Shielding of Electrons
in Atoms from H (Z=1) to Lw (Z=103)

When we study the binding energies of electrons in the atoms, we note that each electron is different. The nuclear charge around which it is in orbit, the nature of its orbit and the orbits of all the electrons, create a unique environment which is a sum of many electrostatic interactions, which change continually from instant to instant as the electrons perform their little dance around and through the nucleus. The average effect of all of these forces conspire to create a stable environment so that physical properties such as energy and angular momentum are conserved in the atom. The actual motions are far to complex to be adequately described (if we could describe them at all) and also be useful in helping us to understand the atom. On the other hand, these conserved properties are the best means at our disposal for aiding our understanding.

The chemical and physical nature of the atom is inherently bound up in the energy and angular momentum of its constitutent electrons. It is this which makes H2O so different from H2S. The concept of shielding was introduced early on as a means to explain the changes in binding energy and it has become a useful pedagodgical tool for teaching and explaining the periodic table.

When several electrons swirl around a positively charged nucleus, they will not only experience the attractive Coulomb potential of that nucleus but also the repulsive Coulomb potential with each other. If we consider a single electron ina particular orbit about a nucleus with a positive charge of Z, we can exactly solve the problem at both the non-relativistic (Schrödinger equation) and the relativistic (Dirac equation) level. But as soon as an additional electron appears in another orbit around the same nucleus, the repulsive force of this new electron will reduce the net attractive force of the nucleus upon the first electron. The extent of this reduction may be large or small depending upon the relative position of the two orbitals. For instance, if the first electron only travels in regions very close to the nucleus while the second is only very far from it, the decrease in the attractive potential may be quite small. However, if the opposite positions are maintained, then the decrease in charge may be almost exactly that equal to the charge of the shielding electron. When many electrons are present, they all contribute in their own, unique way to the shielding of each other from the attractive force of the nucleus. Each will be less strongly bound to the nucleus because of this shielding. The extent to which this attractive force is diminished is a measure of the change in the physical (i.e. spectroscopy) and chemical (i.e. reactivity) properties of the atom.

All the motions which contribute to the shielding of a given electron are far to complicated to measure (and cannot even be measured because of the Heisenberg Uncertainty principle) but their average effect is manifested directly in the change of binding energy. Based on this, we have taken all of the known electron binding energies and have compared them with the exact Dirac (relativistic solution) for an electron in the same quantum state for a single electron atom of the same charge. By using an iterative solution, we have calculated the shielding that must be present for each electron to give rise to the observed binding energy. The following links go to various tables and graphs which record these shielding constants. With this information, you can readily explain the changes in chemistry that are observed as you go down a group or across a row in the periodic table.

Atomic Shielding Constants
Hydrogen and the Alkali MetalsGroup 1: H to FrGroup 1: H to Fr
The Alkaline Earth MetalsGroup 2: Be to RaGroup 2: Be to Ra
Transition ElementsGroup 3: Sc, Y, La, AcGroup 3: Sc, Y, La, Ac
Transition ElementsGroup 4: Ti, Zr, HfGroup 4: Ti, Zr, Hf
Transition ElementsGroup 5: V, Nb, TaGroup 5: V, Nb, Ta
Transition ElementsGroup 6: Cr, Mo, WGroup 6: Cr, Mo, W
Transition ElementsGroup 7: Mn, Tc, ReGroup 7: Mn, Tc, Re
Transition ElementsGroup 8: Fe, Ru, OsGroup 8: Fe, Ru, Os
Transition ElementsGroup 9: Co, Rh, IrGroup 9: Co, Rh, Ir
Transition ElementsGroup 10: Ni, Pd, PtGroup 10: Ni, Pd, Pt
Transition ElementsGroup 11: Cu, Ag, AuGroup 11: Cu, Ag, Au
Transition ElementsGroup 12: Zn, Cd, HgGroup 12: Zn, Cd, Hg
Boron FamilyGroup 13: B to TlGroup 13: B to Tl
Carbon FamilyGroup 14: C to PbGroup 14: C to Pb
Nitrogen FamilyGroup 15: N to BiGroup 15: N to Bi
Oxygen Family
The Chalcogenides
Group 16: O to PoGroup 16: O to Po
The HalogensGroup 17: F to AtGroup 17: F to At
The Noble or Inert GasesGroup 18: He to RnGroup 18: He to Rn
The LanthanidesCe to LuCe to Lu
The ActinidesTh to LwTh to Lw
More Graphs of Electron Shielding Constants
All ElectronsAll n=1 ElectronsAll n=2 ElectronsAll n=3 Electrons
All n=4 ElectronsAll n=5 ElectronsAll n=6 ElectronsAll n=7 Electrons
All s ElectronsAll p ElectronsAll d ElectronsAll f Electrons

Author: Dan Thomas Email: <>
Last Updated: Sun, Feb 9, 1997