Calculating Electron Magnetic Moment: Spin & Orbital Contributions

In summary, the total magnetic moment of an electron can be written as \mu = \gamma J. However, the g factor for S and L are different, so \mu will not be in the direction of J. The Lande g factor can be defined as g_J = g_L\frac{J(J+1)-S(S+1)+L(L+1)}{2J(J+1)}+g_S\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}, which is used in measuring the total angular momentum in a magnetic resonance experiment. This is different from the result \gamma = \gamma_{spin} + \gamma_{orbital} and
  • #1
andrewm
50
0
Say I know the total angular momentum of my electron as J. If I write the total magnetic moment as [tex] \mu = \gamma J [/tex] then does [tex] \gamma = \gamma_{spin} + \gamma_{orbital} [/tex] ?
 
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  • #2
yes, you have one contribution from orbital motion around nucleus and one from its intrinisc spin. The g-factors and so on of course differs so one has to be careful.
 
  • #3
andrewm said:
Say I know the total angular momentum of my electron as J. If I write the total magnetic moment as [tex] \mu = \gamma J [/tex] then does [tex] \gamma = \gamma_{spin} + \gamma_{orbital} [/tex] ?
No. Mu will not be in the direction of J, since the g factor for S and L are different.
For a single electron, [tex]{\vec\mu}=(-e/2mc)[{\vec L}+2{\vec S}][/tex].
This is the origin of the Lande g factor.
 
  • #4
clem said:
No. Mu will not be in the direction of J, since the g factor for S and L are different.
For a single electron, [tex]{\vec\mu}=(-e/2mc)[{\vec L}+2{\vec S}][/tex].
This is the origin of the Lande g factor.

My research suggests one can define a [tex]\mu[/tex] in the direction of J with a Lande factor

[tex] g_J= g_L\frac{J(J+1)-S(S+1)+L(L+1)}{2J(J+1)}+g_S\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)} [/tex]

if one is measuring the total angular momentum, say in a magnetic resonance experiment. But as clem said, [tex] \mu_J \neq \mu_S + \mu_L [/tex].
 
  • #5
Ok, maybe my answer was not careful enogh, what I meant with "yes" was not referring to your result [tex] \gamma = \gamma_{spin} + \gamma_{orbital} [/tex]

I didn't know at what level you was asking. Sorry
 
  • #6
Mu will not be in the direction of J for a single electron. The Lande g factor is for the
component of mu in the direction of J. It follows by dotting my formula for mu with J and doing some algebra, leading to Andrew's (and Lande's) formula.
 

1. What is an electron magnetic moment?

An electron magnetic moment is a measure of the strength and direction of the magnetic field produced by an electron. It is a fundamental property of electrons and is important in understanding their behavior and interactions with other particles.

2. What are the spin and orbital contributions to the electron magnetic moment?

The spin contribution to the electron magnetic moment is due to the intrinsic angular momentum of the electron, while the orbital contribution is due to the motion of the electron around the nucleus. Both of these contributions are necessary to fully describe the electron's magnetic moment.

3. How is the electron magnetic moment calculated?

The electron magnetic moment can be calculated using quantum mechanical equations that take into account the spin and orbital contributions. These equations involve the electron's mass, charge, and speed, as well as other physical constants.

4. How does the electron magnetic moment affect the behavior of electrons?

The electron magnetic moment plays a crucial role in determining the behavior of electrons in atoms and molecules. It affects the energy levels of electrons and their interactions with external magnetic fields.

5. Is the electron magnetic moment constant?

No, the electron magnetic moment can vary depending on the environment and external factors. For example, the electron's magnetic moment can change when it is in motion or when it is in the presence of a magnetic field.

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