Louis.de Broglie Relationship Class 11 Chemistry Notes

 Louis.de Broglie Relationship Class 11 Chemistry Notes

Einstein proposed in 1905 that light had a dual nature, acting as both a particle and a wave. All material particles in motion, such as electrons, protons, neutrons, atoms, molecules, and so on, have a dual character, according to Louis de Broglie (1924), a French scientist. Any moving electron in an atom, according to Louis de Broglie, is a material particle with wave qualities, and he compared electrons to photons with insignificant masses.

The de Broglie equation connects the wavelength of a moving particle to its momentum. The de Broglie wavelength,, is linked with a large particle and is connected to its momentum, p, via the Planck constant, h: To put it another way, matter acts similarly to waves. De Broglie claimed that electrons contain wave-like features, similar to how light has both wave-like and particle-like properties. Through the Planck constant, we can determine a relationship between the wavelength associated with an electron and its momentum by rearranging the momentum equation presented in the previous section.

The wavelength of a particle of mass m and velocity u, according to L. de Broglie, is given by the relation:

λ = h/mu

Derivation of de Broglie’s equation

The relation between the particle nature and wave nature of electron is known as the de Broglie equation. According to Planck, the energy of a quantum of radiation is given by:

E= hν…………………………….(1)

According to Einstein, mass and energy are related as:

E= mc2……………………………(2)

Where c is the velocity of light

Combining these two equations, we have:

hν = mc2

orhν/c = mc…………………………………….. (3)

Frequency, ν can be expressed in terms of wavelength, λ as,

ν = c/λ

or                            λ =c/ν

or                         1/λ = ν/c

Substituting the value of ν/c in equation

or                               h/λ =mc

or                                   λ= h/mc

This equation is applicable for a photon. According to L. de Broglie, the above equation can also be applied to the material by substituting the mass of the particle m and its velocity u in place of the velocity of light c. Thus wavelength λ of the material particle is given by:

λ= h/mu

The above equation is de Broglie equation and the wavelength is called as de Broglie wavelength.

or                               λ= h/p

where p is the momentum of the particle.

Thus, the significance of de Broglie equation lies in the fact that it relates the particle character to the wave character of matter.λ = h/mu

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