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Atom

An atom as it actually is: a nucleus wrapped in electron standing waves — orbitals with real nodal planes and phase — plus a volumetric mode that raymarches the true |ψ|² probability cloud.

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the study

The idea

The planetary atom — dots circling on rings — was obsolete by 1926, but it still decorates logos, and unlearning it is most of the work of learning atomic physics. An electron bound to a nucleus is a standing wave, and an orbital is one of those waves: a solution of the Schrödinger equation labelled by quantum numbers n (size and energy) and l (shape). s orbitals (l = 0) are spherical; p orbitals (l = 1) are two-lobed dumbbells whose waist pinches to a nodal plane through the nucleus — a plane on which the electron will never be found, not because something blocks it, but because the wave passes through zero there.

The two lobes of a p orbital carry opposite wavefunction sign — rendered warm and cool here — and that sign is not bookkeeping: chemistry runs on it. Bonds form where neighbouring atoms' waves overlap in phase and reinforce; anti-phase overlap cancels and repels. The colour on these lobes is the hidden variable behind bonding rules.

An atom's electron configuration is all its occupied orbitals at once, which this view renders literally as translucent shapes superposed around one nucleus. The 'scientific' style then drops the stylization entirely and raymarches |ψ|² itself for a chosen hydrogen orbital — the honest fuzzy cloud, dense where the electron is likely, fading with no edge, its nodal surfaces showing as dark gaps in the volume.

What to look for

  • The pinched waist on every p orbital is the nodal plane. Click a subshell for its quantum numbers and check: the number of nodes grows with n — more energy means a faster-oscillating wave.
  • Warm and cool lobes are the sign of ψ. Same shape, opposite phase — the difference between bonding and antibonding when two atoms meet.
  • Step through elements and watch shells fill: H's single 1s, carbon's four outer-shell waves, argon's completed n = 3 shell. The periodic table is a filling order made visible.
  • In the 'scientific' style, note what an orbital really is: not a balloon with a skin but a density. The textbook shapes are just contours drawn around clouds like this one — conventionally at 90% probability.

Getting it right

  • Electrons do not orbit. Nothing is circling; the standing wave simply persists. "Orbital" is a fossil word for a shape of probability.
  • Textbook orbital pictures are isosurfaces of clouds like the one the scientific mode shows — a drawn boundary on something that has no boundary. The cloud is the truth; the surface is the summary.
  • "Atoms are mostly empty space" is only half right. The nucleus is indeed ~10⁻⁵ of the atom's diameter, but the rest is not empty — it is filled with exactly the standing waves you are looking at, and their extent and stiffness are why matter is solid.

Turn the knobs

  • element (or Z) picks the atom; H through Ar render their full s and p configurations.
  • style is the register switch: 'artistic' for the whole atom in faithful stylized waves, 'scientific' for the raymarched |ψ|² of a single hydrogen orbital.
  • orbital chooses which cloud the scientific mode marches — climb 1s → 2s → 2p → 3dz2 and watch nodes appear and multiply as n and l grow.

the knobs

The world above is one recipe — every knob below is a parameter of it. In a mojulo workshop you rarely touch them directly: you ask your agent in a sentence, and the agent sets the knobs.

parameter manual
  • style (string) — 'artistic' (default) = the mesh wave-primitive atom (element-based, the whole atom). 'scientific' = a ray-marched volumetric |ψ|² electron-probability cloud of a single hydrogen orbital (real density + nodal surfaces); pair with orbital.
  • orbital (string) — For style:'scientific' — which |ψ|² cloud to render (default '3dz2'). Atomic hydrogen: 1s/2s/2p/3s/3p/3dz2/3dx2y2/3dxy. H₂ MOLECULAR ORBITALS (two nuclei, LCAO of 1s): 'h2_sigma' (σ bonding — density piles up between the atoms → the bond) and 'h2_sigma_star' (σ* antibonding — a nodal plane between the atoms).
  • element (string) — For style:'artistic' — element symbol (e.g. 'C', 'Ne', 'O', 'Na'). H…Ca known; default 'Ne' (the full, symmetric 1s² 2s² 2p⁶ set).
  • Z (number) — Atomic number (1–20) — an alternative to element. Takes precedence if both given.
  • mode (string) — For style:'artistic' — 'orbitals' (default) = the static occupied-orbital set. 'tour' = an ANIMATED hydrogen wave-tour: the orbitals as faint wireframe mazes (1s/2s/2p) with one electron tracing each orbital's wave-path in turn (a teaching animation, not a literal Bohr orbit).

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