Explanation of Wave-Particle Duality

You might have read about the characteristics and nature of light. This article will expand your understanding further with an explanation of wave-particle duality.

In 1923, Louis De Broglie suggested that matter experiences duality. He explained that each and every particle of matter has momentum and wavelength associated with it. 

The Theories of Wave-Particle Duality

Both light and matter hold particles and hold characteristics of a wave. In short, light and matter can be represented in the form of wave nature of light and particle nature. In the early 19th century, physicists proposed various theories of the particle-wave duality of light. Most researchers found out that in various cases, waves behave like particles, and particles behave like waves. This phenomenon of duality brought forward various theories.

Following are some of the theories:

The De Broglie Wavelength

Louis de Broglie suggested that matter can also exhibit the duality of wave particles. This was proved when the different beams of electrons, as well as neutrons, passed through a crystal, and various diffraction patterns were observed. 

He also theorised that matter has a certain momentum along with a wavelength that is associated with it:

λ = h/p.

λ= This refers to the associated wavelength

p = This refers to momentum

h= Planck’s constant

This equation is also applicable to a photon. He explains that small objects also exhibit matter-like properties. Also, other theories substantiated this proof that waves, as well as particles, can overlap.

The Huygens Wave Theory

This theory was proposed by Huygens in 1678. This theory suggested that every point of light waveform can be considered a source of spherical waves. This theory has assisted in the development of the wave theory of light theorised by other physicists such as Kirchhoff.

The Corpuscular Theory by Newton

According to this theory, Newton defined light to be made up of certain corpuscles. These corpuscles of light travel in a straight line. The theory or law of reflection also justifies that the wave-like nature of light bounces to a planar surface on reflection. 

However, it has been observed in refraction that light generally travels in a much denser material, which explains the particle nature of light.

Quantum Property of Light

Light also exhibits certain properties on the quantum scale of atoms, which proves the photoelectric effect. This explains the particle treatment for refraction of light: a sufficient localization of energy must be ejected from a surface. 

Planck’s Wave-Particle Duality

The first experiment that was conducted related to Wave-Particle duality was conducted by German Physicist Max Planck. With the help of a blackbody radiator, Planck explained the equation regarding the small amount of energy that can be changed to light.

E= hv

Here h refers to the Planck’s constant, which is 6.626 x 10-34 J.S, where v is the frequency.

In 1905, Einstein said that Planck’s discrete energies are available in various packets of energy, which are known as photons. The energy of a system in totality is equal to the sum of potential energy as well as kinetic energy; it is also important to note that here the Law of Conservation of energy is applicable.

Einstein explains the photoelectric effect: the photon energy absorbed by one or more electrons in any metal results from what the electron can eject if the energy of the photon is greater than that of the threshold energy.

The threshold energy is the amount of energy that is needed to be ejected from an electron, and this is known as the work function.

Now 

E= hv

However, we can rewrite the equation to show that the total energy is equal to the summation of Φ and kinetic energy.

E = Φ + KE = hv

Now the photoelectric effect shows that light behaves in the way of a photon or a particle that is packed with energy. In other ways, we can say that light waves behave like particles.

As per the Particle theory of light, the energy of light increases to a discrete as well as finite value until λ is zero, which practically never occurs. 

Wave-Particle Duality Equation

As both the particle as well as wave theory of light explains the major property of light, let us understand how the equation was derived.

So 

E = hv = hc/λ—-(1)

Now 

                           λ=hc/E—– (2)

and

p = E/c = mv

That is P: This is the momentum of the object

M – This is the mass of the object

V – This is the velocity of the object.

So, we can say 

λ = hc/mvc = h/mv

This equation states that all objects that move are coupled with a mass and a wavelength, which we often refer to as the de Broglie wavelength. However, these wavelengths can be seen with an object that has a really small mass.

This relationship was further established by experiments of other physicists such as Davisson and Germer, where the wavelength of various electrons that gave various diffraction patterns was the same as that for the wavelength predicted by the relationship established by de Broglie.

Conclusion

Both light and matter hold particles and hold characteristics of a wave. In short, light and matter can be represented in the form of wave nature of light and particle nature. Thus, these were some theories that were postulated that confirmed that light exhibits wave-particle duality and how the de Broglie equation comes into place.