= Solution
The configurations are $\mathrm{C}:1s^22s^22p^2$ and $\mathrm{N}:1s^22s^22p^3$. A simple complete-core-screening estimate subtracts the two $1s$ <electrons>, giving \b[$Z_{\rm eff}\approx4$ for <carbon> and $5$ for <nitrogen>]. This neglects screening by the other valence <electrons>, and is an explicitly rough estimate.
A more systematic estimate using <Slater's rules> includes $0.85$ for each $1s$ <electron> and $0.35$ for each other <electron> in the $2s,2p$ group:
$$
Z_{\rm eff}(\mathrm C)=6-[2(0.85)+3(0.35)]=3.25,\qquad Z_{\rm eff}(\mathrm N)=7-[2(0.85)+4(0.35)]=3.90.
$$
Both models predict the important trend: <nitrogen>'s valence shell experiences a greater <effective nuclear charge>. There is no unique numerical <effective nuclear charge> without specifying an orbital and a screening prescription; the one-electron formula in (a) does not by itself define neutral-atom orbital energies.<Atomic Shielding Constants by John C. Slater>[1930, printed pp. 58–59: screening prescription and grouping of ns and np electrons]{ref}
Back to article page
