Important Topics Covering Dual Nature Of Matter

The chapter on “Dual Properties of Matter” in physics is based on the knowledge of the various properties of matter. The important topics covering dual nature of matter include various hypotheses or trials. These have been developed to show that the nature of matter can be either particles or waves.

In the past, the various characteristics of light and matter have been described in the course of the properties of their particles. 

Primitive steps supported that it was the particle theory. After that, through various experiments, it became clear that matter has wave properties. Therefore, it can be concluded that matter has dual properties, having the characteristics of both particles and waves.

Maxwell’s electromagnetic equations and experiments on origination and observation of Hertz’s waves of electromagnetism in the year 1887 provide strong evidence, and these theories hold to the wavy nature of light. Therefore, the concept of duality of the wave particles of matter is important in the mechanism of quantum theory. It explains that any particle or quantum establishment can be represented in terms of particles or waves. 

In addition, this concept helps to correct the powerlessness of classical mechanical approaches or hypotheses, which completely explain the behaviour of matter.

Important notions for dual nature of matter 

To understand the concept of important topics concerning the dual nature of matter, the following should be understood.

Emission of electrons

The amount of energy that is required to release electrons from a metal surface is minimal, and the methods to supply these free electrons are:

Thermionic emission

The essential amount of thermal energy is supplied by proper heating of the metallic body, which releases the free electrons. 

Field emission 

Release of electrons from the surface of the metal under great electric field impact.

Photoelectric emission

Electrons are emitted when a suitable frequency of light is illuminated on the surface of the metal. The emitted photogenerated electrons are known as photo electrons.

Photoelectric effect 

The phenomenon by which electrons are released from the surface of the material is the photoelectric effect. Metals are composed of negative and positive ions. When the surface of a metal is hit by light, some electrons absorb enough energy. This helps them to overcome the effect of positive ion attraction. In addition, when the electrons get enough energy they need, they escape from the metal surface to the surrounding space. This is how the photoelectric effect occurs. 

De Broglie hypothesis

Keeping in mind the theory (quantum) of matter, the relationship between wavelength and momentum was formulated by De Broglie. According to the mathematical expression,

 the wavelength ƛ = h / P. Here,

P = the momentum of the particle under investigation and 

h = Planck’s constant.

Bohmian mechanics

Also known as the De Broglie theory, it takes into account the nature of waves in the matter, so it prevails, and the duality of the particle wave disappears somewhere. DeBroglie-Bohm theory describes the behaviour of waves as a De Broglie wave-like phenomenon, and the representation of particles is influenced by gold-plated equations or quantum potentials.

Derivation of equation of De Broglie

hf=mc2

We know that

frequency f=c/ ƛ

This implies that

hc/ ƛ=mc2 or ƛ = h/mc

If c=v; then ƛ=h/mv

We know that

 the momentum of a particle, 

P= mv.

Hence, ƛ = h/P.

Heisenberg’s Uncertainty Principle

Heisenberg’s uncertainty principle  states that the determination of the momentum and position of a particle is not possible at the same time. 

It is demonstrated mathematically as  ∆ x ∆P ≥ (h / 4π). 

Here, ∆x indicates the position uncertainty, and 

∆P indicates momentum uncertainty.

Planck’s quantum theory 

According to Planck’s quantum theory, 

• Applying heat to a blackbody emits thermal radiation of various wavelengths and frequencies.
•  A few important points to note in this theory are: 
• Matter radiates or absorbs energy discontinuously and is generated in the form of a small package. 
• This procedure is done in integer form in multiples of quanta such as hf, 2hf, 3hf, 4hf, …..nhf. 

Where n = a positive number.

•  Quanta is the tiniest package of power, and in the ‘light’ case, it is a photon. The frequency of radiation is proportionate to quantum energy.

Electron under an electric field

Let us consider a mass of an electron- m

            Charge- q and 

            potential V. 

Work done on the electric field is proportionate to the produced kinetic energy. 

Equation of an electron under an electric field 

The kinetic energy = work done on it by the electric field, i.e. qV

 K = qV 

K = ½mv2 

K = P2 / 2m

 P= √2mK 

= 2mqV

The de Broglie wavelength of an electron is given by the following equation.

 ƛ = h / P

 = h / √2mK

 = h / √2mqV 

Substitute the numbers h, m, e; there is ƛ = 1.227 / nm.

 Here, V is the magnitude of the acceleration potential (in volts).

Conclusion 

We have touched upon the important topics covering dual nature of matter here. Their  importance is felt even in our everyday life. There have been several theories that prove the nature of waves. The kinetic mass of photon, photoelectric equation and De Broglie equation have helped to solve the wave theory of light and is an important chapter in quantum mechanics.

 For exam preparations, ensure that you touch upon important topics covering dual nature of matter and the previous year questions.