= Solution
\b[<Photoelectron spectroscopy> measures orbital-dependent binding energies from which an effective charge can be inferred using a stated model.] Ultraviolet <photoelectron spectroscopy> accesses outer-shell ionizations; <X-ray photoelectron spectroscopy> accesses deeper core states. For an isolated gas-phase atom and a calibrated threshold, measure emitted-electron kinetic <energy> and use $I=h\nu-E_{\rm kin}$, with the appropriate energy reference. Optical atomic term spectra and series limits also constrain valence ionization energies.
A hydrogenic inference would set $I\simeq R_\infty Z_{\rm eff}^2/n_{\rm eff}^2$, hence $Z_{\rm eff}\simeq n_{\rm eff}\sqrt{I/R_\infty}$, with $R_\infty$ here an energy of approximately $13.6\,\mathrm{eV}$ and $n_{\rm eff}$ a chosen effective shell parameter. \b[The measured binding energies are experimental; the extracted $Z_{\rm eff}$ values remain model dependent.] They need not equal Slater screening parameters fitted to radial functions.
Unlike the equal $ns,np$ values in <Slater's rules>, spectroscopic values distinguish s from p because their penetration and shielding differ; the more tightly bound s states usually imply larger binding-energy-derived effective charges at a common shell parameter. Subshell, atomic-term and, especially for heavier atoms, <spin-orbit coupling> structure give further distinctions. Electron relaxation following ionization and electron correlation also matter. Thus real binding energies vary across the heavier group-15 atoms even where the simple Slater outer-shell estimates plateau; no universal constant correction to the Slater values follows.<Electron Spectroscopy for Atoms, Molecules and Condensed Matter by Kai Manne Börje Siegbahn>[1981, binding-energy measurements and resolved atomic and chemical environments]{ref}
Back to article page
