# Homework Help: Zeeman effect

1. Jun 10, 2015

### Yaste

1. The problem statement, all variables and given/known data
A zeeman experience is made in the transition 3s4s $^3S_1$ -> 3s3p $^3P_2$ in Magnesium with a magnetic field of 2Teslas (20 000 Gauss). With no magnetic field the emission occurs in 518.360nm.

a) Draw the spectrum of what you hoped you observe when you're watching the system in a direction parallel to the applied magnetic field.
b) What are the deviations of the observed lines in units of GHz?

2. Relevant equations

$$\Delta E = g_J \mu_B M_J B$$

$$g_J = \frac{3}{2} + \frac{S(S+1)-L(L-1)}{2J(J+1)}$$

3. The attempt at a solution

The term $^3S_1$ has S=1, L=0 and J =1 and $^3P_2$ has S=1, L=1, J=2. So we have $\Delta L =1$, $\Delta S =0$ and $\Delta J =1$. Using the following equations I can have the deviations of the observed lines in Joules:

$$\Delta E = g_J \nu_B M_J B$$

$$g_J = \frac{3}{2} + \frac{S(S+1)-L(L-1)}{2J(J+1)}$$

After that, I can use $E=h/\nu$ to find the frequency. Those are the deviations between the sub-lines of $^3S_1$ and $^3P_2$, right? I mean, these lines are going to have 3 ($M_J=1,0,-1$) and 5 ($M_J=2,1,0,-1,-2$) sub-lines, respectively.

I have, however, no idea how to solve a)! Would be very thankful for any help.

Last edited: Jun 10, 2015
2. Jun 10, 2015

### unscientific

For part (a), what are the allowed transitions? Draw them on a spectrum in units of $Ghz$?

3. Jun 10, 2015

### unscientific

You will need the selection rules. Also, this is the anomalous zeeman effect, not the normal zeeman effect.

4. Jun 10, 2015

### Yaste

I was able to solve the problem. One question though: Why is it an anomalous zeeman effect?

5. Jun 10, 2015

### unscientific

Because spin is included (check formula for $g_J$).