Electron Wave in Bohr Model of Atom!! (Quantization)

Electron Wave Quantization in Bohr Model of Atom:
When we apply de Broglie Hypothesis to the (angular momentum) quantisation in a Bohr Atom, we find something very interesting..

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Video Contains:
1) Rutherford Model of Atom - After a series of scattering experiments, Rutherford proposed what is called- the planetary model of the atom. In this model the electrons revolve around the nucleus in circular orbits due to Coulombic force between electrons and positively charged nucleus.

2) Failures of Rutherford Model - The Rutherford model was unable to explain the stability of the electron orbit (Acc to classical Electrodynamics, a charged particle accelerating around a nucleus must loose energy in the form of EM radiation, and the it should spiral and fall into the nucleus ) AND the discrete absorption spectra (Since there is no restriction in the possible orbits, it suggests a continuous spectrum and not a discrete spectra as seen in experimental observations)

3) Bohr Model of Atom - Bohr suggested that to explain discrete absorption spectra, the electron orbits must be restricted. So he gave the quantization of electron orbit - L=nh/2*pie - he said if the electrons are in these specific orbits, they do not loose energy

4) de Broglie Hypothesis - De Broglie stated that if a particle is in motion, then there is a 'matter' wave associated with its motion, and the wavelength of such a wave is inversely proportional to its momentum

5) Hydrogen Atom - Ground State - when we apply the de broglie expression to the orbital velocity of the electron in the ground state of the hydrogen aton, we find that the wavelength of the corresponding matter wave is equal to the circumference of the orbit!! What is going on???

6) Electron Wave Quantization - When we look at the expression of quantization provided by Bohr, and apply the de Broglie hypothesis, we find the the quantisation rule takes a new form - Electrons are restricted to those orbits where the circumference is an integral multiple of the electron wavelengths. This explains why certain orbits are allowed and others are not. If the circumference is an integral multiple of electron wavelengths, then the electron wave forms stable circular standing wave patterns and due to constructive interference these waves never die out. However, in the case that the circmference is a fractional multiple of the electron wavelenghts, the circular standing wave patterns are not stable since as the wave travels on complete revolution, it joins itself at a point different from its earlier phase. This leads to destructive interference and the electron wave dies out.

Peace.

“ Truth is the offspring of silence and unbroken meditation. ”
— Isaac Newton

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