Is the magnetic moment of a hydrogen atom not equal to Bohr's magneton?

[computer]

Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of Stern and Gerlach, it seems that only moment of one magneton was detected, I could not find other information. But maybe I'm wrong and didn't search well?
For single-electron ions, I would also like to get acquainted with the data of experiments, for example, for He+.
There is a lot of information on nuclei on the Internet, but somehow there is no information on hydrogen-like ions.

 

[DrClaude]

Not sure this is what you are after, but Rydberg states have high magnetic moments, see e.g. https://arxiv.org/abs/1702.05556v2

 

[vanhees71]

Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of Stern and Gerlach, it seems that only moment of one magneton was detected, I could not find other information. But maybe I'm wrong and didn't search well?
For single-electron ions, I would also like to get acquainted with the data of experiments, for example, for He+.
There is a lot of information on nuclei on the Internet, but somehow there is no information on hydrogen-like ions.

In the SGE you meausure the magnetic moment of silver atoms which is given by the magnetic moment of its valence electron (as long as you don't need to consider excited states of the silver atoms). The magnetic moment of the electron is to a good approximation one Bohr magneton, corresponding to a Lande/gyro factor of 2. Taking into account higher-order corrections of the Standard model you get some deviation from this "tree-level value" of $g=2$. It's among the best understood fundamental quantities of physics, i.e., the prediction from theory and the findings from experiments coincide very accurately with the theoretical predictions. This precision cannot be reached with a standard SGE, of course, but by similar variants of it, e.g., by keeping a single electron in a Penning trap.

 

[computer]

Not sure this is what you are after, but Rydberg states have high magnetic moments, see e.g.

It is interesting information. Of course, cautious approach is required, because Rydberg states can be associated with whole electron cloud circular motion around a nucleus.

 

[computer]

It's among the best understood fundamental quantities of physics, i.e., the prediction from theory and the findings from experiments coincide very accurately with the theoretical predictions. This precision cannot be reached with a standard SGE

I have no doubts that own magnetic moment of a single electron is equal to the Bohr's magneton. I suspect an electron in a "cloud" has no "orbital" motion, like planets are moving around the Sun. Motions are completely chaotic, with abrupt changes of direction and velocity. So, magnetic moment of entire cloud will be equal to own moment of electron. Except Rydberg states, maybe. But experimental confirmation would come in handy.

 

[PeterDonis]

I suspect an electron in a "cloud" has no "orbital" motion, like planets are moving around the Sun.

Correct.

Motions are completely chaotic, with abrupt changes of direction and velocity.

Not correct. The correct statement is that the concept of "orbital motion" is a classical concept and does not apply to electrons in atoms at all. Those electrons are in quantum states that do not correspond to anything classical.

 

[computer]

Those electrons are in quantum states

What is "quantum state" depends on interpretation of QM. There are 10 or more different interpretations. I prefer Hartree-Fock explanation of QM: statistical approach, separate wavefunction for each electron, physical reality of cloud and independence from observer.

 

[computer]

It seems to be a quite simple experiment, whether there is a difference between magnetic moments e.g. in the 2s and 2p states of an electron cloud of hydrogen or helium atom. But for some reason there is no such experimental data.

 

[PeterDonis]

What is "quantum state" depends on interpretation of QM.

No, it doesn't. "Quantum state" is just a shorthand for the actual mathematical representation, and that is the same (more precisely, equivalent) for all interpretations.

I prefer Hartree-Fock explanation of QM

Can you give a reference?

 

[vanhees71]

In standard QT a system of $n$ electrons in non-relativistic QM is described (in the position representation) by a wave function $\psi(\vec{x}_1,\sigma_1;\vec{x}_2,\sigma_2;\ldots;\vec{x}_n,\sigma_n)$, where $\vec{x}_j$ are position vectors and $\sigma_j$ the spin component in quantization direction (usually one chooses the $z$-direction). Since electrons are fermions, the wave function is antisymmetric under exchange of any two configuration-variable arguments $(\vec{x}_j,\sigma_j)$ and $(\vec{x}_k,\sigma_k)$.

If the system of electrons is prepared in a (pure) state described by such a wave function, $|\psi(\vec{x}_1,\sigma_1;\ldots;\vec{x}_n,\sigma_n)|^2 \mathrm{d}^3 x_1 \cdots \mathrm{d}^3 x_n$ is the probability to find the electrons at positions $\vec{x}_1,\ldots,\vec{x}_n$ with spin components $\sigma_1,\ldots,\sigma_n$.

 

[computer]

Can you give a reference?

Some information is here:
https://en.wikipedia.org/wiki/Hartree–Fock_method

 

[PeterDonis]

Some information is here:
https://en.wikipedia.org/wiki/Hartree–Fock_method

This describes the Hartree-Fock method of making numerical predictions for things like energy levels. It is not a QM interpretation or an "explanation" of anything; it's just a method of making approximate calculations for cases where the equations cannot be solved exactly.

 

[computer]

It is problematic to acquaint you in more detail with the works of Fock, since they are written in Russian language. I will try to translate from here:
https://ru.wikipedia.org/wiki/Интер...и,выдвинута В. А. Фоком и А. Д. Александровым.

 

[PeterDonis]

the works of Fock

If there are works of Fock where he made claims about quantum states being somehow different from the ones in the math of standard QM, I would be very surprised. Fock knew perfectly well that methods like Hartree-Fock were approximations for doing mathematical calculations, not claims about "reality".

If there are works of Fock where he made claims about QM interpretations or the "reality" of quantum states, independent of any mathematical calculation method, those would be off topic in this thread. Discussion of such things belongs in the QM interpretations forum, not here.

 

[computer]

Fock's interpretation is the interpretation of quantum mechanics in terms of the concept of the reality of quantum states of a microobject. It was nominated by V. A. Fok and A. D. Alexandrov. He asserts that the wave function of each microobject is an objective characteristic of its real state in the external conditions determined in the classical way. It determines the probabilities of the appearance of various results of the interaction of a given microobject with other objects. With repeated repetition of certain external conditions, the probabilities of the results of interaction with other objects manifest themselves in the form of a certain frequency of occurrence of results. These frequencies make it possible to carry out a statistical interpretation of the wave function.

It is from page I mentioned above.

 

[PeterDonis]

What is "quantum state" depends on interpretation of QM.

Fock's interpretation

Please see my post #14. Discussion of interpretations of QM is off topic in this forum; it belongs in a separate thread in the QM interpretations subforum.

The statement I originally made that you objected to about the quantum states of electrons in atoms was a statement about the math of standard QM, independent of any interpretation. Hartree-Fock, as mathematics, is, as I said, just a way of making approximate calculations consistent with the math of standard QM, in cases where we cannot solve the equations exactly.

 

[vanhees71]

If there are works of Fock where he made claims about quantum states being somehow different from the ones in the math of standard QM, I would be very surprised. Fock knew perfectly well that methods like Hartree-Fock were approximations for doing mathematical calculations, not claims about "reality".

If there are works of Fock where he made claims about QM interpretations or the "reality" of quantum states, independent of any mathematical calculation method, those would be off topic in this thread. Discussion of such things belongs in the QM interpretations forum, not here.

Well, concerning "interpretations of quantum mechanics" Fock had to do some work to ensure that he and his colleagues could work on the subject without getting into political trouble. An "interesting" source about the results of his and other physicists' efforts in this direction can be found in the textbook by Blokthintsev

 

[computer]

is off topic in this forum

You are right. The topic initially was about experiments. I can hardly imagine what experiments can confirm the presence of magnetic moments in hydrogen-like ions. It is probably necessary to maintain a certain concentration of monatomic hydrogen or ionized helium with the help of radiation, taking as a basis diatomic gas or neutral helium atoms. Then to maintain a stable concentration of excited states, again with radiation, for example, 2s or 2p, to measure magnetic moment and compare with obtained without action of radiation?

 

[PeterDonis]

I can hardly imagine what experiments can confirm the presence of magnetic moments in hydrogen-like ions.

The Penning trap experiments referred to by @vanhees71 in post #3 might be a good place to look.

 

[computer]

Wherever the practical use of the magnetic moments of atoms is carried out, only the electrons own spins appear. For example, Wikipedia gives the following rule for calculating the moments of transition metals with a large number of unpaired electrons.

Many transition metal complexes are magnetic. The spin-only formula is a good first approximation for high-spin complexes of first-row transition metals. Number of unpaired electrons, Spin-only moment (μB)
1 1.73
2 2.83
3 3.87
4 4.90
5 5.92

The relationship is almost linear, although it is obvious that electrons occupy d-orbitals with different "magnetic numbers" M at the same L and N. The type of electron cloud does not affect magnetic phenomena, at least at relatively large distances from the atom. It seems that the images of electrons spinning around a nucleus in books for schoolchildren and students are fiction and are of purely historical interest. Except for "Rydberg atoms," where an entire electron cloud can make coordinated movements. Which is not surprising, since the solutions of the Schrödinger or Pauli equations give the probabilities of finding an electron, respectively, the distribution of charge density and proper magnetic moment (spin),
but do not indicate the prevailing direction of velocity at that point. Consequently, the movements are either completely chaotic, with equal probability in either direction, or mutually compensated so that no resulting magnetic moment is formed. For example, if the prevailing direction of velocity coincides with the gradient of the wave function or its square, and since the vector potential would be directed so, and the magnetic field represents its curl, and the curl of any gradient is zero.

 

[PeterDonis]

Wikipedia gives the following rule

Please provide a link.

 

[computer]

https://en.wikipedia.org/wiki/Magnetic_moment

 

[PeterDonis]

Wherever the practical use of the magnetic moments of atoms is carried out, only the electrons own spins appear.

The Wikipedia article you linked to contradicts this, since it notes that the H2 molecule exhibits nuclear magnetism.

the solutions of the Schrödinger or Pauli equations give the probabilities of finding an electron,

As as function of position, yes.

respectively, the distribution of charge density and proper magnetic moment (spin),

I'm not sure what you're referring to here, but I suspect it is to outdated ideas about what wave functions represent. They do not represent "distribution of charge density and proper magnetic moment". That interpretation was abandoned in the 1920s.

but do not indicate the prevailing direction of velocity at that point

That's because the solutions you refer to are in the position representation. You could also write solutions in the momentum representation, and for many purposes that is indeed done. It just isn't usually done for atoms.

Note, though, that I said momentum, not velocity. There is no "velocity representation" because the complementary observable to position is momentum, not velocity. In the bound states that electrons occupy in atoms, neither of these observables, position or momentum, have definite values. The best you can do is describe the spatial distribution of the position wave function, or the momentum space distribution of the momentum wave function.

the movements are either completely chaotic, with equal probability in either direction, or mutually compensated so that no resulting magnetic moment is formed

For electrons in atoms, there are no "motions" of the kind you keep making claims about. There is no point in continuing this discussion if you continue to assert the same wrong statements that you did at the start.

Thread closed.