Energy Level notation in relation to the Zeeman Effect

[Kris2456]

I am doing an Atomic & Molecular physics course in Germany as part of my year abroad. A notation that is used in this course to denote energy levels is in the form below. I cannot find a good explanation of how it works, (and this may sound stupid) but i cannot find a mention of it in the notes as it was used outright, and has not been named so i am not sure what to look for.

The closest thing i found was this:
http://hyperphysics.phy-astr.gsu.edu/HBASE/Nuclear/nstate.html"

However the form used here is eg. N^xP_J
The number x is unclear, but in all the questions it has 3 for P orbitals, and 4 for D orbitals.
Can anyone clarify this notation for me, the notes being in German does not help

The questions on the sheet are about the Zeeman Effect, and one of the things we have to do is calculate the Lande g-factor for the ground state of Magnesium and Boron. My assumption is that (in the aformentioned notation) magnesium is 3²S_0.5

I initially thought that J should be 0, since Mg has an S sub shell with 2 electrons, so it's total spin should be 0.5 + (-0.5) = 0, and L is also 0. Apparently in this case it is 0.5 i read somewhere, why is this?

However later on the state ³P₀ is mentioned, asking how many "components" it would split into in a magnetic field. This time the initial N value is not used, so I am getting really confused.

I have a feeling that the answer is probably quite simple, but the combination of QM (which i am not great at) and the German is making this a big stumbling block.

 

[NateD]

The notation you are referring to is the so-called quantum number notation. It is a way of representing the different energy levels of an atom or molecule. The notation consists of four parts, N, L, J and M. N is the principal quantum number, which denotes the energy level of the electron. L is the angular momentum quantum number, which describes the orbital angular momentum of the electron. J is the total angular momentum quantum number, which takes into account both the orbital and spin angular momentum. Finally, M is the magnetic quantum number, which describes the orientation of the electron's spin. In the case of magnesium, the notation 32S0.5 indicates that the electron is in the 3rd energy level (N=3), has an s-orbital (L=0) and a spin of 0.5 (J=0.5). The 0.5 comes from the fact that the two electrons in the s-orbital have opposite spins. In the case of 3P0, the notation denotes a single electron in the 3rd energy level with an p-orbital (L=1) and a spin of 0 (J=0).