Bohr Model Postulates: Understand Discrete Angular Momentum Orbits

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In summary, Bohr did not come to the conclusion that only discrete angular momentum orbits are stable. He used known formulas to create a simple model of the electron orbiting the proton. De Broglie's analysis, based on wave mechanics and phase invariance, coincided with Bohr's model for hydrogen only. However, a full analysis of how wave mechanics restricts possible modes of radiation was not fully realized until David Bohm's book "Quantum Theory" was published. This book does not involve his variant of "Pilot Wave" theory.
  • #1
Bassalisk
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Hello,

I am interested if anybody knows, how did Bohr came to the conclusion that only discrete angular momentum orbits are stable? In other words,

m*v*r=n*h/(2*pi)

and how did de Broglie came to the same conclusion, just through another way 2*pi*r=n*h/(m*v)

Thanks
 
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Hi Bassalisk,

Bohr didn't come to that conclusion. He was already familiar with the various formulas for determining the ratios between the various discrete wavelengths or frequencies of emission of a hydrogen atom. He apparently intuitively recognized the pattern could likely be derived from a model of the electron orbiting the proton and set about creating the most simple model possible using energies (kinetic and potential) balanced in a standard classical model.

De Broglie's analysis is based on wave mechanics and phase invariance in any frame of reference. Numerically, it happened to coincide with Bohr's model (for hydrogen only) But a full analysis of how wave mechanics restricts the possible modes of radiation didn't really come until Bohm had studied and documented the situation ("Quantum Theory" -David Bohm) That particular book is general and doesn't involve his variant of "Pilot Wave" theory.
 
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  • #3
Thank you very much, you answer was very helpful!
 

What is the Bohr Model and what are its postulates?

The Bohr Model is a model of the atom proposed by Niels Bohr in 1913. It is based on the idea that electrons move in discrete orbits around the nucleus, and that each orbit has a specific energy level. The postulates of the Bohr Model are:

  • Electrons move in circular orbits around the nucleus.
  • Each orbit has a fixed energy level.
  • Electrons can only exist in certain orbits with specific energy levels.
  • Electrons can jump from one orbit to another by either absorbing or emitting energy.
  • The energy of an electron in an orbit is proportional to the distance from the nucleus.

What is the significance of discrete angular momentum orbits in the Bohr Model?

Discrete angular momentum orbits in the Bohr Model explain why electrons do not spiral into the nucleus. In classical physics, an electron moving in a circular orbit would continuously lose energy and spiral into the nucleus. However, in the Bohr Model, electrons are only allowed to exist in specific orbits with fixed energy levels, so they do not lose energy and spiral into the nucleus.

How does the Bohr Model explain the line spectra of atoms?

The Bohr Model explains the line spectra of atoms by stating that when an electron jumps from a higher energy level to a lower one, it emits a photon of light with a specific wavelength. This wavelength corresponds to the difference in energy between the two energy levels. As each element has a unique set of energy levels, each element also has a unique line spectrum.

What are the limitations of the Bohr Model?

The Bohr Model has several limitations. It only works for hydrogen and other single-electron systems, as it does not take into account the repulsion between multiple electrons. It also does not fully explain the shapes of atomic orbitals or the fine structure of spectral lines. Additionally, it is based on classical physics and does not account for the principles of quantum mechanics.

How does the Bohr Model compare to the modern understanding of atomic structure?

The Bohr Model was an important step in understanding atomic structure, but it has been replaced by the modern quantum mechanical model of the atom. The modern model takes into account the principles of quantum mechanics and explains atomic structure in terms of wave functions and electron probability distributions. It also accounts for the behavior of multiple electrons and accurately predicts the shapes of atomic orbitals and the fine structure of spectral lines.

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