# lyman alpha anomalous zeeman effect

I am generally confused by this issue, and have been over my lecture notes so many times, I am now confusing myself, and would appreciate if anyone could explain what is going on.

I will have to post all the questions leading up to the question I am having a problem with but due to it being a marked assignment I cannot put up my full workings, but in truth my issue is with the diagrams and the physics of it all.

So here are my question that I have been given and d) is where the problem lies as such, as I will state now, I am not looking for an answer just an explanation to what I am seeing in my lecture note and with what I have drawn personally.

So I will post a picture now of the diagram that I have drawn for d)

Now here is a diagram from my lecture notes and this is where the confusion lies, I dont know if the $2s_{1/2}$ has been left out on purpose as it give the answer to the question or that I have done something wrong and the $2s_{1/2}$ should not be in my diagram, the problem is no where in my notes dose it explain if true why the $2s_{1/2}$ what troubles me more is if I calculate the g factor for the anomalous zeeman like so

$$g=1+\frac{j\left(j+1\right)+s\left(s+1\right)-l\left(l+1\right)}{2j\left(j+1\right)}$$

for the $2s_{\frac{1}{2}},2p_{\frac{1}{2}}$ I should see an energy split which is shown on my diagram yet in my lecture notes this diagram is displayed for the the transition:

As you can see this is very different to mine, which I assume the spin/orbit and fine structure are not needed, but it still raises the issue where has the $2s_{1/2}$ gone? is there something I am missing within the physics, is this a typo, Iv looked in books and google, to not much help as there seem to be many interpretation of how these diagrams are drawn, which confuses me more.

Is there a possibility some could maybe explain.

I have had a throught, is it beacuse of the selction rule $\Delta l=\pm1 ?$

• It is indeed because of the selection rules, the transition from 2s to 1s is forbidden so the 2s is left out of the diagram as only transitions from 2p to 1s happen – Triatticus May 10 '18 at 5:58
• Ah thank you very much, I kept looking thing maybe I was missing something. Much appreciated – james2018 May 10 '18 at 12:43