Screening and Penetration

On different orbitals the relative screening effect can be understood by looking at their radial probability distributions. Refer a lithium atom with two electrons in the lowest-energy 1s orbital. Which is the lowest energy orbital exists for the third electron? The orbitals 2s and 2p are degenerate in hydrogen, i.e., they have similar energy. But their radial distributions are dissimilar. An electron in 2p will almost always be outside the distribution of the 1s electrons and will be well screened. The 2s radial distribution has more probability of penetrating the 1s distribution and screening will not be so effective. So in lithium and in all many-electron atoms an electron has a higher effective nuclear charge and so lower energy in 2s than in 2p. Ground-state electron configuration for Li is (1s)2(2s)1, and the different (1s)2(2p)1 is an excited state, establish by spectroscopy to be 1.9 eV high.

In an identical way with n=3, the 3s orbital has most penetration of any other occupied orbitals, 3d the least. So the energy order in any many-electron atom is 3s<3p<3d.