Sampling |ψ|²…
Bohr’s rings are a counting tool. They tell you how many electrons sit in each shell. That is why the 3D atom inspector still uses them. However, they do not tell you where an electron actually is. That answer is a wavefunction ψ. The picture above is |ψ|² for hydrogen, a one-electron atom whose orbitals we can write in closed form. The same formulas also cover hydrogen-like ions (He⁺, Li²⁺) after you rescale the Bohr radius by Z.
How to read the cloud
Each dot is a sample in space. The vertex shader evaluates a simplified hydrogen ψ at that point. It then sets the point’s size from |ψ|², so dense regions bloom and nodes vanish. Additive blending stacks overlapping samples. The glow is therefore probability, not a surface.
Blue is ψ > 0. Orange is ψ < 0. The two colors are phase, not charge. So an electron in a 2p orbital is not “positive on top and negative on the bottom.” The sign matters when two orbitals overlap. Matching phases reinforce a bond. Opposite phases, however, cancel.
1s — a ball, no nodes
Switch the dropdown to 1s. The cloud is spherical because the wavefunction depends only on r. The density |ψ|² is highest at the nucleus, then dies exponentially. The radial probability 4πr²|ψ|² — the chance of finding the electron in a thin shell — peaks at one Bohr radius. There is no angular node. That is why s orbitals can sit close in and shield the ones outside them. Helium’s 1s² pair is this shape, filled.
2p_z — the slice textbooks skip
2p_z is two lobes along z, with a knife of empty space through the xy-plane. That plane is not a rendering artifact. ψ contains a factor of z (or cos θ), so it is identically zero when z = 0. An electron in 2p_z therefore has zero probability on that plane. 2p_x and 2p_y have different nodal planes.
2p_x and 2p_y are the same function pointed along the other axes. A full p subshell is all three. That is why the p-block is six columns wide: two electrons × three orbitals.
3d_xy — four lobes between the axes
3d_xy looks like a clover in the xy-plane. Its lobes point between x and y, not along them. Two nodal planes (xz and yz) then cut through the nucleus. That between-the-axes geometry is why ligand-field splitting exists: ligands sitting on the axes overlap some d orbitals more than others. The d-block is ten columns wide because five d orbitals hold two electrons each.
What this is not
These are hydrogen orbitals (Z = 1, one electron, no shielding). Carbon does not walk around with a pure 2p_z sticking out. Its four equivalent bonds are a later story — hybridization — in which 2s and 2p mix. Even so, the hydrogen clouds are still the right starting shapes. Every qualitative node you meet in general chemistry is already on screen.
For the Bohr-style shell count of any element, stay on the inspector. For how those subshells carve the table, see s, p, d, and f blocks. For the integers that pick each shape, see quantum numbers.
Questions this picture answers
Why are parts of the orbital blue and others orange?
The colors are the sign of the wavefunction ψ, called phase. They are not positive and negative charge. Chemistry cares because orbitals only mix strongly when their phases match in the overlap region.
Is the electron bouncing around inside the cloud?
No. The cloud is the probability density |ψ|². Brighter regions are where a measurement is more likely to find the electron. Between measurements, however, the electron does not have a planetary path.
Why is there a flat empty slice through the 2p orbital?
That slice is a nodal plane, where ψ = 0 so |ψ|² = 0. Each 2p orbital has one angular node. For 2p_z, that node is the xy-plane. Probability there is exactly zero, not merely small.
Do other elements have the same orbital shapes?
The shapes are hydrogen’s exact one-electron solutions. The same closed forms also work for He⁺, Li²⁺, and other hydrogen-like ions, after you scale the radius by Z. Multi-electron atoms then use those orbitals as a starting picture. Extra electrons and shielding change the energies and slightly distort the clouds, but the s / p / d / f nodal patterns remain the teaching model.