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The configurations are $\mathrm{C}:1s^{2}2s^{2}2p^2$ and $\mathrm{N}:1s^{2}2s^{2}2p^3$. A simple complete-core-screening estimate subtracts the two $1s$ electrons, giving $Z_{\mathrm{eff}}\approx 4$ 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: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.^[ref]

For the outer $ns,np$ valence electrons, Slater's rules predict a modest initial rise down group 15, followed by approximately constant values. Write the effective nuclear charge as $Z_{\mathrm{eff}}=Z-S$, where $S$ is the shielding constant. Each atom has $n{s}^{2}n{p}^3$, so the other four electrons in the outer group contribute $4(0.35)=1.40$. Electrons in shell $n-1$ contribute $0.85$ each, and those deeper contribute $1.00$ each.^[ref]

Applying those weights gives the following original calculations:The increasing nuclear electric charge is largely offset by additional inner-electron shielding; once the preceding shell contains $18$ electrons, these simple weights give a plateau. The $n-1$ shell includes its d electrons. This trend concerns outer-shell values, not every orbital: a $1s$ electron is shielded only by its partner, so $Z_{\mathrm{eff}}(1s)=Z-0.30$ rises strongly down the group. The larger principal shell also means nearly constant outer $Z_{\mathrm{eff}}$ does not imply nearly constant atomic size or binding energy.

An empirical orbital-screening prescription. Other electrons in an $ns,np$ group count $0.35$ each; electrons in shell $n-1$ count $0.85$, deeper electrons $1.00$, and outer electrons zero. For $1s$, the partner contributes $0.30$. d and f groups use separate rules.^[ref]