Orbital atlas
The shapes themselves, drawn from the wavefunction rather than sketched.
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A flat slice through the middle of a three-dimensional shape. The plane is chosen per orbital, because a d_xy sliced through xz would show nothing at all.
Cross-section: the xz plane
Description of this simulation
2pz: n = 2, l = 1. The shape is two lobes on opposite sides of the nucleus, one of each phase, with a nodal plane between them. It has 1 angular node and 0 radial nodes, 1 in total, which is always n − 1. The cross-section is taken through the xz plane. An electron in it is most likely found 4.0 Bohr radii from the nucleus, about 212 picometres.
2pz
Quantum numbers
- Principal, n
- 2
- Angular momentum, l
- 1 (p)
- Radial nodes
- 0
- Angular nodes
- 1
- Total nodes
- 1
- Most probable radius
- 4.0 Bohr radii · 212 pm
- First occupied by
- Boron (B)
Radial plus angular is always n − 1.
Radial distribution
How likely the electron is to be found at each distance from the nucleus. Every touch of zero is a radial node.
Phase
- Positive
- Negative
The two colours are the sign of the wavefunction, not electric charge. Where lobes of opposite sign overlap they cancel — which is the whole difference between a bonding and an antibonding combination.
Not a path
An electron does not travel round this shape. The surface encloses the region where it is most often found — the shape is where the electron is, not where it goes.
Put electrons into these orbitalsWhat this model shows — and what it simplifies
Educational ModelThese are the exact wavefunctions of a one-electron atom.
Where do we see this in real life?
The shapes decide the geometry of matter. Methane is tetrahedral, water is bent, and a benzene ring is flat because of which orbitals point where and which of them can overlap — the same reason a transition metal complex is coloured at all.