Magnetic Moments of Atoms/Ions

In summary, magnetic moments of atoms and their ions are the first term in the multipole expansion of a current distribution. This is because electrons move around the nucleus, creating a net current. The magnetic moment of a free atom has no effect on itself, but it does have an influence on the electronic states when interacting with external magnetic fields. This is known as the Zeeman effect. There are two types of multipole expansion: one for charge distribution and one for current distribution. The monopole term for magnetic expansion is always zero, making the dipole term the most important. Electric and magnetic dipole moments are different, but equivalent to charge and current dipoles, respectively. There are also other types of dipole moments, such
  • #1
Priyadarshini
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Hi! I recently learned about magnetic moments of atoms and their ions. I understand the formula and the calculations. However, what exactly IS a magnetic moment? What does the value in Bohr Magnetons give us? How does this value affect the properties of the atom/ion?
Thanks in advance!
 
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  • #2
Magnetic (dipole) moment is just the first term in the multipole expansion of a current distribution. In an atom, electron moves with some velocity around the nucleus, therefore there must be a net current associated with this movement. The magnetic moment of a free atom does nothing upon itself, however its influence to the electronic states begins to emerge when the atom interacts with external magnetic fields. See also "Zeeman effect".
 
  • #3
blue_leaf77 said:
Magnetic (dipole) moment is just the first term in the multipole expansion of a current distribution. In an atom, electron moves with some velocity around the nucleus, therefore there must be a net current associated with this movement. The magnetic moment of a free atom does nothing upon itself, however its influence to the electronic states begins to emerge when the atom interacts with external magnetic fields. See also "Zeeman effect".
What do you mean by "the multipole expansion of a current distribution"? Magnetic moments are the same as dipole moments? (excuse my ignorance, but I'm not exactly sure what dipole moments are... In covalent bonds due to electronegativity and electropositivity, the bonded atoms develop a charge. Dipole moments apply to these situations, right? But where and what exactly is the dipole moment?)
 
  • #4
This subject might be more of a physics subject rather than chemistry. First of all, it's important to realize that there are in general two groups of multipole expansion: multipole expansion of charge distribution and multipole expansion of current distribution. To go further you must go through the related chapter which I don't really recommend if you are only interested in the practical aspect of it. Anyway, I hope this link http://www.pas.rochester.edu/~dmw/phy217/Lectures/Lect_20b.pdf can give you a more graphical picture about multipole expansion for charge distribution, especially in the first slide bottom part where there are 4 different charge configuration. The left most one is the so-called monopole, as we go to the right: dipole, quadrupole, and octopole. They are just the first 4 of infinite number of expansion terms, however as we go to higher terms, the contribution to the expanded quantity (e.g. electric potential) will usually die down and we can simply take the first few terms.

The same goes for current distribution which will generate magnetic multipole expansion. Likewise there are also monopole, dipole, quadrupole terms and so on, however it had been shown that the monopole term for magnetic expansion is always zero, leaving the dipole term to be the most important term in the expansion.
Priyadarshini said:
Magnetic moments are the same as dipole moments?
As you see there are electric dipole moment and magnetic dipole moment, but sometimes the first word is dropped and is assumed to be known form the context being discussed.
Priyadarshini said:
In covalent bonds due to electronegativity and electropositivity, the bonded atoms develop a charge. Dipole moments apply to these situations, right?
The dipole moment mentioned in this context must be the electric dipole moment. But of course one can also calculate the magnetic dipole moment of an atom or molecule.
 
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  • #5
blue_leaf77 said:
This subject might be more of a physics subject rather than chemistry. First of all, it's important to realize that there are in general two groups of multipole expansion: multipole expansion of charge distribution and multipole expansion of current distribution. To go further you must go through the related chapter which I don't really recommend if you are only interested in the practical aspect of it. Anyway, I hope this link http://www.pas.rochester.edu/~dmw/phy217/Lectures/Lect_20b.pdf can give you a more graphical picture about multipole expansion for charge distribution, especially in the first slide bottom part where there are 4 different charge configuration. The left most one is the so-called monopole, as we go to the right: dipole, quadrupole, and octopole. They are just the first 4 of infinite number of expansion terms, however as we go to higher terms, the contribution to the expanded quantity (e.g. electric potential) will usually die down and we can simply take the first few terms.

The same goes for current distribution which will generate magnetic multipole expansion. Likewise there are also monopole, dipole, quadrupole terms and so on, however it had been shown that the monopole term for magnetic expansion is always zero, leaving the dipole term to be the most important term in the expansion.

As you see there are electric dipole moment and magnetic dipole moment, but sometimes the first word is dropped and is assumed to be known form the context being discussed.

The dipole moment mentioned in this context must be the electric dipole moment. But of course one can also calculate the magnetic dipole moment of an atom or molecule.
The maths on the pdf link you provided was a wee bit confusing (I haven't learned integration or limits yet :/ ) But I get the general idea about the differences between monopoles, dipoles, quadrupoles and octopoles. The pdf talks about just the multipole expansion of charge distribution only, right? Is the graphical idea of current distribution similar/the same? Also, electric dipole moments, magnetic dipole moments and charge dipole moments are all different, right? Besides charge, electric and magnetic, are there any other sorts of dipole moments?
 
  • #6
Priyadarshini said:
The pdf talks about just the multipole expansion of charge distribution only, right?
Yes it does.
Priyadarshini said:
Is the graphical idea of current distribution similar/the same?
Up to now I have never seen the graphical representation of different magnetic multipole expansion, I guess because it's too difficult to put it into drawing.
Priyadarshini said:
Also, electric dipole moments, magnetic dipole moments and charge dipole moments are all different, right?
The electric dipole is equivalent to the charge dipole, while magnetic dipole to the current dipole.
Priyadarshini said:
Besides charge, electric and magnetic, are there any other sorts of dipole moments?
Gravitational field due to arbitrary mass density can also be described by multipole expansion, I guess it's something you would call mass multipole expansion.
 
  • #7
blue_leaf77 said:
Yes it does.

Up to now I have never seen the graphical representation of different magnetic multipole expansion, I guess because it's too difficult to put it into drawing.

The electric dipole is equivalent to the charge dipole, while magnetic dipole to the current dipole.

Gravitational field due to arbitrary mass density can also be described by multipole expansion, I guess it's something you would call mass multipole expansion.
Thank you for your help! :)
 

1. What is a magnetic moment of an atom/ion?

A magnetic moment of an atom/ion refers to the measure of the strength and orientation of the magnetic field generated by the particle. It is a result of the spinning and orbital motion of electrons in an atom/ion.

2. How is the magnetic moment of an atom/ion determined?

The magnetic moment of an atom/ion can be determined through experimental measurements, such as spectroscopy, or through theoretical calculations using quantum mechanics and magnetic moment operators.

3. What factors affect the magnetic moment of an atom/ion?

The magnetic moment of an atom/ion is affected by the number of electrons, their spin and orbital angular momentum, the presence of a magnetic field, and the electronic structure of the atom/ion.

4. What are the units of magnetic moment?

The SI unit of magnetic moment is the ampere-meter squared (A⋅m²), but it is commonly expressed in Bohr magnetons (μB) or nuclear magnetons (μN) for atoms and ions.

5. How is the magnetic moment of an atom/ion used in research?

The magnetic moment of an atom/ion is an important property used in various fields of research, such as materials science, quantum mechanics, and nuclear physics. It can help determine the electronic structure of atoms/ions, study the magnetic properties of materials, and understand the behavior of particles in magnetic fields.

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