- #1

Frigorifico9

- 21

- 9

- TL;DR Summary
- Can the electron g factor be understood as electrons having roughly twice as much momentum as the Bohr Mageton?

I'm trying to make sure I understand the g-factor of the electron, so if my question is flawed please don't just point out my flaws, but help me correct my understanding

If I understand correctly the magnetic moment of an object depends on it charge, its mass and its momentum

$$

\mu = \frac{q}{2m} L

$$

Now, given that charge and angular momentum are quantized, you'd think the smallest magnetic moment would correspond to the smallest charge and the smallest momentum it is possible to have, this is Bohr's magneton

$$

\mu = \frac{e}{2m_e} \hbar

$$

But then it turns out electrons in the hydrogen atom have twice that much magnetic moment, and (this is the part where I think I may be wrong) this is due to the fact that electrons have $\hbar$ momentum around the nucleus AND $\hbar$ intrinsic momentum (spin)

$$

\mu = \frac{e}{2m_e} (\hbar+\hbar)=\frac{e}{m_e} \hbar

$$

So it makes sense it would be twice as much... But of course it then turns out they have slightly more than that because of self interactions in QED and this is still an active area of research

Did I say everything right? Could you correct me on my misunderstandings?

If I understand correctly the magnetic moment of an object depends on it charge, its mass and its momentum

$$

\mu = \frac{q}{2m} L

$$

Now, given that charge and angular momentum are quantized, you'd think the smallest magnetic moment would correspond to the smallest charge and the smallest momentum it is possible to have, this is Bohr's magneton

$$

\mu = \frac{e}{2m_e} \hbar

$$

But then it turns out electrons in the hydrogen atom have twice that much magnetic moment, and (this is the part where I think I may be wrong) this is due to the fact that electrons have $\hbar$ momentum around the nucleus AND $\hbar$ intrinsic momentum (spin)

$$

\mu = \frac{e}{2m_e} (\hbar+\hbar)=\frac{e}{m_e} \hbar

$$

So it makes sense it would be twice as much... But of course it then turns out they have slightly more than that because of self interactions in QED and this is still an active area of research

Did I say everything right? Could you correct me on my misunderstandings?