Slaters Rules for Screening Constants

In an alkali metal atom such as sodium, the 3s electron penetrates the neon core, i.e., it moves into the field of attraction of the nucleus, being only partially screened by the K and L shells. In an excited sodium atom the electron in a 3p orbital penetrates the electron cloud to a lesser extent, and the electron raised to a 3d orbital is practically non-penetrating. Thus the 3s, 3p, and 3d orbital in a many-electron atom have different energies whereas these orbitals in hydrogen atom have the same energy. 

An alternative way of discussing penetration effects is to speak of the effective nuclear charge Zeff for a particular electron. The following rules for estimating the screening (or shielding) constant T (where Zeff = Z — a) were proposed by Slater. [J.C. Slater, Atomic shielding constants. Phys. Rev. 36, 57-64(1930)]. 

Note that the s and p subsheUs are grouped together, the d and f subsheUs are separate, and the subshells are arranged in the order of increasing n, e.g., 3d comes before 4s. Note that this is the approximate order of the average distances of the subsheUs from the nucleus. 

As a first example we take nitrogen, Z = 7. Here we have two / Is/ electrons, and five /2s, 2p/ electrons. The effective nuclear charges are  

---