Can we improve the Bohr model or is a new model needed for multi-electron atoms?

[MonsieurWise]

Could someone explain to me why the Bohr model was not able to explain the spectrum of multi-electrons atoms? I though we just need to add more stuff to it (more quantum numbers...). i tried and it gives me not so bad answer for Helium (neutral). At least without using the other quantum numbers I was able to calculate the ground-state energy of neutral Helium...It is wrong because it does not have the other quantum numbers...? Can we find a way to improve the Bohr model, or we have to totally make a new model?
Thank you!

 

[dx]

An improvement of Bohr's model is Sommerfeld's model (elliptical orbits etc.), both of which are of course obsolete as fundamental theories since we have quantum mechanics now.

 

[alxm]

Bohr's model was bad experimentally because it did not reproduce the fine or hyperfine structure of electron levels.
Bohr's model was bad theoretically because it didn't work for atoms with more than one electron, and relied entirely on an ad hoc assumption about having certain 'allowed' angular momenta.

Quantum mechanics has completely replaced Bohr's model, and is in principle exact for all atoms. While relying on sounder assumptions. It also explains a huge amount of other things. (like why Bohr's model was a good approximation)

 

[MonsieurWise]

So it's there any short experiment that I can show that the Bohr theory failed?

 

[MonsieurWise]

But his assumption based one the De Broglie wavelength does not seems really bad to me... So is his assumption also wrong?

 

[jtbell]

Bohr did not use de Broglie's wave hypothesis in developing his model. de Broglie came along several years later. By that time I think it was already pretty clear that the Bohr-Sommerfeld model had to be replaced with something better. de Broglie's idea did get people thinking along the lines that led to Schrödinger's quantum mechanics.

 

[MonsieurWise]

Oh...so how was Bohr able to pick the number for his quantized angular momentum L=n x (h bar)? Is there a reason he picked it up...?

 

[Redbelly98]

Oh...so how was Bohr able to pick the number for his quantized angular momentum L=n x (h bar)? Is there a reason he picked it up...?

I doubt he had any "justification" for it, other than it gave the correct answer.

Note that he was actually wrong about the angular momentum. We have L=0 for the n=1 state, where the Bohr model says L=hbar.

 

[MonsieurWise]

So the De Broglie wave hypothesis justification afterward was also wrong?

 

[Redbelly98]

I would say it is misapplied. If one calculates the de Broglie wavelength for an electron in a circular orbit, when in reality the electron is not in a circular orbit, the error is not with the de Broglie hypothesis.

 

[Count Iblis]

The integral of p dq over one period is supposed to be a multiple of Planck's constant. So, if you take q to be the angular variable, then the canonical momentum p is the angular momentum. This gives:

2 pi L = n h ---------->

L = n hbar

 

[epenguin]

:shy: Wasn't one early inadequacy relative to the Schrodinger theory which solved it, that the Bohr model got angular momentum, magnetic field and magnetic splitting of spectral lines wrong - or not quite right? that the lowest l=0 or s circular orbits should have had a magnetic field whereas in Schrodinger they don't?

In another thread I argued it was worth knowing and teaching something about the Bohr theory but was told it was better not to.

https://www.physicsforums.com/showthread.php?t=277593&highlight=Bohr&page=2&nojs=1#goto_share

 

[Count Iblis]

:shy: Wasn't one early inadequacy relative to the Schrodinger theory which solved it, that the Bohr model got angular momentum, magnetic field and magnetic splitting of spectral lines wrong - or not quite right? that the lowest l=0 or s circular orbits should have had a magnetic field whereas in Schrodinger they don't?

In another thread I argued it was worth knowing and teaching something about the Bohr theory but was told it was better not to.

https://www.physicsforums.com/showthread.php?t=277593&highlight=Bohr&page=2&nojs=1#goto_share

http://insti.physics.sunysb.edu/~siegel/history.html" for why that's a bad idea.

 

[MonsieurWise]

Thank you all!
So...does the 2nd quantum number l, the spin s, Hund's rules... are they counted as Bohr theory or counted as Quantum Mechanics...?

 

[alxm]

Thank you all!
So...does the 2nd quantum number l, the spin s, Hund's rules... are they counted as Bohr theory or counted as Quantum Mechanics...?

Well the second quantum number is angular momentum, so it represents a thing with a classical analogue.
But yes, it's all quantum mechanics.

(Of course, Bohr's model, as atoms were concerned, was 'the quantum theory' up until the Schrödinger equation. And then for a short while as 'the classical quantum theory' or 'the old quantum theory'. But nobody's used that terminology since the 1930's to avoid confusion)

 

[MonsieurWise]

Oh, thank you ^^

 

[ytuab]

To study about Bohr model (multi-electrons), first search using "Google"

For example, search by this phrase "bohr helium ground state energy"

(The two-electron atom Helium by Bohr model was "historically" very important).

 

[Dadface]

Reasons for teaching Bohr theory to school students:
1.Spicing up lessons ,for example by including a little bit of history,can make those lessons more memorable.
2.It is helpful and interesting for students to know that physics has been and is likely to continue to be a developing subject.A good example of this can be giving them a quick chronological review of the different atomic models that have existed ;solid atom, plum pudding atom, nuclear atom,Bohr atom.There is nothing wrong in doing the Bohr atom as long as students are made aware that we have gone beyond that.Some may be tempted to investigate further.
3.Only a tiny fraction of U.K. students opt to take A level and it is only these that might study the Bohr atom, depending on the syllabus that the school follows, so teaching the Bohr atom may be a syllabus requirement.Of this tiny fraction only a small fraction opt to take a degree in physics and I think university is the place to deal with more advanced atomic models.
4.The syllabus should appeal to and hopefully be useful to all students and not just the small minority who take the subject further.Some quantum theory should be included and in U.K. schools the topics usually covered are the Bohr atom,energy levels and spectra, with particular reference to the hydrogen atom,the wave nature of matter and the photoelectric effect.These are not covered in a lot of detail but are reasonable introductions to the subject.If the Bohr atom or any of the other topics was removed then what could replace it and be suitable for school level physics?
Do these,or any other reasons for outweigh the reasons against?

 

[ytuab]

Reasons for teaching Bohr theory to school students:
Do these,or any other reasons for outweigh the reasons against?

There were historically "two main problems" about Bohr-Sommerfeld model.

1. the two-electron atom Helium spectrum by Bohr model.
2. Anomalous Zeeman effect.

When three particles are interacted (for example, 1 sun + 2 planets), the particle's orbital doesn't become elliptical or circular. (its shape becomes complex.)
This is a well-known fact.

So if we treat three-particle's interaction (for example, 1 nucleus + 2 electrons),
we must use computers. (Of course when in 1920's Bohr.. tried Helium problems, there were no computers).

In Bohr model, there was no spin of an electron.
Anomalous Zeeamn effect is said to be caused by the spin of an electron.
One-electron atom hydrogen usually shows "Normal Zeeman effect"
(Sodium.. show anomalous Zeeman effect).
http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/zeeman.html#c4

So is it possible that the anomalous Zeeman effect is caused not by the spin?
(Is it possible that the effect is caused by the influence of the inner electrons?)

 

[ytuab]

Bohr's model was bad experimentally because it did not reproduce the fine or hyperfine structure of electron levels.
Bohr's model was bad theoretically because it didn't work for atoms with more than one electron, and relied entirely on an ad hoc assumption about having certain 'allowed' angular momenta.

Quantum mechanics has completely replaced Bohr's model, and is in principle exact for all atoms. While relying on sounder assumptions. It also explains a huge amount of other things. (like why Bohr's model was a good approximation)

alxm, the fine structure was first named by Sommerfeld, and it meant the relativistic effect(by the difference of the relativistic mass).
Later, the fine structure was replaced by the spin-orbital interaction.
But accidentally, these values coincided.

In the hydrogen atom, there are more coincidences when you consider the spin-orbital interactions.

In page 167 Atomic physics by Max Born
-------------------------------------------------------------------------
The case of hydrogen is peculiar in one respect. Experiment gives distinctly fewer terms than are specified in the term scheme of fig 9; for n=2 only two terms are found, for n=3 only three, and so on.
The theoretical calculation shows that here (by a mathematical coincidense, so to speak) two terms sometimes coincide, the reason beeing that the relativity and spin corrections partly compensate each other. It is found that terms with the same inner quantum number j but different azimuthal quantum numbers l always strictly coincide.
----------------------------------------------------------

In QM, the Dirac equation doesn't mean the probability amplitude, and the uncertainty principle(HUP) needs the probability density. This means HUP and the relativistic correction (by the Dirac Eq.) are inconsistent? I have not yet found the clear answer.

For multi-electron atoms, for example, the 3s electron of the Sodium D line comes close to the nucleus through the inner electrons.
But the Lande-g-factor does not contain the influence of the inner electrons at all. The delicate spin and orbital precession is so stable to stand the influence of the inner electrons? (See also this thread.)

About the nucleus,
also in the Bohr model, considering the nuclear mass and movement, if we use "the reduced mass" of an electron, the better results are obtained.

In QM, The orbital angular momentum of the S state electron is zero.
This means the electron is scattered or trapped by the nucleus each time it hits the nucleus? If so, can this keep the two electrons of Helium stable?
There are some experiments using the probability density of the electron at the nucleus ($$\mid\psi_{1s}(0)\mid^2 = 1 / \pi r_{0}^3$$). $$r_{0}$$ is the Bohr radius).
In the Bohr model, the similar value exists. The magnetic field at the nucleus created by the S state electron is proportional to $$1 / r_{0}^3$$.(The Story of Spin).

The spin has the strange property such as the "two-valued" rotation.
So you mean "What is real" is the strange thing which goes back to its original form by the 4pi rotaion (not 2pi)?

In QM, whether you measure or not,
the probability density of the hydrogen S state electron near the point at infinity is not zero. And this electron has the ground state nergy. But why can it have the ground state energy which sign is minus? (though the potential energy is almost zero near the point at infinity.)