Atomic Orbitals · Electron Cloud

Electron cloud

We cannot pin down an electron's position and velocity at the same time. We can only say how likely it is to be found in a given place.

Each dot on the stage is one electron position recorded by a “measurement”. The more we record, the more clearly the density of dots reveals the probability density |ψ|². That is the electron cloud.

Dense regions are where the electron is most likely to be found, not places with many electrons.

Orbital shapes

Draw a surface around the region where the electron is found 90% of the time, and you get what we call the shape of an atomic orbital.

s orbitals are spheres; p orbitals are dumbbells, one along each of x, y and z; most d orbitals are four-leaf clovers, five in all.

Warm and cool colours show the positive and negative phase of the wavefunction ψ, not charge. Phase decides whether atoms can bond. Each glowing shell is a surface of equal probability; the deeper inside, the higher the probability density.

Radial distribution and nodes

The radial distribution function P(r) = r²R² gives the probability of finding the electron in a thin spherical shell at radius r.

The 1s peak lies exactly at r = a₀ (the Bohr radius). Between the peaks of 2s and 3s are spheres where the probability is zero, called radial nodes; there are n − l − 1 of them.

In the slice, dark rings are radial nodes and dark straight lines are angular nodes.

Energy levels and the Aufbau principle

In a many-electron atom, electrons fill orbitals one by one following these rules:

Aufbau principle: lower energy levels fill first. Note that 4s fills before 3d.

Pauli principle: an orbital holds at most 2 electrons, with opposite spins.

Hund's rule: within one level, electrons first occupy separate orbitals with parallel spins.

Electron configuration

Click an element in the periodic table to see its electron configuration and orbital diagram. The stage shows the cloud of its valence electrons: blue for s, orange for p, violet for d.

Quantum numbers

Three quantum numbers identify an atomic orbital:

n, the principal quantum number, sets the shell and size; l, the angular quantum number (0 ≤ l ≤ n − 1), sets the shape; m, the magnetic quantum number (−l ≤ m ≤ l), sets the orientation.

Total nodes = n − 1: l angular nodes and n − l − 1 radial nodes.

Library

All 30 atomic orbitals from 1s to 4f. Drag to rotate and scroll to zoom.