Bohr's Radius: Is His Calculation Right?

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Discussion Overview

The discussion revolves around the validity of Bohr's calculation of the atomic radius, particularly in the context of the ground state of neutral Helium and singly ionized Lithium. Participants explore the implications of Bohr's model in relation to electron behavior and probability density in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the accuracy of Bohr's method for calculating the radius, noting that their results for Helium and Lithium were close to established data.
  • Another participant states that the Bohr radius is considered correct for Hydrogen and nearly correct for Helium, linking it to the radius of maximal electron density.
  • A participant emphasizes that electrons do not orbit in fixed paths but are described by wavefunctions, suggesting that Bohr's radius corresponds to the maximum probability density rather than a physical orbit.
  • One participant reports that while Bohr's radius aligns with the probability density for the ground state, it fails for higher energy states, indicating a limitation in Bohr's model.
  • Another participant raises a question about the relationship between the Bohr radius and the maximum probability density in excited states, particularly for s orbitals, expressing uncertainty about the outcome.
  • A participant mentions Mosley's law as potentially relevant to the calculations being discussed.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the applicability of Bohr's radius. While some find it useful for certain calculations, others challenge its validity, particularly for excited states, indicating that the discussion remains unresolved.

Contextual Notes

Participants note limitations in Bohr's model, particularly regarding the assumptions of circular orbits and the behavior of electrons in higher energy states. There is also mention of the dependence on definitions of radius and probability density.

MonsieurWise
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I know that the Bohr theory is like "Santa Claus" in Physics, but is his way of calculating radius right? Because I've made some calculations for ground state of neutral Helium and singly ionized Lithium using the Bohr's radius. What I did for Helium was to take the energy level of singly ionized Helium (negative sign) add the Coulomb repulsive energy between 2 electron (because Helium neutral has 2 electrons) in the same shell of Bohr radius. I did almost a similar thing to singly ionized Lithium. The ground state energy I've got was surprisingly close to NIST database.
So can I say Bohr was right at least at the radius of the s-orbital?
 
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The Bohr radius is considered 'correct' for Hydrogen, in that his radius corresponds to the radius of maximal electron density in quantum theory (which inspired Bohr's 'theory of equivalence' between (semi-)classical and quantum results). The Bohr radius is also very nearly correct (using that definition) for Helium.
 
Wow...this makes me so happy :D. I was surprised with such a random idea I've got. thank you ^^.
 
I think the point is there is no "radius" at which the electron "orbits". The electron doesn't really make circular orbits around the nucleus, there is only a wavefunction. But the Bohr's radius does correspond to the maximum of the probability density in a Hydrogen atom as alxm suggests (though not the expectation value). (IIRC)
 
yeah...base on my result, I would say that Bohr was right at least at the radius of the probability density in a Hydrogen atom, but for higher state of n, using the same approach, the Bohr radius failed miserably: adding the repulsion energy of 2 electrons to the Bohr's energy level, I got positive answer (when it supposed to be negative...). So I say electron in higher n does not travel in circular orbit, which mean the Bohr's assumption was wrong.
Does the Bohr radius have the same value with the maximum of the probability density in an excited atom, at least for the s orbital (the s because the wavefunction look kinda circular)? My guest is no, but I'm not that sure...
Thanks!
 
MonsieurWise said:
I know that the Bohr theory is like "Santa Claus" in Physics, but is his way of calculating radius right? Because I've made some calculations for ground state of neutral Helium and singly ionized Lithium using the Bohr's radius. What I did for Helium was to take the energy level of singly ionized Helium (negative sign) add the Coulomb repulsive energy between 2 electron (because Helium neutral has 2 electrons) in the same shell of Bohr radius. I did almost a similar thing to singly ionized Lithium. The ground state energy I've got was surprisingly close to NIST database.
So can I say Bohr was right at least at the radius of the s-orbital?

For this type of calculation, Mosley's law may be of interest to you.
 
Oh...thanks!
 

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