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

An electron, which is negatively charged, is attracted to the nucleus of an atom because of the positive charge that is there. The amount of energy that is required to be given to the electron to pull it away from this attractive (Coulombic) force is called the binding energy. For the hydrogen atom, this is an exactly solvable problem (both at the non-relativistic level -the Schršdinger equation- and at the relativistic level -the Dirac equation). However, when more than one electron is present in orbit around a nucleus one most further consider the electrostatic repulsion which arises between the electrons. Because of this additional repulsion, the energy one needs to give a certain electron to remove it from the nucleus is now less than would be needed otherwise. This electron-electron repulsion makes the problem unsolvable analytically. However, many effective and accurate numerical methods have been developed to calculate the binding energies including these additional terms.

The most basic description of the electrons around an atom are in terms of their orbital angular momentum. This gives rise to the commonly known labels 1s, 2s, 2p, etc. The next most important term is that of the spin-orbit interaction and splits all of the non-s electrons into two different levels, for instance, 2p(1/2) and 2p(3/2). The splitting becomes very large for the heavy atoms so that the use of these same labels is no longer accurate. Nevertheless, it is possible to identify each electron with this type of label. The spin-orbit splitting is averaged for each spin-orbit pair, accounting for the different degeneracies of the two states. Therefore the binding energies that are reported are what would be expected considering only Coulombic electrostatic forces and is what might be observed in a spectrometer with very poor resolution.

It has sometimes proven useful to consider the effect that the other electrons have upon a given electron as if they "stood in the way" between it and the nucleus to which it was attracted. This effect would be to diminish the effective nuclear charge by "shielding" the actual nuclear charge from the electron. This shielding is discussed elsewhere.

Reported here are the best values for the binding energy of every electron in every atom from Hydrogen (with a nuclear charge Z of 1) to Lawrencium (with Z = 103). Since the data set is HUGE (there are 5356 different electrons), you can select to view the information in a few different ways, and then either as numbers or graphically. Choose the appropriate link below.

Atomic Binding Energies
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 Binding Energies
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