Question

de broglie principles​

Answer 1

In 1924, Louis de Broglie proposed a new speculative hypothesis that electrons and other particles of matter can behave like waves.

Explanation:

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 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.

Answer 2

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⭐The Dual Nature of Matter⭐

=> de-Broglie's Principle states that "All material particles in motion possess wave characteristics..."

=> de-Broglie's Relationship can be derived by combining the mass and energy relationships proposed by Max Planck, and Albert Einstein...

E = ∫c²dm = Σc²Δm = mc²

E = hν

=> The combination of these two yielded the desired result:

λ = h/mc

=> The above equation is valid for a Photon(γ⁰)

=> The same relation can be extended to every particle of this universe, if the speed of light in vacua(c) is replaced by the ordinary velocity of the particle:

$\: \: \: \: \: \: \: \: \: λ = \frac{h}{ \: mv⃗}$

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