finding and the Compton effect discovered by Arthur Compton established the wave-particle duality hypothesis, which was a fundamental step in the development of quantum theory.

Wave Nature of Matters

The wave nature of matter, also known as matter waves or de Broglie waves, is a fundamental concept in quantum mechanics, demonstrating that all matter exhibits wave-like behavior. This phenomenon allows particles to exhibit characteristics of other waves, such as diffraction and interference.

Matter Waves theory

Matter waves are a central part of the theory of quantum mechanics and exhibit the wave-particle duality of matter. The theory of matter waves predicts that particles like electrons can exhibit wave-like behavior and can be added together to form a superposition of waves, just as light waves can be added together.

Key aspects of matter waves include:

• De Broglie Wavelength: The wavelength associated with a particle with momentum p through the Planck constant, h. The de Broglie wavelength is given by the formula

λ= p/h

• Wave-Like Behavior: Matter waves demonstrate diffraction, interference, and other wave-like properties.
• Superposition: Matter waves can be added together to form a superposition of individual waves. This phenomenon is essential to the interference of waves.
• Probability Waves: The waves associated with elementary particles are probability waves, which are unitless numerical ratios that represent the probability of finding a particle at a particular place and time.

Blackbody Radiation

Black body radiation refers to the thermal electromagnetic radiation emitted by a hypothetical “black body,” which absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

Radiation emitted by a black body in thermal equilibrium with its environment is called Blackbody radiation. This radiation provides insight into the thermodynamic equilibrium state of cavity radiation and is a fundamental principle in understanding the emission of electromagnetic radiation by objects.

Dual nature of radiation, which encompasses both particle and wave nature, is evident in the behavior of black body radiation. The nature of waves is demonstrated by the specific, continuous spectrum of wavelengths emitted by a black body, which depends only on the body’s temperature, as Planck’s law describes.

Max Postulate of Quantization of Energy

Max Planck’s postulate of quantization of energy is a fundamental principle of quantum mechanics, stating that energy can only exist in discrete, quantized amounts rather than a continuous range.

• Planck’s constant, denoted by (h), is the proportionality constant between a quantum’s energy and the radiation’s frequency.

• Energy of each quantum is directly proportional to the frequency of the radiation.

• Planck’s law of black body radiation describes the spectral distribution of electromagnetic radiation emitted by a black body in thermal equilibrium with its surroundings.

• Quantization of energy is a critical concept in understanding the behavior of electromagnetic radiation and the photoelectric effect.

De-Broglie Hypothesis

The de Broglie hypothesis, proposed by Louis de Broglie in 1924, suggests that matter consists of both particle-like and wave-like properties, known as matter waves. This hypothesis can be applied to both microscopic and macroscopic particles.

Some critical aspects of the de Broglie hypothesis include:

Wave-Particle Duality: De Broglie’s hypothesis demonstrated that wave-particle duality was not just an unusual behavior of light but a fundamental principle of nature

De Broglie Wavelength

The wavelength of a matter wave can be calculated using the relation.

λ = h/m.v

where,

• h is Planck’s Constant
• m is Mass of Particle
• v is Velocity of Particle

Quantization of Angular Momentum: De Broglie’s hypothesis and Bohr’s early quantum theory led to the development of a new theory of wave quantum mechanics to describe the physics of atoms. This theory provided a rationale for the quantization of angular momentum in atomic orbitals.

De Broglie-Bohm Theory

De Broglie-Bohm theory, also known as pilot-wave theory or Bohmian mechanics, is a non-relativistic interpretation of quantum mechanics first proposed by Louis de Broglie in 1927 and later developed by David Bohm in 1952. The theory introduces particle positions as hidden variables, in addition to the wave function, to describe the complete state of a system of particles.

The theory is deterministic and avoids the concept of wave-particle duality. It has been experimentally tested and has been found to give the same results as standard quantum mechanics. The theory has been used to explain various quantum phenomena, such as quantum tunneling and quantum entanglement.

Derivation of De Broglie Equation

The de Broglie equation, which relates the wavelength of a particle to its momentum, can be derived as follows:

Step 1: Start with the energy-momentum relationship for a photon:

E = h/ν

p = h/λ

Step 2: According to Einstein’s mass-energy equivalence, E = mc²

Step 3: De Broglie hypothesized that particles and waves have the same traits, so he equated the energies of a photon and a particle: (E = mc² = h/ν).

Step 4: Since real particles do not travel at the speed of light, de Broglie substituted the velocity (v) for the speed of light (c), leading to the equation (mv² = h/ν).

Step 5: Using the relationship (v = ν/λ), where (λ) is the de Broglie wavelength, de Broglie arrived at the final expression that relates the wavelength and the particle’s speed:

λ = h/mv

λ = h/p

This shows how de Broglie related the wavelength of a particle to its momentum, providing a critical insight into the wave-particle duality of matter.

Heisenberg Uncertainty Principle

Heisenberg’s Uncertainty Principle is a fundamental concept in quantum mechanics, stating that there is a limit to the precision with which physical properties, such as position and momentum any fundamental particle, can’t be simultaneously known.

In other words, the more accurately one property is measured, the less accurately the other property can be known.

The principle can be mathematically expressed as follows:

Δp.Δx ≥ h/4π

where,

• Δx is Uncertainty in Position
• Δp is Uncertainty in Momentum
• h is Reduced Planck’s Constant

Planck’s Quantum Theory

Planck’s quantum theory, proposed by the German physicist Max Planck in 1900, is a fundamental concept in quantum physics. It introduces the idea that energy is quantized, meaning that it is emitted or absorbed in discrete units, or “quanta,” rather than in a continuous manner.

This theory was initially developed to explain the observed spectrum of black-body radiation, which is the electromagnetic radiation emitted by a heated object.

Key equation associated with Planck’s quantum theory is the relationship between the energy (E) of a photon and its frequency (ν), given by the equation:

E = hν

where,

• E is Energy of Photon
• h is Planck’s Constant
• ν is Frequency of Electromagnetic Wave

This equation implies that the energy of a photon is directly proportional to its frequency, with Planck’s constant being the proportionality constant.

Electron Under an Electric Field

When an electron is placed in an electric field, it experiences a force due to the electric field. The direction of the force depends on the electron’s charge and the electric field’s direction. If the electron is negatively charged, it will experience a force in the opposite direction to the electric field. In contrast, if it is positively charged, it will experience a force in the same direction as the electric field.

The acceleration of an electron in an electric field can be calculated using the equation:

a = F/m

where,

• a is Acceleration of Electron
• F is Force on Electron due to Electric Field
• m is Mass of Electron

The force on an electron in an electric field can be calculated using the equation:

F = qE

where,

• F is Force on Electron
• q is Charge of Electron
• E is Electric Field Strength

Read More, Dual Nature of Light

Dual Nature of Matter IIT JEE Questions

Q1: What is De-broglie wavelength of an alpha-particle accelerated through a potential difference V

1. 0.287/√V A
2. 12.27/√V A
3. 0.101/√V A
4. 0.202/√V A

Option (3) is Correct

I = h/√2mE = h/√2m_a×Q_a×V

Putting Q_a = 2×1.6×10^-19 C

m_a = 4mp = 4× 1.67×10^-27 kg

I = 0.101/√V

Q2: Kinetic energy of electron and proton is 10^-32 J. Then the relation between their de-broglie wavelength is

1. Ip < Ie
2. Ip > Ie
3. Ip = Ie
4. Ip = 2Ie

Option (1) is Correct

Q3: A metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V_o . If the same surface is illuminated with radiation of wavelength 2λ. The stopping potential becomes V_o/4. The threshold wavelength for this metallic surface will be

1. 3λ
2. 4λ
3. 3/2 λ
4. λ/4

Option (1) is Correct

Q4: In photo electric effect

• A. The photocurrent is proportional to the intensity of the incident radiation.

• B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.

• C. Max. K.E with which photoelectrons are emitted depends on the frequency of incident light.

• D. The emission of photoelectrons require a minimum threshold intensity of incident radiation.

• E. Max. K.E of the photoelectrons is independent of the frequency of the incident light.

Choose Correct Statements from the options given below:

1. A and E only
2. A and B only
3. B and C only
4. A and C only

Option (4) is Correct

Q5: If maximum kinetic energy of a photoelectron is 3 eV. What is its stopping potential?

Since K_max = eV_o

Stopping Potential (V_o) = K_max/e = 3V

Q6: Find the ratio of de-Broglie wavelengths associated with two electrons accelerated through 25 V and 36 V.

λ = 1/√V

λ₁/ λ₂ = √V₂/V₁ = √ 36/25 = 6/5

Therefore, λ₁ : λ₂ = 6 : 5

Dual Nature of Matter-FAQs

What is De-Broglie Dual Nature of Matter?

Matter, like electrons and other particles, exhibits both particle and wave characteristics. This concept is known as De Broglie’s dual nature of matter.

Who was the First to Propose Matter has Dual Nature?

Louis de Broglie proposed that matter, at the quantum level, possesses both particle and wave properties.

Who Proposed Dual Nature of Light?

The dual nature of light was first proposed by Albert Einstein, who suggested that light behaves as both particles (photons) and waves.

What are Matter Waves?

Matter waves refer to the wave-like characteristics exhibited by particles, as described by de Broglie’s theory.

Do Charged Particles Exhibit Wave Properties?

Yes, charged particles, like electrons, can display wave properties, as explained by quantum mechanics.

What is Photoelectric Effect?

Photoelectric effect is the phenomenon where light (photons) striking a material surface causes the emission of electrons, showcasing the particle nature of light.

Why Does Matter Exhibit Dual Nature?

Matter exhibits dual nature because at the quantum level, particles behave as both discrete entities (particles) and extended waves, depending on the experimental context.

What is De-Broglie Equation?

De Broglie equation, λ = h/p, relates wavelength (λ) of a particle’s wave to its momentum (p).