What an atomic orbital actually shows you

An orbital is not an orbit.

The most common mistake when you first see the 3D visualization of a 2p or a 3d is to think the electron sits there, that it moves between those lobes, that it orbits like a planet around the Sun.

It doesn't.

What an orbital is

An orbital is the solution of the Schrödinger equation for an electron bound to a nucleus. It does not describe where the electron is: it describes where it might be, and with what probability.

Formally, an orbital is a wavefunction ψ(r, θ, φ). The square of its modulus (|ψ|²) is the probability density: it tells you the probability per unit volume of finding the electron at that point in space.

What you see in the periodic table's orbital inspector is a cloud of points sampled with probability proportional to |ψ|². More points in a region → more likely to find the electron there. Fewer points → less likely.

Phase: teal and pink don't mean charge

The colour in the visualizer does not indicate charge or density.

It indicates the phase of the wavefunction ψ.

ψ is a function that can be positive or negative in different parts of space. In the 2pz orbital the upper lobe has ψ > 0 (teal) and the lower lobe has ψ < 0 (pink). Yet both lobes contribute equally to the probability density, because |ψ|² is always positive.

Phase becomes relevant in chemical bonding: two wavefunctions add (constructive interference → σ bond) or subtract (destructive interference → σ* antibond). Same phase between two atoms = bond. Opposite phases = antibond.

Nodes: where the electron cannot be

A node is a surface where ψ = 0, and therefore where the probability of finding the electron is exactly zero.

There are two kinds:

Radial nodes: spherical surfaces. The 2s orbital has one radial node: a concentric sphere where ψ changes sign. In the visualization it appears as a spherical gap between two regions of density.
Angular nodes: planes or cones. The 2pz orbital has one angular node: the xy plane, where ψ = 0 and the point cloud is absent.

General rule for an orbital with principal quantum number n and angular momentum l:

radial nodes = n − l − 1
angular nodes = l
total nodes = n − 1

Why s is spherical, p has two lobes, d is more complex

The shape depends on the angular-momentum quantum number l:

l = 0 (s): full spherical symmetry. ψ depends only on the distance from the nucleus r, not on direction. The result is a sphere.
l = 1 (p): two lobes separated by a nodal plane. ψ depends on cos θ or sin θ. The three 2px, 2py, 2pz orbitals are identical but oriented along the three Cartesian axes.
l = 2 (d): more complex structures. 3dxy and 3dx²−y² have four lobes in the xy plane (they differ only by a 45° rotation). 3dz² is the most unusual: two polar lobes and an equatorial torus, separated by two nodal cones.

As l rises, the angular structure gets richer: more nodes, more lobes, more possible directions in space.

In heavy atoms reality is more complicated

The orbitals shown in the Fosforonero inspector are hydrogenic (Z=1): computed for a single electron around one proton. They are exact solutions of the Schrödinger equation for that specific case.

In multi-electron atoms (that is, all the others) each electron feels not only the nucleus but also the repulsion of the other electrons. Exact closed-form solutions don't exist. Approximate methods are used: Hartree–Fock, DFT, post-HF.

Hydrogenic orbitals stay useful because they:

give the right qualitative structure (lobes, nodes, spherical symmetry for s)
explain the filling rules (Aufbau principle, Hund's rule, Pauli exclusion)
are the basis of the 1s²2s²2p⁶… notation used everywhere

But they are not an exact simulation of real atoms. They are a teaching model: precise in the principles, simplified when applied to heavy elements. The table states this explicitly in the inspector: "hydrogenic (Z=1): exact for hydrogen, indicative for the rest."

How the visualizer works

The orbital inspector uses a rejection-sampling algorithm. For each point it generates a random position in space, computes |ψ(x,y,z)|², and accepts the point with probability proportional to |ψ|² relative to the known maximum for that orbital.

The result is a cloud of ~9000 points (3500 on mobile) whose density faithfully mirrors the quantum probability density. Each point's colour depends on the sign of ψ there: teal if ψ > 0, pink if ψ < 0.

The random-number generator is deterministic (mulberry32 with a fixed per-orbital seed): the cloud is the same on every load, reproducible and comparable across sessions.

The cloud rotates slowly about the y axis to give the three-dimensional structure depth. Nodes appear as empty regions, zones where no point is accepted because the probability is zero.

It is not decorative graphics. It is a quantitative visualization of the hydrogen wavefunction.