Electron Configurations and Orbitals

Learning Objectives (OCR Spec 2.2.1)

By the end of this lesson you should be able to:

• Describe shells and sub-shells (s, p, d, f) and the orbitals they contain
• Sketch the shapes of s and p atomic orbitals
• Explain the filling order of orbitals (aufbau), Pauli exclusion and Hund's rule
• Write the full electron configuration (1s2 2s2 2p6 ...) of atoms and ions up to krypton (Z = 36)
• Explain the anomalous configurations of chromium and copper

Shells and Sub-Shells

Electrons occupy shells (principal quantum number, n = 1, 2, 3, ...). Within each shell, electrons are further organised into sub-shells labelled s, p, d and f. Each sub-shell contains one or more orbitals - regions of space in which there is a high probability of finding an electron.

Sub-shell	Number of orbitals	Max electrons
s	1	2
p	3 (px, py, pz)	6
d	5	10
f	7	14

Number of sub-shells available increases with n:

• n = 1: 1s
• n = 2: 2s, 2p
• n = 3: 3s, 3p, 3d
• n = 4: 4s, 4p, 4d, 4f

Each orbital holds a maximum of 2 electrons, which must have opposite spins (Pauli exclusion principle).

Shapes of Atomic Orbitals

s orbitals

Spherical, centred on the nucleus. Larger n means a larger, more diffuse sphere. All s orbitals have no angular nodes.

  _____
 /     \
|   .   |    s orbital: spherical
 \_____/

p orbitals

Dumbbell-shaped, with a node at the nucleus. Three p orbitals per sub-shell (px, py, pz), oriented along the three mutually perpendicular Cartesian axes.

    ___
   |   |
    ---
    | |         p orbital: two lobes
    | |         along one axis
    ---
   |   |
    ---

d orbitals

Five d orbitals per sub-shell with more complex shapes (four "cloverleaf" + one dumbbell with torus). OCR A-Level requires you to know that d sub-shells contain five orbitals holding up to 10 electrons, but you do not need to draw individual d shapes.

Filling Order (Aufbau Principle)

Electrons fill orbitals in order of increasing energy. The order you must remember is:

1s -> 2s -> 2p -> 3s -> 3p -> 4s -> 3d -> 4p -> 5s -> 4d -> 5p

Critical point: 4s fills before 3d because 4s is at lower energy than 3d in a neutral ground-state atom. Similarly, 4s empties before 3d when transition metals form cations (this is a common exam trap).

Orbital Filling Diagram

graph TD
  A[1s] --> B[2s]
  B --> C[2p]
  C --> D[3s]
  D --> E[3p]
  E --> F[4s]
  F --> G[3d]
  G --> H[4p]
  H --> I[5s]

Hund's Rule

When filling degenerate orbitals (orbitals of the same energy, e.g. the three 2p orbitals), electrons occupy them singly with parallel spins before pairing up. This minimises electron-electron repulsion.

Using arrow-in-box notation for the 2p sub-shell in nitrogen (1s2 2s2 2p3):

2p:  [up]  [up]  [up]
     px    py    pz

All three p orbitals contain one electron with the same spin.

Full Electron Configurations

Write the configuration as (nl)^x with ^x the number of electrons in sub-shell nl.

Element	Z	Configuration
H	1	1s1
He	2	1s2
Li	3	1s2 2s1
C	6	1s2 2s2 2p2
N	7	1s2 2s2 2p3
O	8	1s2 2s2 2p4
Ne	10	1s2 2s2 2p6
Na	11	1s2 2s2 2p6 3s1
Al	13	1s2 2s2 2p6 3s2 3p1
Ar	18	1s2 2s2 2p6 3s2 3p6
K	19	1s2 2s2 2p6 3s2 3p6 4s1
Ca	20	1s2 2s2 2p6 3s2 3p6 4s2
Sc	21	1s2 2s2 2p6 3s2 3p6 3d1 4s2
Fe	26	1s2 2s2 2p6 3s2 3p6 3d6 4s2
Zn	30	1s2 2s2 2p6 3s2 3p6 3d10 4s2
Br	35	1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5
Kr	36	1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6