 Solution

Phosphorus has electron configuration $1s^{2}2s^{2}2p^{6}3s^{2}3p^3$, with $Z=15$. For a $1s$ electron, the only shielding contribution in Slater's rules is $0.30$ from the other $1s$ electron:For a $3p$ electron, the other four electrons in the $3s,3p$ group contribute $4(0.35)$, the eight $n=2$ electrons contribute $8(0.85)$, and the two $1s$ electrons contribute $2(1.00)$:The compact core electron experiences nearly the full nuclear charge, while the valence electron is strongly shielded by the core. The two numbers describe different orbitals of the same atom. Outer electrons do not shield the core in this Slater approximation, and the selected electron never counts toward its own shielding.