01 · Radial
Where the electron sits, by distance
Each subshell’s radius is drawn from P(r) = r²Rnl(r)², the hydrogen-like radial probability, sampled through an inverse cumulative table.
Orbital Atlas · ψ² electron probability clouds
Every element, drawn as a cloud of probability.
An electron has no path, only places it is likely to be. Each point below is one Monte-Carlo sample of |ψ|²: the whole atom shell by shell, or a single orbital coloured by the sign of its wavefunction.
computing ψ²
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02 · Screening
Inner electrons shield the outer
Slater’s rules give every subshell its effective nuclear charge Zeff, which is why heavy atoms don’t collapse to a point.
03 · Angular
Lobes only where they matter
Closed subshells are spherical (Unsöld’s theorem). The valence subshell keeps its shape, filled by Hund’s rule across real spherical harmonics.
04 · Honest limits
A model, not a photograph
Hydrogen-like orbitals with Slater screening are a teaching model. Values for elements beyond fermium are predictions.