# Homework Help: Nuclear Magnetic Moments - Oxygen 15

1. Oct 31, 2016

### BOAS

1. The problem statement, all variables and given/known data
I am trying to calculate the nuclear magnetic moment for Oxygen 15 but my answer differs strongly from the value quoted in literature.

2. Relevant equations

3. The attempt at a solution

$\mu_J = g_J \mu_N J$

This isotope of Oxygen has an unpaired Neutron with $J = \frac{1}{2}$.

Calculating the nuclear g-factor for $J = l + \frac{1}{2}$

$g_J = g_l (1 - \frac{1}{2J}) + g_s(\frac{1}{2J})$

For a neutron $g_l = 0$ and so in this case $g_J = g_s = -3.82$

I therefore find that $\mu_J = -1.91 \mu_N$ which is significantly different from the value I find in the NIST table of $\pm 0.7189 \mu_N$

http://nist.gov/data/PDFfiles/jpcrd85.pdf

Is my treatment too simplistic to get a decent prediction, or am I making a fundamental error?

2. Oct 31, 2016

### BOAS

I think I have found my mistake.

My case is for J = L - S, with L = 1.

My g-factor is therefore $g_J = g_l (1 + \frac{1}{2l + 1}) - g_s (\frac{1}{2l + 1})$, with $g_l = 0$

I find that $g_J = -0.63 \mu_N$ which is much closer to my expected value.

Sorry for posting prematurely.