My question is: Why the energy levels for sodium are different from those for hydrogen even though sodium is described as a "hydrogen-like atom"? Here I have posted the energy diagrams for sodium, and hydrogen. So, I have noted that sodium has 11 protons, whereas the hydrogen has only 1 proton. So sodium has a heavier nucleus having a charge 11 times greater than that of hydrogen. And sodium has 11 electrons while hydrogen has only 1. I wanted to argue that the difference of the number of protons and electrons somehow affects the spin-orbit coupling. But in sodium the nucelus with Z=11 is "screened" by 10 negative charges. So we have 1 free electron, exactly like the hydrogen atom! So shouldn't we end up with the same energy diagram? I am very confused about this. Any explanation would be greatly appreciated.