Solution (source code)

= Solution

The $2s$ <atomic orbital> is spherically symmetric and has one <radial node>. A real $2p$ <atomic orbital> has two lobes of opposite <quantum phase>, one <atomic-orbital nodal plane> through the nucleus and no <radial node>. The three spatial orientations $2p_x,2p_y,2p_z$ remain degenerate in a spherically symmetric atom when external fields and fine structure are neglected.

In a many-electron atom, $2s$ penetrates the screened core more effectively than $2p$, experiences a stronger attraction and is lower in energy: \b[$\varepsilon_{2s}<\varepsilon_{2p}$]. The <hydrogen-like ion> degeneracy therefore does not survive screening. Both valence orbital types are generally more tightly bound and spatially contracted in <nitrogen> than in <carbon>, because of the larger <effective nuclear charge>. These are central-field orbital statements; the detailed atomic multiplet structure also involves <electron> repulsion and <Hund's rules>.