Drawing the Zeeman Spectrum in Magnesium

[Yaste]

Homework Statement

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?

Homework Equations

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

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

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.

 

[unscientific]

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

 

[unscientific]

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

 

[Yaste]

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

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

 

[unscientific]

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

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