# How to read electron energy levels abbreviations?

The electron energy transfer diagrams I've been coming across all have energy levels labeled as e.g. $^{2}F_{5/2}$ or $^{4}S_{3/2}$. I've tried to Google "quantum energy level abbreviations" but haven't come across anything too useful, just explanations of electron configurations. Can anyone explain or point to a website or textbook that goes through what these numbers/letters/fractions mean for someone who's taken general chemistry but not quantum mechanics?

Thanks!

• It's a bit tough to understand where these numbers come from without QM, and I don't really want to write any technical inaccuracies (because this topic is confusing enough for QM students and having another sloppy account online won't help). However, as a general chemistry student, perhaps you are aware of the quantum numbers of an electron: $(n, l, m_l, m_s)$. $m_s$ has to do with the spin of the electron, which is an "intrinsic angular momentum" of the electron. $m_l$ has to do with the orbital the electron is in, which confers a certain amount of angular momentum on the electron as well. – orthocresol May 18 '17 at 14:27
• ... If you add up the angular momenta of all the electrons in an atom, you can get the angular momentum of the atom. In short, then, the top-left number represents the spin angular momentum of an atom, the middle letter represents the orbital angular momentum of an atom, and the bottom-right number represents the total angular momentum of an atom, which is simply a sum of the previous two angular momenta. – orthocresol May 18 '17 at 14:27

The notation scheme is $^{2S+1}L_J$ where $2S+1$ is the spin multiplicity, $L$ is the angular momentum quantum number and $J$ is the total angular momentum due to the coupling between the former two.