Is there magnetic moment of hydrogen atom that is 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?
 

[joigus]

Yes. A classic one:

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

Bohr's magneton is the magnetic moment due to orbital motion. That's all it is. The magnetic moment of the electron's spin is expected to be about that when looking at Dirac's equation as if it were a one-particle equation, but it happens to be different. The difference is due to radiative corrections (contributions of virtual particles.) This displaces the values of all physical constants from their quasi-classical value (often called "tree level") to a different value.

13 hours ago, computer said:

Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts.

I'm not sure what you mean, but the g-factor or gyromagnetic ratio (a factor that essentially tells you how much it deviates from a Bohr magneton) of nuclei is all over the place:

https://en.wikipedia.org/wiki/Nuclear_magnetic_moment#g-factors

Because nuclei are composite objects, I'm sure a lot of the variation has to do with nucleon-nucleon interactions calculable in approximate models, even before you get to radiative corrections.

Elementary particles have considerable variance in their magnetic moments too:

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

 

[swansont]

47 minutes ago, joigus said:

Elementary particles have considerable variance in their magnetic moments too:

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

I like how they say “the magnetic moment, often measured in Bohr magnetons or nuclear magnetons” and then proceed to not do that, LOL

[joigus]

14 minutes ago, swansont said:

I like how they say “the magnetic moment, often measured in Bohr magnetons or nuclear magnetons” and then proceed to not do that, LOL

🤣🤣🤣 Well, they say "often." So often but not here. They want to keep their readers on their toes.

[computer]

7 hours ago, joigus said:

Bohr's magneton is the magnetic moment due to orbital motion.

I suspect an electron in a hydrogen atom doesn't make any "orbital" motions. Just electron's own magnetic moment is statically smeared over probability cloud during chaotic throwing, like its electric charge. But if in excited states, that differ from the ground one, much greater moments are experimentally detected, then my assumption is incorrect.

[joigus]

On 10/17/2022 at 7:25 AM, computer said:

I suspect an electron in a hydrogen atom doesn't make any "orbital" motions. Just electron's own magnetic moment is statically smeared over probability cloud during chaotic throwing, like its electric charge. But if in excited states, that differ from the ground one, much greater moments are experimentally detected, then my assumption is incorrect.

Any conserved quantities are just conserved quantities. After you find out they're conserved, you can look upon these quantities as defined by local densities for them: local density of energy, angular momentum, and so on. But once you mathematically integrate over all values of space, they're just what we call a quantum number. The quantum number is neither here, nor there, but an overall property of the state.

Same goes for non-conserved quantities that are nevertheless defined by local densities. Example: expected value of position. Only, we don't call them quantum numbers.

 

[computer]

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?
 

[swansont]

6 hours ago, computer said:

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?
 

I would recommend finding the papers on how the proton’s or antiproton’s magnetic moment was measured. (a proton being a “hydrogen-like” ion) Then you won’t have to imagine.

There are no 2s or 2p states if it’s ionized.

[computer]

14 hours ago, swansont said:

There are no 2s or 2p states if it’s ionized.

After ionization of helium neutral atom. It might be simpler from technical viewpoint than creation of monoatomic hydrogen.

Edited October 22, 2022 by computer

[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 an 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.

[Louloukaformula]

Is magnetic moment and Bohr magneton same?

 

 

The quantity that multiplies with n is constant and is known as the Bohr Magneton µ_B. The Bohr Magneton is used very widely to express magnetic moments at the atomic scale.
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Watch the video to learn more about magnetic lines and its properties.

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Edited November 10, 2022 by Louloukaformula