(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I was looking the calculation of Landé g factor. It starts with

[tex]\mu=-\frac{e}{2m_{e}} (\vec{L}+2\vec{S})[/tex] assuming that g of electron =2

The lecture notes then proceed by calculating [tex]g=1+\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}[/tex] using the cosine rule.

2. Relevant equations

the second equation is

[tex]\mu=-\frac{e}{2m_{e}} (\vec{J}+\vec{S}) [/tex] using [tex]\vec{L}=\vec{J}-\vec{S}[/tex]

which is, i think, just applying the third hund's rule J=L+S

However, the third Hund's rule also states that for less than half filled

[tex]J=\left|L-S\right|[/tex]

This then does not give the well known solution posted above. What am i doing wrong? The rest of the calculation is perfectly clear to me, I just don't get the step from

[tex]\mu=-\frac{e}{2m_{e}} (\vec{L}+2\vec{S})[/tex] to [tex]\mu=-\frac{e}{2m_{e}} (\vec{J}+\vec{S}) [/tex]

3. The attempt at a solution

Tried various vector equations, but no luck. Please help me, i'm really stuck. I hope and think there is a simple solution! thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Landé g factor derivation

**Physics Forums | Science Articles, Homework Help, Discussion**