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  De-Broglie Relation

De-Broglie Relation:

The wavelength of the wave related with any material particle was computed by analogy with photon as follows:

In case of photon, when it is assumed to have wave character, its energy is specified by,

E = hν (i.e., according to the Planck’s quantum theory)

Here,
ν is the frequency of the wave and h is the Planck’s constant.

If the photon is assumed to have particle character, its energy is specified by,

E = mc2 (i.e., according to Einstein equation)
Here,
m is the mass of photon and c is the velocity of light.

From the above two equations, we obtain:

h ν =mc2

Since, ν =c /λ
∴ h . c/λ =mc2
or λ = h/mc

de Broglie indicated that the above equation is appropriate to any material particle. The mass of the photon is substituted by the mass of the material particle and the velocity “c” of the photon is substituted by the velocity v of the material particle. Therefore, for any material particle such as electron, we might write,

880_De-broglie.jpg

Here,
mv = p is the momentum of the particle.

The above equation is termed as de Broglie equation and ‘λ’ is referred as de Broglie wavelength.

Therefore the importance of de Broglie equation lies in the fact that it associates the particle character with the wave character of matter.

Louis de-Broglie’s concept of dual nature of matter gets application in the construction of electron microscope and in the study of surface structure of solids by electron diffraction. The de-Broglie’s concept can be apply not only to electrons although also to other small particles such as protons, neutrons, atoms, molecules and so on.

 

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