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Explain de Broglie wave theory


Solution

Matter-wave or a de Broglie wave

Louis de Broglie, a French physicist, in 1924, suggested that all microscopic, as well as

macroscopic objects, possess dual character. The wave associated with the particle is

called a matter-wave or a de Broglie wave.

The wavelength of the wave associated with any material particle was calculated as:

In the case of a photon, if it is assumed to have a wave character, its energy is given by

E=hν

where ν is the frequency of the wave and h is Planck’s Constant.

If the photon is supposed to have particle character, its energy is given by

E=mc2

where m is the mass of the photon and c is the velocity of light.
As the smaller particle exhibits dual nature, and energy being the same, de Broglie equated both these relations for the particle moving with velocity ‘v’ as,

                                             hν=mv2

hcλ=mv2

λ=hmv                 

This equation relating the momentum of a particle with its wavelength is the de-Broglie equation and the wavelength calculated using this relation is the de-Broglie wavelength.                                 

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