- #1

- 9

- 0

## Homework Statement

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.

## Homework 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]

## 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.