 Solution

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 $I=h\nu -E_{\mathrm{kin}}$, with the appropriate energy reference. Optical atomic term spectra and series limits also constrain valence ionization energies.

A hydrogenic inference would set $I\simeq R_{\infty }{Z}_{\mathrm{eff}}^2/n_{\mathrm{eff}}^2$, hence $Z_{\mathrm{eff}}\simeq n_{\mathrm{eff}}\sqrt{I/R_{\infty }}$, with $R_{\infty }$ here an energy of approximately $13.6\mathrm{eV}$ and $n_{\mathrm{eff}}$ a chosen effective shell parameter. The measured binding energies are experimental; the extracted $Z_{\mathrm{eff}}$ 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.^[ref]