University11 min

s, p, d, f orbitals: shapes, nodes and counting

Go from an orbital's name to its quantum numbers, shape and nodes, and count the orbitals and electrons of a subshell without hesitation.

The essentials

1

What an orbital is

A single-electron wavefunction, solution of the Schrödinger equation for hydrogen: ψ(r,θ,φ)=Rn,ℓ(r)×Yℓmℓ(θ,φ)\psi(r, \theta, \varphi) = R_{n,\ell}(r) \times Y_\ell^{m_\ell}(\theta, \varphi) The radial part RR sets the extent, the angular part YY (spherical harmonic) sets the shape. It is not a trajectory: ∣ψ∣2|\psi|^2 is a probability density.
2

From the number ℓ to the letter, and the counting

Members only

3

Counting nodes

Members only

4

The shapes to recognise

Members only

5

What the shape controls

Members only

ƒWrite my own sheetOr start from a blank page: rewriting a concept in your own words is how it sticks.