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 Incoming links: Atomic-orbital nodal plane

Denote the two complex spatial atomic orbitals by

ψ_{+}

and

ψ_{-}

, retaining the same spin state. With the phases specified by the supplied spherical harmonics, choose

ψ_{x} = \frac{ψ _{-} - ψ _{+}}{2}, ψ_{y} = \frac{i ( ψ _{-} + ψ _{+} )}{2} .

The two original atomic orbitals are orthonormal, so the squared coefficients add to one and these combinations are normalized and mutually orthogonal. Explicitly,

ψ_{x} = \frac{1}{32 π} x e^{- r /2}, ψ_{y} = \frac{1}{32 π} y e^{- r /2},

which are real spatial wavefunctions. An overall sign on either orbital has no physical consequence.

These are the familiar $2 p_{x}$ and $2 p_{y}$ p orbitals. Each has two lobes of opposite wavefunction sign, with an atomic-orbital nodal plane through the atomic nucleus:

x = 0

for

2 p_{x}

and

y = 0

for

2 p_{y}

. The sign is a phase convention, not a positive or negative electric charge; the probability density is nonnegative on both lobes.

The

2 s

atomic orbital is spherically symmetric and has one radial node. A real

2 p

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

2 p_{x}, 2 p_{y}, 2 p_{z}

remain degenerate in a spherically symmetric atom when external fields and fine structure are neglected.

2 s

penetrates the screened core more effectively than

2 p

, experiences a stronger attraction and is lower in energy: $ε_{2 s} < ε_{2 p}$ . 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.