## NCERT Chemistry Class 11 – Unit 2 – Louis.de Broglie Relationship

*NCERT Chemistry Class 11*: In 1905, Einstein suggested that light has a dual character, and behaves both as a particle and a wave.Louis de Broglie, a French physicist,(1924) suggested that all material particles in motion such as electrons, protons, neutrons, atoms, molecules etc. have a dual character. According to Louis de Broglie, any moving electron in an atom is a material particle associated with **wave properties **and he compared electrons with the photons having negligible masses.

The de Broglie equation relates a moving particle’s wavelength with its momentum. The de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, through the Planck constant, h: In other words, we can say that matter also behaves like waves. De Broglie proposed that just **as light has both wave-like and particle-like properties, electrons also have wave-like properties.** By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength associated with an electron and its momentum through the Planck constant.

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

**λ = h/mu**

Where h is Planck’s constant and mu is the momentum of the particle.

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**Derivation of de Broglie’s equation**

The relation between the particle nature and wave nature of electron is known as **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= mc^{2}……………………………(2)

Where c is the velocity of light

Combining these two equations, we have:

hν = mc^{2}

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.*

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**Every particle has wave nature, but it is truly evident when a particle is very light, such as an electron (mass = 9.11 x 10**^{-28}g)

Louis de Broglie’s concept of dual nature of matter finds application in the construction of electron microscope and in the study of the surface structure of solids by electron diffraction. The de-Broglie’s concept can be applied not only to electrons but also to other small particles like neutrons, protons, atoms, molecules etc.The wave nature of matter, however, has no significance for objects of ordinary size because the wavelength of the wave associated with them is too small to be detected.

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