Atomic_orbital - Wikiparency

# Atomic orbital  ## Microsims — three.js ### Atomic orbital (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Atomic_orbital.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Atomic orbital — three.js microsim"></iframe> </div> **Open it full-screen:** [Atomic_orbital.html](https://wikitube-3d-microsims.netlify.app/Atomic_orbital.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Allotropes_of_oxygen]] - [[Hemoglobin]] - [[Hydrogen_bond]] - [[Molecular_orbital]] - [[Ozone_layer]] - [[Silicon_dioxide]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Overview An atomic orbital is not a path an electron follows. It is a one-electron wavefunction, psi, whose squared magnitude gives the probability density of finding the electron at each point in space. The word survives from Bohr's 1913 planetary model, but the meaning was replaced entirely by Schroedinger's 1926 wave equation and Born's probabilistic reading of psi later that year; what remains of the older picture is only the name. For a hydrogen-like atom the solutions separate into a radial part and an angular part, psi = R_nl(r) * Y_lm(theta, phi), labelled by three quantum numbers: n (shell), l (subshell shape, giving s, p, d, f) and m (orientation). Oxygen's ground-state configuration is 1s2 2s2 2p4, so oxygen's chemistry is the chemistry of a half-filled 2p subshell -- two of the three 2p orbitals hold a lone pair each and one holds two unpaired electrons. Everything in this room follows from that. ## The physics The radial functions carry the shell structure and the angular functions carry the shape. Nodes -- surfaces where psi passes through zero -- come in two kinds, and their counts are fixed: - radial nodes: n - l - 1 (spherical shells where R_nl = 0) - angular nodes: l (planes or cones where Y_lm = 0) - total nodes: n - 1 So 1s has none, 2s has one spherical node, 2p has one nodal plane, and 3d_z2 has two angular nodes forming a cone, which is why it renders as two axial lobes threaded by an equatorial torus. The mean radius of a hydrogen-like orbital is <r> = (3n^2 - l(l+1)) / (2Z) in units of the Bohr radius, so raising the effective nuclear charge Z contracts every orbital. This sim samples |psi|^2 * r^2 (the r^2 is the volume Jacobian; without it the cloud piles up wrongly at the nucleus) and colours each point by the SIGN of psi. That sign is not decoration -- it is the entire reason atoms bond. Two orbitals overlapping with the same sign reinforce and lower the energy; with opposite signs they cancel and raise it. That is the bridge to [[Molecular_orbital]]. ## Controls -> what each maps to | Control | Maps to | Range / values | Physical meaning | |---|---|---|---| | Which orbital to sample | n, l, m | 1s to 3d | Selects the wavefunction; node counts follow from n and l | | Effective nuclear charge Z | Z | 1 - 8 | Contracts or expands the cloud as <r> scales with 1/Z | | Number of sampled points | -- | sampling density | Statistical resolution of the density, not a physical quantity | | Cutaway | -- | on / off | Hides the near half so interior radial nodes become visible | | Oxygen Z from Slater rules | Z = 4.55 | preset | Jumps to oxygen's own effective nuclear charge for its 2p electrons | | Spin the cloud | -- | on / off | Rotation only; disabled under prefers-reduced-motion | ## Learning objective After playing, a learner can state why an orbital is a probability distribution rather than a trajectory, predict the radial and angular node counts of any orbital from n and l, and explain why the sign of psi -- not its magnitude -- is what makes chemical bonding possible. ## Limits and connections These are exact one-electron (hydrogen-like) solutions. Real many-electron atoms have no closed-form orbitals: electron-electron repulsion means the true wavefunction is not a product of one-electron functions, and what chemists draw as "the 2p orbital of oxygen" is a self-consistent-field approximation with a screened, non-integer effective charge. The Slater-rule value used here (Z_eff = 4.55 for oxygen 2p) is one such estimate. Combining these shapes gives [[Molecular_orbital]]; filling them by energy gives the periodic table. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Atomic_orbital) : [Wikitube](https://en.wikitube.io/wiki/Atomic_orbital) ## Previous hub tags Tree parent: [[Oxygen]]. Legacy hubs: `REACTION`. --- *Created 2026-08-05 - append-only - hand-authored to WIKI_REPOPULATION_PROTOCOL v1.0 section 5 - 0 deletions*