GITAM, Department of Engineering Physics
Wave particle duality
The Bohr model of the atom involved two puzzling features - the electron
was treated as a wave, and light was treated as a particle (a photon).
Wave Nature of Electron
As a young student at the University of Paris, Louis DeBroglie had been
impacted by
relativity and the
photoelectric effect, both of which had been introduced in his lifetime.
The evidence for the description of light as waves was well established at the
turn of the century when the
photoelectric effect introduced firm evidence of a particle nature as
well. He wondered if electons and other "particles" might exhibit wave
properties. The DeBroglie
hypothesis and the subsequent experiments by Davisson
and Germer established the wave
nature of the electron. The application of these two new ideas to light
pointed to an interesting possibility:
DeBroglie Hypothesis
Suggested by De Broglie in about 1923, the path to the wavelength expression for a particle is by analogy to the momentum
of a photon.
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Starting with the Einstein formula: |
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Another way of expressing this is |
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Therefore, for a particle of zero rest mass ie m0 = 0 |
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The momentum-wavelength relationship for a photon |
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The momentum-wavelength relationship for a photon can then be derived and this DeBroglie wavelength relationship applies to other particles as well.
Examples supporting wave nature of light
Davisson-Germer Experiment
This experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of deBroglie. Putting wave-particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. The Bragg law for diffraction had been applied to x-ray diffraction, but this was the first application to particle waves.
Electron Diffraction
Two specific examples supporting the wave nature of electrons as
suggested in the DeBroglie hypothesis are the discrete
atomic energy levels and the diffraction of electrons from crystal planes
in solid materials.
