Hydrogen-like atoms (those with just one electron) are simple because there is just one interaction to consider: the attractive force between the opposite charges of the (+) nucleus and the one (-) electron. When there are two or more electrons in an atom, the situation becomes more complicated by the effects of electron-electron interactions.
The effects of electron-electron interactions are difficult to describe mathematically, and there is no equation that can accurately predict the energies and behavior of electrons in multi-electron atoms. When describing the shapes of orbitals of mutli-electron atoms, we use hydrogen-like atoms as an analogy. This unit covers how properties of multi-electron atoms can be further described by the combination of Coulomb's Law with the phenomena of electron shielding and orbital penetration. Together, these three things can be used to rationalize the periodic trends in electron affinity, ionization energy, and atomic (and ionic) sizes.
- 1.1.1: Coulomb's Law
- Coulomb's law is a fundamental principle from Physics. In short, particles with opposite charges experience an attractive force while particles with the same charge experience a repulsive force. The closer the particles are to one another, the stronger the magnitude of the force. Coulomb's law can be applied to explain interactions between an atom's nucleus and electrons.
- 1.1.2: Effective Nuclear Charge
- Electrons in multi-electrons do not experience the full charge of the nucleus (Z). Effective nuclear charge (Z_eff) is the reduced nuclear charge experienced by an electron. It is useful to know general trends in Z_ef, and its actual value can be approximated using Slater's Rules.
- 1.1.3: Shielding and Penetration
- Penetration is the extent to which an electron orbital can approach the nucleus. Shielding is the reduction of true nuclear charge to effective nuclear charge; the extent to which electrons shield each other depends partly on penetration. Penetration and shielding are responsible for periodic trends in effective nuclear charge, and in turn cause other trends including that of ionization energy, electron affinity, electronegativity, and atomic/ionic radius.