The Hydrogen Atom (Schrodinger vs original Bohr theory)

In summary, the quantities that appear in both the Schrodinger approach and the original Bohr theory of a hydrogen atom are the energy levels and angular momentum. However, the two approaches differ in that the Bohr model describes the electron as a particle in circular orbits around the nucleus, while the Schrodinger approach describes the electron as a wave and does not have definite radial values.
  • #1
aheizler
3
0
What quantities appear in both the Schrodinger approach and the original Bohr theory of a hydrogen atom?
Also, in what ways do the two approaches differ?

I'm not sure which quantities appear in both approaches. My guess would be that it has something to do with the energy levels and angular momentum, but I'm not sure. I'm also not sure how to show it.

I think a couple of ways they differ are as follows:
The original Bohr model suggests that the electron travels in a circular orbit around the nucleus, while the Schrodinger approach suggests that the electron travels in an elliptical orbit.
Another way they differ is that the Bohr model treats the electron as a particle orbiting the nucleus, while the Schrodinger model assumes the electron is a wave and tries to describe the regions in space, or orbitals.

Is any of this correct?

Thank you for any and all help.
 
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  • #2
The "energy levels", i.e. the quantum number, n, does appear in both both Bohr Theory and Schrodinger Theory.

When solving the hydrogen atom problem using the the Schrodinger equation, you assume the electron is described by a wavefunction.

The eigensolutions for the S.E.Q. do not have definite radial values, so it not correct to say that the Schrodinger approach assumes elliptical orbits.
 

Related to The Hydrogen Atom (Schrodinger vs original Bohr theory)

1. What is the difference between Schrodinger's and Bohr's theory of the Hydrogen Atom?

Schrodinger's theory of the Hydrogen Atom is based on quantum mechanics, while Bohr's theory is based on classical mechanics. Schrodinger's theory takes into account the wave-like behavior of particles, while Bohr's theory only considers the particle-like behavior. Additionally, Schrodinger's theory uses a mathematical equation to describe the behavior of electrons, while Bohr's theory uses a set of postulates.

2. Which theory is considered more accurate for describing the behavior of the Hydrogen Atom?

Schrodinger's theory is considered more accurate because it takes into account the wave-like behavior of particles and has been able to successfully predict the behavior of electrons in the Hydrogen Atom. It also has a more solid theoretical foundation, as it is based on mathematical equations rather than postulates.

3. How does Schrodinger's theory explain the energy levels of the Hydrogen Atom?

Schrodinger's theory explains the energy levels of the Hydrogen Atom by describing the electrons as standing waves. These standing waves have quantized energy levels, which correspond to the allowed energy levels in the Hydrogen Atom. The energy levels are determined by the solutions to the Schrodinger equation.

4. What is the significance of the Schrodinger equation in understanding the behavior of the Hydrogen Atom?

The Schrodinger equation is a fundamental equation in quantum mechanics and is used to describe the behavior of particles, including electrons in the Hydrogen Atom. It takes into account the wave-like behavior of particles and has been able to successfully predict the behavior of electrons in the Hydrogen Atom, making it an essential tool for understanding this system.

5. Can Schrodinger's theory be applied to other atoms besides Hydrogen?

Yes, Schrodinger's theory can be applied to other atoms besides Hydrogen. However, the equations become more complex as the number of electrons and energy levels increases, making it more challenging to solve. Additionally, other factors, such as electron-electron interactions, can also affect the behavior of atoms and must be taken into account. Nevertheless, Schrodinger's theory remains the basis for understanding the behavior of atoms and molecules in general.

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