Chemistry · Chapter 6

Orbital Shapes in Three Dimensions

Drag the black panel to turn the cloud. Every shape here is the real angular part of a hydrogen orbital, so the lobes and the nodes sit exactly where the math puts them.

Turn the orbital drag, or use the arrow buttons

Positive lobe Negative lobe x, y and z axes

The surface marks where the chance of finding the electron has one fixed value. Teal and coral are the two signs of the wave, not two charges.

Distance from the nucleus radial probability

This curve is built from the real radial function for the n and l you chose. Each dip to zero is a radial node, a thin shell where the electron is never found.

2pzTwo lobes on the z axis, split by one flat node.
Pick a subshell
Pick the orbital in that subshell

The quantum numbers read them off

Principal, n
2
Angular, l
1 (p)
Allowed ml
−1, 0, +1
This picture
ml = 0
Orbitals here
3
Electrons it holds
6
Lobes in this picture
2
Shell total, 2n2
8
Nodes through the center
1
Radial nodes
0
Node arithmetic
Angular nodes equal l. Radial nodes equal n minus l minus 1. Together they always add to n minus 1.
What to notice
Shape comes from l alone

Raise n and the cloud spreads out, but the lobe pattern stays the same. Change l and the whole shape changes. That is the split of work between the two numbers.