Question

Give the statement of de Broglie's principle.

Answer 1

De Broglie hypothesis says that all matter has both particle and wave nature. The wave nature of a particle is quantified by de Broglie wavelength defined as [math]\lambda = \frac{h}{p}[/math] where [math]p[/math] is the momentum of the particle. This was called a hypothesis because there was no evidence for it when it was proposed, only analogies with existing theories. (The wavelength-momentum relation holds exactly for photons.)

Historically, de Broglie hypothesis was the next step in quantum theory after Planck, Einstein and Bohr.

In 1900, Max Planck introduced the notion that radiation is quantized to derive the black body radiation spectrum.In 1905, Albert Einstein used Planck's idea to explain photoelectric effect, which led to wide acceptance of the quantum nature of radiation.In 1913, Niels Bohr used quantization of radiation along with the Bohr hypothesis (that the angular momentum of electrons is quantized) to correctly predict the line spectrum of hydrogen atom and explain .In 1923, Lois de Broglie took this idea further and proposed that matter has wave nature as radiation has particle nature.

Bohr hypothesis comes as an immediate consequence of de Broglie hypothesis - angular momentum must be conserved if an electron in an atom is seen as a wave going in circles around a nucleus such that the electron wave interferes constructively everywhere in the orbit.

In 1926 Erwin Schrödinger published the Schrödinger equation which generalized de Broglie's concept of matter waves and put them in a more robust theoretical footing.

The direct experimental confirmation came in 1927 when Clinton Davisson and Listor Germer and independently, GP Thomson observed electron diffraction.

Answer 2

★☆〖Qบęຮτ ı¨ ø nˇ〗☆★

⭐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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