Why the electron orbit is a integer multiple of De Broglie wavelength?

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SUMMARY

The discussion centers on the relationship between electron orbits and De Broglie wavelengths, emphasizing that electron paths must be integer multiples of the De Broglie wavelength for stable states. The traditional Bohr model is deemed inadequate, as modern quantum mechanics focuses on eigenstates derived from the Schrödinger equation rather than fixed orbits. The wave nature of electrons necessitates that their wave functions remain in phase around the nucleus to maintain stability.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly the Schrödinger equation.
  • Familiarity with De Broglie wavelength and its implications in wave-particle duality.
  • Knowledge of eigenstates and their significance in quantum systems.
  • Basic grasp of the limitations of the Bohr model in describing atomic structure.
NEXT STEPS
  • Study the Schrödinger equation and its solutions for hydrogen-like atoms.
  • Explore the concept of wave functions and their role in quantum mechanics.
  • Investigate the implications of wave-particle duality in electron behavior.
  • Review the limitations of the Bohr model and its historical context in atomic theory.
USEFUL FOR

Students of quantum mechanics, physicists exploring atomic theory, and educators seeking to clarify the relationship between wave functions and electron stability.

jaumzaum
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I cannot understand why the electron orbit should be an integer multiple of De Broglie wavelength. Why should the wave path "fit" the electron orbit for it to be stationary?
 
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When you say "electron path", and "orbit", I suspect you are thinking in thinking in terms of the Bohr atom, but the Bohr atom with an orbiting electron is no longer considered a good description. To solve the Schrödinger equation, we are looking for a stable electron state, or eigenstate. Orbits are not a part of this picture.
 

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