Are De-Broglie & Bohr's Stationary Orbits Different?

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In summary, de Broglie stationary orbits are similar to Bohr's stationary orbits in that only waves with an integral number of de Broglie wavelengths around the orbit are allowed. However, de Broglie's hypothesis was proposed in 1923, which is later than Bohr's theory in 1913. It was later confirmed by Davisson and Germer in the interference experiment in 1927. The de Broglie theory is also used in the Schrodinger equation. In the Bohr model, the angular momentum is quantized and the minimum value is h/2pi, resulting in an orbital length of lambda times 1. Only one electron is included in one orbit of one de Broglie wavelength
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roshan2004
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Are De-Broglie stationary orbits different from Bohr's stationar orbits? I really haven't been able to figure out.
 
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Only waves with an integral number of
de Broglie wavelengths around the orbit are allowed
 
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I see. They are equivalent to the Bohr's stationary orbits.
 
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roshan2004 said:
Are De-Broglie stationary orbits different from Bohr's stationar orbits? I really haven't been able to figure out.

The result is that they are the same.
But de Broglie's hypothesis was in 1923, which is later than the Bohr's theory in 1913.
And later in 1927 de Broglie's hypothesis ([tex]\lambda = h/mv[/tex]) was confirmed by Davisson and Germer in the interference experiment.
(Of course, the de Broglie's theory is used also by the Schroedinger equation in making the end of the phases the same.)

For example, In the Bohr model, the angular momentum is quantized. Its minimum value is [tex]\hbar[/tex]. So, the orbital length (2 pi *r) is,

[tex]mvr = \hbar = h/2\pi \quad \to \quad 2\pi r = h/mv = \lambda \times 1 [/tex]

Also in the elliptical orbit, it can be used (See this thread).

The important point is that in the Bohr-Sommerfeld model, only one electron is included in one orbit of one de Broglie's wavelength.
 
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Related to Are De-Broglie & Bohr's Stationary Orbits Different?

1. What are De-Broglie and Bohr's stationary orbits?

De-Broglie and Bohr's stationary orbits are concepts in quantum mechanics that describe the energy levels and corresponding orbits of electrons around an atomic nucleus. According to Bohr's model, electrons can only exist in specific, discrete energy levels, while De-Broglie's theory of wave-particle duality states that electrons exhibit both wave-like and particle-like behavior.

2. How do De-Broglie and Bohr's stationary orbits differ from each other?

While both theories describe the behavior of electrons in an atom, they differ in their fundamental assumptions. Bohr's model is based on classical mechanics and assumes that electrons move in circular orbits around the nucleus, while De-Broglie's theory incorporates the wave-like nature of particles and describes electrons as standing waves with specific energy levels. Additionally, De-Broglie's model allows for the possibility of electrons existing between energy levels, whereas Bohr's model does not.

3. Which theory is more accurate in describing the behavior of electrons in an atom?

Neither theory can fully explain the behavior of electrons in an atom on its own. Bohr's model provides a simplified understanding of atomic structure and is still used in introductory chemistry courses, but it does not take into account the wave-like nature of particles. De-Broglie's theory provides a more comprehensive understanding of the behavior of electrons, but it is often combined with other quantum mechanics principles to fully describe atomic structure.

4. How do De-Broglie and Bohr's stationary orbits relate to the modern understanding of atomic structure?

De-Broglie and Bohr's theories were important stepping stones in the development of quantum mechanics and our current understanding of atomic structure. While they were not entirely accurate, they laid the foundation for further research and discoveries, such as the Schrödinger equation which accurately describes the behavior of particles in an atom.

5. Are De-Broglie and Bohr's stationary orbits still relevant in modern science?

Yes, De-Broglie and Bohr's theories are still relevant in modern science as they provide a basis for understanding the behavior of particles in an atom. While they may not fully explain atomic structure, they are still used in introductory courses and are important in understanding the history and development of quantum mechanics.

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