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Magnetic moment of an atom formula

The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current such as electromagnetspermanent magnets, moving elementary particles such as electronsvarious moleculesand many astronomical objects such as many planetssome moonsstarsetc.

More precisely, the term magnetic moment normally refers to a system's magnetic dipole momentthe component of the magnetic moment that can be represented by an equivalent magnetic dipole : a magnetic north and south pole separated by a very small distance. The magnetic dipole component is sufficient for small enough magnets or for large enough distances. Higher-order terms such as the magnetic quadrupole moment may be needed in addition to the dipole moment for extended objects.

The magnetic dipole moment of an object is readily defined in terms of the torque that object experiences in a given magnetic field.

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The same applied magnetic field creates larger torques on objects with larger magnetic moments. The strength and direction of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. The magnetic moment may be considered, therefore, to be a vector. The direction of the magnetic moment points from the south to north pole of the magnet inside the magnet.

The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object. The magnetic moment can be defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by: [1]. This definition is based on how one could, in principle, measure the magnetic moment of an unknown sample.

For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the calculation of the expected magnetic moment for any known macroscopic current distribution. An alternative definition is useful for thermodynamics calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy, U intwith respect to external magnetic field:.

Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is essentially the eigenenergy of the 2p state, which includes Coulomb potential energy and the kinetic energy of the electron.

The interaction-field energy between the internal dipoles and external fields is not part of this internal energy. This unit has equivalents in other SI derived units including: [3] [4].

Among these, there are two alternative non-equivalent units of magnetic dipole moment:. All formulae in this article are correct in SI units; they may need to be changed for use in other unit systems. Other units for measuring the magnetic dipole moment include the Bohr magneton and the nuclear magneton.

The magnetic moments of objects are typically measured with devices called magnetometersthough not all magnetometers measure magnetic moment: Some are configured to measure magnetic field instead. If the magnetic field surrounding an object is known well enough, though, then the magnetic moment can be calculated from that magnetic field.

The magnetic moment is a quantity that describes the magnetic strength of an entire object. Sometimes, though, it is useful or necessary to know how much of the net magnetic moment of the object is produced by a particular portion of that magnet.

This equation is often represented using derivative notation such that. The magnetization is often not listed as a material parameter for commercially available ferromagnetic materials, though.

The preferred classical explanation of a magnetic moment has changed over time. Before the s, textbooks explained the moment using hypothetical magnetic point charges. The sources of magnetic moments in materials can be represented by poles in analogy to electrostatics.Hot Threads. Featured Threads. Log in Register. Search titles only. Search Advanced search…. Log in. Contact us. Close Menu.

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magnetic moment of an atom formula

Magnetic moment of an atom. I Thread starter Malamala Start date Sep 13, I want to make sure I understand mainly qualitatively what happens to an atom in a magnetic field. Assume we have an atom with an even number of protons and electrons. This means that all proton electrons are paired up, except for one of them I am not totally sure if this pairing is always the case, especially for mid-shell nuclei, but let's assume this for now.

Ignoring higher order effects, in a magnetic field these 2 magnetic moment would interact with the magnetic field and assuming we have very low temperature, they would align or anti align with the magnetic field. Is this it, or does something else happens in terms of the behavior of the 2 magnetic moments? Can I treat them separately i. Related Quantum Physics News on Phys. Charles Link Homework Helper.

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Atomic Structure - Ions

Besides aligning with the applied magnetic field, an additional effect with the nuclear spins is that energy splittings occur, e. These magnetic resonance effects have been studied in great detail, and are used in magnetic resonant imaging. Charles Link said:. Malamala said:. Thank you for this! So shouldn't the exactly same effect exist for the electron energy splitting between the 2 different states?

So overall there would be a 4 level splitting of the whole atom 2 from nucleus times 2 from electron? Last edited: Sep 13, DrClaude Mentor. Usually, the nuclear and electronic angular momenta do not align independently with the external field. One has to consider the total angular momentum F. DrClaude said:. There are nuclear magnetic resonance experiments where they first get the nuclear spins to align with a static magnetic field in the z direction, and then by applying a transverse r-f magnetic field at the resonant frequency, the nuclear spins can be made to change their direction in unison.

Last edited: Sep 14, So you mean that it is the overall atomic magnetic moment that aligns with the magnetic field? Is this because of coupling between the magnetic moments of the nucleus and electrons?

It can be the case that the atomic moment is aligned but the 2 individual moment of nucleus and electron are not?In the study of magnetism, we saw that a current-carrying wire produces magnetic fields.

It is therefore reasonable to conclude that the hydrogen atom produces a magnetic field and interacts with other magnetic fields. The orbital magnetic dipole moment is a measure of the strength of the magnetic field produced by the orbital angular momentum of an electron.

From Force and Torque on a Current Loopthe magnitude of the orbital magnetic dipole moment for a current loop is. For brevity, we refer to this as the magnetic moment. If we assume that the electron travels in a perfectly circular orbit, the orbital period is. Thus, the magnitude of the orbital angular momentum is. The negative sign appears because the electron has a negative charge. Quantization of the magnetic moment is the result of quantization of the orbital angular momentum.

As we will see in the next section, the total magnetic dipole moment of the hydrogen atom is due to both the orbital motion of the electron and its intrinsic spin. For now, we ignore the effect of electron spin. Assume that the spin of the electron is zero. The magnetic momentum of the electron is related to its orbital angular momentum L. For the hydrogen atom, this quantity is related to the orbital angular quantum number l.

The states are given in spectroscopic notation, which relates a letter spdetc. In the s state, there is no orbital angular momentum and therefore no magnetic moment. This does not mean that the electron is at rest, just that the overall motion of the electron does not produce a magnetic field. In the p state, the electron has a magnetic moment with three possible values for the z -component of this magnetic moment; this means that magnetic moment can point in three different polar directions—each antiparallel to the orbital angular momentum vector.

In the d state, the electron has a magnetic moment with five possible values for the z -component of this magnetic moment. In this case, the magnetic moment can point in five different polar directions. A hydrogen atom has a magnetic field, so we expect the hydrogen atom to interact with an external magnetic field—such as the push and pull between two bar magnets. This torque acts to rotate the magnetic moment vector of the hydrogen atom to align with the external magnetic field.

Because mechanical work is done by the external magnetic field on the hydrogen atom, we can talk about energy transformations in the atom. If the magnetic moment is antiparallel to the external magnetic field, the potential energy is large, but if the magnetic moment is parallel to the field, the potential energy is small.

The energy of the system is conserved, however, because a drop in potential energy produces radiation the emission of a photon. These energy transitions are quantized because the magnetic moment can point in only certain directions. If the external magnetic field points in the positive z -direction, the potential energy associated with the orbital magnetic dipole moment is. The splitting of energy levels by an external magnetic field is called the Zeeman effect.

The separation of these lines is proportional to the strength of the external magnetic field. This effect has many applications. Samuel J. Learning Objectives By the end of this section, you will be able to: Explain why the hydrogen atom has magnetic properties Explain why the energy levels of a hydrogen atom associated with orbital angular momentum are split by an external magnetic field Use quantum numbers to calculate the magnitude and direction of the orbital magnetic dipole moment of a hydrogen atom.

Strategy The magnetic momentum of the electron is related to its orbital angular momentum L. Contributors and Attributions Samuel J.Magnetic moments are often used in conjunction with electronic spectra to gain information about the oxidation number and stereochemistry of the central metal ion in coordination complexes. A common laboratory procedure for the determination of the magnetic moment for a complex is the Gouy method which involves weighing a sample of the complex in the presence and absence of a magnetic field and observing the difference in weight.

A template is provided for the calculations involved. For first row transition metal ions in the free ion state, i. A simple crystal field theory approach to the bonding in these ions assumes that when they form octahedral complexes, the energy of the d orbitals are no longer degenerate but are split such that two orbitals, the d x2-y2 and the d z2 e g subset are at higher energy than the d xyd xzd yz orbitals the t 2g subset. Tetrahedral complexes are ALL high spin since the difference between the 2 subsets of energies of the orbitals is much smaller than is found in octahedral complexes.

Square planar complexes are less common than tetrahedral and d 8 e. Robert J. Contributors and Attributions Prof.In atomic physicsthe electron magnetic momentor more specifically the electron magnetic dipole momentis the magnetic moment of an electron caused by its intrinsic properties of spin and electric charge.

The electron magnetic moment has been measured to an accuracy of 7. Its angular momentum comes from two types of rotation: spin and orbital motion. From classical electrodynamicsa rotating electrically charged body creates a magnetic dipole with magnetic poles of equal magnitude but opposite polarity.

This analogy does hold, since an electron indeed behaves like a tiny bar magnet. One consequence is that an external magnetic field exerts a torque on the electron magnetic moment depending on its orientation with respect to the field.

8.3: Orbital Magnetic Dipole Moment of the Electron

Note that the angular momentum L in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. It turns out that the classical result is off by a proportional factor for the spin magnetic moment. As a result, the classical result is corrected by multiplying it with a dimensionless correction factor gknown as the g -factor :.

Classical notions such as the center of charge and mass are, however, hard to make precise for a quantum elementary particle. The spin magnetic moment is intrinsic for an electron. Here S is the electron spin angular momentum. The magnetic moment of an electron is approximately twice what it should be in classical mechanics. The factor of two implies that the electron appears to be twice as effective in producing a magnetic moment as the corresponding classical charged body.

The z component of the electron magnetic moment is. For the electron spin, the most accurate value for the spin g -factor has been experimentally determined to have the value. Note that it is only two thousandths larger than the value from the Dirac equation. The small correction is known as the anomalous magnetic dipole moment of the electron; it arises from the electron's interaction with virtual photons in quantum electrodynamics.

In fact, one famous triumph of the quantum electrodynamics theory is the accurate prediction of the electron g-factor. The most accurate value for the electron magnetic moment is. The revolution of an electron around an axis through another object, such as the nucleus, gives rise to the orbital magnetic dipole moment.

Magnetic moment of an atom

Suppose that the angular momentum for the orbital motion is L. Then the orbital magnetic dipole moment is. The value of g L is exactly equal to one, by a quantum-mechanical argument analogous to the derivation of the classical gyromagnetic ratio. The total magnetic dipole moment resulting from both spin and orbital angular momenta of an electron is related to the total angular momentum J by a similar equation:.

The necessity of introducing half-integral spin goes back experimentally to the results of the Stern—Gerlach experiment. A beam of atoms is run through a strong non-uniform magnetic field, which then splits into N parts depending on the intrinsic angular momentum of the atoms.Amazon Appstore Return Policy There's a problem loading this menu right now.

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magnetic moment of an atom formula

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