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# De Broglie Hypothesis on Wave Particle Duality

To explain the theory of atomic structure, a hypothesis was offered by Louis de Broglie. De Broglie hypothesized that particles can hold wave characteristics. Scientists tested de Broglie’s concept by electrons and light rays through slits and noticed that electron stream behaved similarly to light, thus supporting De Broglie theory. De Broglie hypothesis on wave particle duality states that particles can behave like waves and waves can behave like particles, like light will behave both like wave as well as like particle. This is called dual nature of light.

According to the de Broglie equation, matter can behave like light and radiation, which are both waves and particles. This equation tells that a beam of electrons can be diffracted in the same way as a beam of light ray. Thus de Broglie equation clarifies the concept of matter having a wavelength. As a result, every moving particle, whether microscopic or macroscopic, has certain wavelength.

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### What is the de Broglie relation?

One of the equations widely used to define the wave nature of particle is the de Broglie equation. It essentially describes the electron’s wave nature. Electromagnetic radiation has the properties of both particle (with momentum) and wave (expressed in frequency and wavelength). This dual nature feature was also discovered in microscopic particle-like electrons.

However, one interesting fact was that the particle and wave natures of matter appeared to be incompatible, as neither property could be demonstrated in a single experiment. This is because every experiment is usually founded on a concept, and the outcomes of that principle are only reflected in that experiment and not in others. For example photoelectric effect, Compton Effect and pair production prove the particle nature of light but at the same time, light also has properties of interference, diffraction, reflection etc., which clearly indicate wave nature of light. As a result, the particle and wave natures of matter are truly complimentary. However, It is not required that both be present at the same moment. The de Broglie relation is significant because it is more beneficial for tiny particles such as electrons (as they have less mass and high velocity).

### De Broglie wavelength calculation

Low mass particles moving at the speed less than that of light behave like a particle and wave. De Broglie derived an expression relating the mass of such smaller particles and their wavelength.

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Plank’s quantum theory relates the energy of an electromagnetic wave to its wavelength or frequency. According to his theory, energy is given by

E = hv = h c / λ                 (1)
but according to Einstein theory,

E = m c2                            (2)

Comparing equation (1) and (2)

h c / λ = m c2

h / λ = mc           (3)

Since momentum is defined as product of mass and velocity, so right side of equation is momentum.

h / λ = p

This is the De Broglie wavelength formula of wave particle duality. De Broglie formula can also be written as

λ = h / p    or     λ = h / mv

This equation clearly indicates that wavelength is inversely proportional to momentum. Particles possess momentum and waves have wavelength, so the above relation combines waves and particles. However, it is best for microscopic objects, which have less mass like electrons.

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