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# Dual Nature of Electron

## Dual Nature of Electron

(1) In 1924, the French physicist, Louis de Broglie suggested that if light has electron, behaves both as a material particle and as a wave.

(2) This presented a new wave mechanical theory of matter. According to this theory, small particles like electrons when in motion possess wave properties.

(3) According to de-broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation λ = h/mv where h = Planck’s constant.

(4) This can be derived as follows according to Planck’s equation, E = hv = hc /λ ∴ v=c/λ(energy of photon (on the basis of Einstein’s mass energy relationship) E = mc2,

Equating both hc/λ = mc2 or λ = h/mc which is same as de-Broglie relation. (∴ mc = p)

(5) This was experimentally verified by Davisson and Germer by observing diffraction effects with an electron beam.  Let the electron is accelerated with a potential of V  than the Kinetic energy is

(1/2) mv2 = eV; m2V2 = 2eVm

mv =  √2eVm = P;λ = h/√2eVm

(6) If Bohr’s theory is associated with de-Broglie’s equation then wave length of an electron can be determined in bohr’s orbit and relate it with circumference and multiply with a whole number 2πr = nλ or λ = (2πr/2π) From de-Broglie equation, λ = (h/mv).

Thus h/mv = (2πr/n) or mvr = (nh/2π)

(7) The de-Broglie equation is applicable to all material objects but it has significance only in case of microscopic particles. Since, we come across macroscopic objects in our everyday life, de-broglie relationship has no significance in everyday life.

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