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Saturday, July 3, 2021

What is the "de Broglie equation" or How can derived "de Broglie equation" or What is the "Wave –Particle Duality" ?

Wave –Particle Duality, Dual Nature of Electron:

Bohr’s and Sommerfield proposed that angular momentum in closed orbit is “Quantized” but they could not derived mathematically.

Derivation of this fact was made by Loius de Broglie in 1924 assuming the dual nature of electron i.e. particle as well as wave nature of electron. This proposal gave birth of a new theory known as “ Wave Mechanical theory of matter”

Loius de Broglie was suggested that a particle in motion also behaves like a wave. The wave length associated with the moving particle is given by the following equation,

Where

 h = Planck’s constant,

 m = mass of the moving particle,

v = velocity of the particle.

This above equation (1) is known as de Broglie equation. De Broglie equation was derived on the basis of Einstein’s equation, E = mc2 and Planck’s equation E = hv. From both of these relation,

                Where p is the momentum of the moving particle.

(1) The wave length associated with a particle in motion is inversely proportional to its momentum.

(2) As the mass of the moving particle increases, the momentum also increases; the wave length of the matter wave (associated with the matter in motion) decreases.

(3) For the particles of finite size, i.e., having appreciable mass, the momentum is very high,  is very small and it can be said that macroscopic bodies in motion do not possess matter waves.

(4) When different particles move with the same velocity, the wave length of the matter wave is inversely proportional to the mass of the particle.

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