write the de broglies matter wave equation and explain the terms
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The wavelength of the wave associated with any material particle was
calculated by analogy with photon as follows :-
In case of a photon, if it is assumed to have wave character, its energy is given by
E = hν (according to the Planck’s quantum theory) ...(i)
(where ν is the frequency of the wave and h is Planck’s constant.)
If the photon is supposed to have particle character, its energy is given by
E = mc2 (according to Einstein equation) ...(ii)
(where m is the mass of photon and c is the velocity of light.)
From equations (i) and (ii), we get
h ν = mc2
But ν = c / λ
∴ h . c / λ = mc2
or λ = h / mc
de Broglie pointed out that the above equation is applicable to any material particle.
The mass of the photon is replaced by the mass of the material particle and the velocity “c” of the photon is replaced by the velocity v of the material particle.
Thus, for any material particle like electron, we may write
λ = h / mv or λ = h / p
(where mv = p is the momentum of the particle.)
The above equation is called de Broglie equation and ‘λ’ is called de
Broglie wavelength.
In case of a photon, if it is assumed to have wave character, its energy is given by
E = hν (according to the Planck’s quantum theory) ...(i)
(where ν is the frequency of the wave and h is Planck’s constant.)
If the photon is supposed to have particle character, its energy is given by
E = mc2 (according to Einstein equation) ...(ii)
(where m is the mass of photon and c is the velocity of light.)
From equations (i) and (ii), we get
h ν = mc2
But ν = c / λ
∴ h . c / λ = mc2
or λ = h / mc
de Broglie pointed out that the above equation is applicable to any material particle.
The mass of the photon is replaced by the mass of the material particle and the velocity “c” of the photon is replaced by the velocity v of the material particle.
Thus, for any material particle like electron, we may write
λ = h / mv or λ = h / p
(where mv = p is the momentum of the particle.)
The above equation is called de Broglie equation and ‘λ’ is called de
Broglie wavelength.
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★☆〖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:
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