= Solution
The one-electron species are $\mathrm{C^{5+}}$ and $\mathrm{N^{6+}}$, so there is no <electron>–<electron> screening and the nuclear charges remain $Z=6$ and $7$.
$$
\boxed{E_{n=2}(\mathrm{C^{5+}})=-13.6\frac{6^2}{4}=-122.4\,\mathrm{eV},\qquad E_{n=2}(\mathrm{N^{6+}})=-13.6\frac{7^2}{4}=-166.6\,\mathrm{eV}.}
$$
Within the stated <hydrogen-like ion> model, $2s$ and all three $2p$ <atomic orbitals> of a given species have the same energy. The energy zero is a separated <electron> and the residual nucleus.
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