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Explanation:
de Broglie Equation
de Broglie equation states that a matter can act as waves much like light and radiation, which also behave as waves and particles. The equation further explains that a beam of electrons can also be diffracted just like a beam of light. In essence, the de Broglie equation helps us understand the idea of matter having a wavelength.
Therefore, if we look at every moving particle whether it is microscopic or macroscopic it will have a wavelength.
In cases of macroscopic objects, the wave nature of matter can be detected or it is visible.
Table of Content
What is the de Broglie Equation?
de Broglie Equation Derivation
de Broglie Equation and Bohr’s Hypothesis of Atom
de Broglie Equation Problems
What is de Broglie Equation?
The de Broglie equation is one of the equations that is commonly used to define the wave properties of matter. It basically describes the wave nature of the electron.
Electromagnetic radiation, exhibit dual nature of a particle (having a momentum) and wave (expressed in frequency, wavelength). Microscopic particle-like electrons also proved to possess this dual nature property.
Louis de Broglie in his thesis suggested that any moving particle, whether microscopic or macroscopic will be associated with a wave character. It was called ‘Matter Waves’. He further proposed a relation between the velocity and momentum of a particle with the wavelength, if the particle had to behave as a wave.
Particle and wave nature of matter, however, looked contradictory as it was not possible to prove the existence of both properties in any single experiment. This is because of the fact that every experiment is normally based on some principle and results related to the principle are only reflected in that experiment and not the other.
Nonetheless, both the properties are necessary to understand or describe the matter completely. Hence, particles and wave nature of matter are actually ‘complimentary’ to each other. It is not necessary for both to be present at the same time though. The significance of de Broglie relation is that it is more useful to microscopic, fundamental particles like electron.
de Broglie Equation Derivation and de Broglie Wavelength
Very low mass particles moving at speed less than that of light behave like a particle and wave. De Broglie derived an expression relating the mass of such smaller particles and its wavelength.
Plank’s quantum theory relates the energy of an electromagnetic wave to its wavelength or frequency.
E = hν =\frac{hc}{\lambda }=
λ
hc
…….(1)
Einstein related the energy of particle matter to its mass and velocity, as E = mc2……..(2)
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,
E = =\frac{hc}{\lambda }=m{{v}^{2}}:=
λ
hc
=mv
2
: Then, \frac{h}{\lambda }=mv
λ
h
=mv or \lambda =\frac{h}{mv}=\frac{h}{\text{momentum}}:λ=
mv
h
=
momentum
h
: where ‘h’ is the Plank’s constant.
This equation relating the momentum of a particle with its wavelength is de Broglie equation and the wavelength calculated using this relation is de Broglie wavelength.