Validate Bohr Radius: Challenges Creating Metallic Hydrogen

[HarryWertM]

Creating metallic hydrogen has proved more difficult than expected. One explanation would be that the Bohr radius of Hydrogen is smaller than expected. Is there any other evidence of an error in Bohr radius predictions?

 

[alxm]

One explanation would be that the Bohr radius of Hydrogen is smaller than expected.

Says who?

Is there any other evidence of an error in Bohr radius predictions?

What do you mean, 'Bohr radius predictions'? The Bohr radius isn't an experimental quantity in-itself, period.
It's defined to be \frac{\hbar}{m_e\,c\,\alpha}, which is the theoretical value of the maximum of the radial distribution function for the clamped-nucleus, non-relativistic Hydrogen atom. Not the real hydrogen atom.

Anyone who's predicting something in terms of the Bohr radius isn't likely to be implying anything about the Bohr radius itself.

 

[HarryWertM]

Says who? Says me. Metallic Hydrogen is expected to be produced by squeezing hydrogen under such high pressure that the nuclei are closer than the Bohr radius, leaving no space for normal electron orbits thereby forcing them into a kind of 'lattice fluid' - possibly exhibiting superconductivity.

If the Bohr radius is a 'theoretical value based on...[an idealized atom]...' my question is simply 'Is the theoretical basis of the Bohr radius validated/invalidated by other experiment?'

 

[alxm]

Says who? Says me. Metallic Hydrogen is expected to be produced by squeezing hydrogen under such high pressure that the nuclei are closer than the Bohr radius, leaving no space for normal electron orbits thereby forcing them into a kind of 'lattice fluid' - possibly exhibiting superconductivity.

That's a vague pop-sci description. What's a 'normal electron orbit'? Whenever you have two atoms near each other, their orbitals change. There is no magical discontinuity in properties at 53 pm.

Seems to me you read some popular-scientific account where they used the Bohr radius as a metric to underline the fact that it's a situation where the atoms are significantly closer than
ordinary chemical-bonding distance, and you then decided to interpret that as implying that the Bohr radius had some special significance here, and that the prediction was somehow dependent on the Bohr radius itself.

If the Bohr radius is a 'theoretical value based on...[an idealized atom]...' my question is simply 'Is the theoretical basis of the Bohr radius validated/invalidated by other experiment?'

The theoretical basis of the Bohr radius is quantum mechanics, which has been theoretically verified by tens of thousands of experiments. It's also the same theoretical basis for predicting the existence of metallic hydrogen in the first place.

 

[HarryWertM]

I now realize that ALXM's dismissive reply was mostly due to my badly framed question. What I SHOULD HAVE asked was:

Are there experiments besides the hunt for metallic hydrogen which challenge simple quantum theory such as the Bohr model?

I know there are experiments with Rydberg atoms which are atypical but in no way challenging to quantum theory. From pop-sci sources [Wikipedia; LLNL news] I have read the story of metallic Hydrogen experiments which is believed to involve electron paths drastically unlike the Bohr model. In addition to reporting the experimental results, these pop-sci sources also report the varying quantum mechanics theory predictions, which have gone from under 1 megabar, to 20 megabar, to 3 megabar, for the metallic hydrogen phase transition - presumably due to variations in quantum mechanics theory, inaccessible to math ignorami like myself.

Perhaps a better question: What would the experts among you cite as hard experimental evidence validating or challenging current quantum theory on hydrogen electron orbits? I don't even want hear about atoms more complex than hydrogen. I might add I wasted considerable time searching for modern experiments regarding diamagnetism for hydrogen and learned only that it may not be diamagnetic. A precise, modern measure of diamagnetism could clearly prove validating or challenging.

 

[ytuab]

Are there experiments besides the hunt for metallic hydrogen which challenge simple quantum theory such as the Bohr model?

I know there are experiments with Rydberg atoms which are atypical but in no way challenging to quantum theory. From pop-sci sources [Wikipedia; LLNL news] I have read the story of metallic Hydrogen experiments which is believed to involve electron paths drastically unlike the Bohr model.

HarryWertM, I don't know well about the metalic hydrogen.
But probably in the metalic hydrogen, other hydrogen nuclei are closer to one electron.
As a result, the potential energy of one electron is lower than the original value.
According to Virial theoreum, when the potential energy is lower, the kinetic energy becomes higher, in which
de Broglie's wavelength becomes shorter.
(Probably the repulsive forces between nuclei are coped with by the external pressure. )

The Bohr radius is gotten from only one nucleus atoms.
This is important.

In the Bohr's original thoeory ( in 1910's), they don't consider de Broglie's theory (=1923).
They only consider the quantization of the angular momentum. (The meanings of them are the same.)
But if you try to consider more than one nuclei acting on the electron, you can NOT calculate the de Broglie's wave
without computers.
(Analytic calculation in Bohr model is possible only in one-nucleus atom.)
Is it right ?

 

[jtbell]

Are there experiments besides the hunt for metallic hydrogen which challenge simple quantum theory such as the Bohr model?

We may have a mixup in terminology here. Most physicists understand "Bohr model" to mean circular electron orbits with fixed radius; the "Bohr-Sommerfeld model" allows for elliptical orbits. Both of these models have been dead for more than eighty years, except for historical-pedagogical purposes.

 

[HarryWertM]

Is there a name for the current, undead hydrogen atom model? Just "standard model"? Do the changes in predictions for metallic hydrogen correlate to major changes in theory? It seems impossible to construct any understanding of modern physics - from a historical view or whatever - without running into the near total dismission of non-mathematicians which seems to be the flavor of much of Wikipedia.

 

[alxm]

The current models of hydrogen are from quantum theory. The Bohr model is not quantum theory, it's a pre-quantum model that has historical relevance because it shared some features with actual quantum theory. The Bohr model is wrong. It's been known to be wrong since around 1920. It is not used for predicting anything anymore, and hardly ever was. Electrons in atoms do not have 'orbits' or 'paths'. The Bohr radius in the Bohr model does not have the significance in quantum theory that it has in the Bohr model. In the Bohr model, it is the radius at which the electron 'orbits' the atom in the ground state. In quantum theory, it is merely the radius at which the electron is most likely to be located, the maximum on http://www.chemistry.mcmaster.ca/esam/Chapter_3/fig3-5.jpg" .

If you want experimental verification, you have it in front of you. The solid-state physical theories that built the semiconductors in your computer is based on the same quantum models as the ones used for atoms and molecules, and which predict metallic hydrogen and predict the maximum of that curve to be approximately the semiclassical Bohr radius. If you want more than that, you can just go to the library and open any random issue of the Journal of Chemical Physics or any other atomic/molecular physics/physical chemistry journal, and find plenty of theoretical caluclations being compared to experimental values. In 80 years of doing that, there has not been a single significant discrepancy found. Every error has turned out to be due to experimental error, theoretical approximations or both. It's as well-tested as almost anything we know. As far as that goes for properties of atomic/molecular hydrogen, we're entirely within experimental limits.

So if you don't want a "dismissive" reply, you're going to have to show that you have some clue about the theory behind metallic hydrogen and the theory behind the Bohr radius before using "Says me." as an argument for why current experiments would be a "challenge" to the Bohr radius.

 

[HarryWertM]

Don't have any clues about anything except what pop media sez and the answers here. Don't have any chemistry or physics journals in local library. Pop media gave crude explanation stating that atoms in hydrogen metal were "closer than Bohr radius... " and therefore electrons forced into some sort of unusual "lattice gas" which might be superconducting. Also there have been dramatic changes in [somebody's] purely theoretical prediction of required pressure, making it hard to claim one single, unchanged theory has remained unchallenged last 40 years. Basically just asking you folks "What's going on?" [In re metallic hydrogen. Extremely interesting subject.]

 

[cgk]

Also there have been dramatic changes in [somebody's] purely theoretical prediction of required pressure, making it hard to claim one single, unchanged theory has remained unchallenged last 40 years.

You need to understand that the "theory" is not everything here. The equations behind quantum mechanics are hard to solve *in practice* (not in theory!), and require many approximations to be made. This may have lead to some poor approximations by some people, due to missing important contributions, or just some ballpark-estimates being proposed by others where people didn't even try to solve attempt the full problem in some way (this was very popular in physics some decades ago). Both of these issues have nothing to do with theory itself.

Knowing how in principle one could calculate something does not imply that one is able to actually do it.