Effective Nuclear Charge and Screening Effect

In any multi-electron atom, the positively-charged nucleus attracts every negatively-charged electron around it, while the electrons simultaneously repel one another — and the repulsion exerted specifically by the INNER-shell electrons on the OUTER-shell electrons matters most, since it effectively pushes the outer electrons further away from the nucleus. As a result, an outer-shell electron is held less tightly than the bare nuclear charge Z would suggest: the nucleus's pull on it is partially cancelled by this inner-electron repulsion, so the outer electron never experiences the full actual positive charge Z sitting in the nucleus. The net charge it DOES experience is called the EFFECTIVE NUCLEAR CHARGE, $Z_{eff}$, and it is always lower than the true nuclear charge Z. In other words, the inner electrons 'shield' or 'screen' the outer electrons from the nucleus to some degree — hence this phenomenon's other name, the screening effect (or shielding effect) of the inner/core electrons. Quantitatively, $Z_{eff} = Z - \sigma$, where $\sigma$ (sigma) is called the shielding constant or screening constant, and its value depends on which particular orbital the electron in question occupies. Moving ACROSS a period, the actual nuclear charge Z rises by +1 at each step while the newly-added electron joins the SAME outer valence shell (not a new inner shell) — so core shielding stays essentially unchanged even as Z climbs, meaning $Z_{eff}$ steadily INCREASES across a period. Moving DOWN a group, by contrast, an entirely new (and larger) valence …