Electron Configurations and Orbitals

Spec Mapping — OCR H432 Module 2.2.1 — Electron structure, covering principal quantum shells, s/p/d/f sub-shells and the orbitals they contain, the shapes of s and p atomic orbitals, the Aufbau filling order with the 4s/3d crossover, the Pauli exclusion principle, Hund's rule, full electron configurations of atoms and ions up to krypton (Z = 36), and the anomalous configurations of chromium and copper (refer to the official OCR H432 specification document for exact wording).

Electron configuration is the foundation on which every chemical periodicity argument, every bonding model, and every spectroscopic prediction in the A-Level course is built. The quantum-mechanical picture of atomic structure — discrete energy shells subdivided into sub-shells, each containing a small number of orbitals that hold at most two electrons of opposite spin — emerged from the work of Bohr, Sommerfeld, Schrödinger, and Heisenberg in the 1910s and 1920s. The OCR specification asks you to operate with that picture rather than to derive it: you must be fluent in the Aufbau filling order, recognise the four building-block rules (Aufbau, Pauli, Hund, and "fill 4s before 3d in neutral atoms but lose 4s first when ionising"), and be able to write configurations for any element or ion up to Kr. This lesson builds that fluency, with particular attention to the Cr/Cu anomalies and the cation-ionisation pitfall that is the single most-examined trap at AS-Level.

Key Definitions:

• Shell — principal quantum number $n = 1, 2, 3, \dots$n=1,2,3,…; sets approximate energy and radial extent.
• Sub-shell — within a shell, labelled s, p, d, f according to angular-momentum quantum number $\ell = 0, 1, 2, 3$ℓ=0,1,2,3.
• Orbital — a region of space within a sub-shell described by a wavefunction; can hold a maximum of two electrons of opposite spin.
• Aufbau principle — electrons fill orbitals in order of increasing energy, lowest first.
• Pauli exclusion principle — no two electrons in an atom can have identical sets of all four quantum numbers; equivalently, any orbital holds at most two electrons of opposite spin.
• Hund's rule — within a sub-shell, electrons singly occupy each orbital with parallel spins before pairing.

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Shells, sub-shells and orbitals

Each principal shell $n$n contains $n$n sub-shells:

Shell $n$n	Sub-shells available	Total orbitals	Max electrons
1	1s	1	2
2	2s, 2p	4	8
3	3s, 3p, 3d	9	18
4	4s, 4p, 4d, 4f	16	32

Each sub-shell contains a characteristic number of orbitals:

Sub-shell	Orbitals	Max electrons	$\ell$ℓ value
s	1	2	0
p	3 (p$_x$x​, p$_y$y​, p$_z$z​)	6	1
d	5 (d$_{xy}$xy​, d$_{xz}$xz​, d$_{yz}$yz​, d$_{x^2-y^2}$x2−y2​, d$_{z^2}$z2​)	10	2
f	7	14	3

Each orbital holds at most two electrons of opposite spin (Pauli exclusion).

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The shapes of s, p and d orbitals

The atomic orbital is a quantum-mechanical wavefunction; its squared modulus gives the probability density of finding the electron at any point in space. OCR asks you to know the shape of s and p orbitals qualitatively; d orbitals appear when you reach transition-metal chemistry in Module 5.3 but you should at least recognise that there are five of them with the names given above.

s orbital Spherical (no angular node) 1 orbital per s sub-shell

p_x orbital x Dumbbell along x-axis Node at nucleus

p_y orbital y Dumbbell along y-axis

p_z orbital Dumbbell along z-axis 3 p orbitals per sub-shell mutually perpendicular

(Boundary-surface diagrams: surface within which there is ~90 % probability of finding the electron)

s orbitals

Spherical, centred on the nucleus, with no angular nodes. 2s is larger and more diffuse than 1s; 3s larger than 2s; each higher-$n$n s orbital has additional radial nodes (places where the wavefunction passes through zero). The OCR specification asks only for the qualitative spherical shape.

p orbitals

Dumbbell-shaped, with a single angular node passing through the nucleus. Three p orbitals per sub-shell, each oriented along one of the three mutually-perpendicular Cartesian axes ($x$x, $y$y, $z$z). The three p orbitals are degenerate (same energy) in a free atom; they split under the influence of bonding (Module 2.2.2) and under ligand field interactions (Year 13 transition metal chemistry).

d orbitals

Five d orbitals per sub-shell. Four of them are "cloverleaf" shapes ($d_{xy}, d_{xz}, d_{yz}, d_{x^2-y^2}$dxy​,dxz​,dyz​,dx2−y2​); the fifth ($d_{z^2}$dz2​) is a dumbbell along the z-axis with a torus around the equator. You do not need to draw d-orbital shapes at AS; you need only to know there are five of them holding up to ten electrons.

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Aufbau filling order

Electrons fill orbitals in order of increasing energy. The standard A-Level filling order is:

$1s \to 2s \to 2p \to 3s \to 3p \to 4s \to 3d \to 4p \to 5s \to 4d \to 5p$1s→2s→2p→3s→3p→4s→3d→4p→5s→4d→5p

The 4s before 3d crossover is the single most important point. In a neutral atom of Sc (Z = 21), the 4s orbital is slightly lower in energy than the 3d, so 4s fills first. Once both are filled, the energy ordering swaps — 3d becomes the lower — and this is why 4s electrons are removed first when a transition metal forms a cation.

flowchart TD
    A[Start with empty atom, count electrons Z] --> B[Fill 1s up to 2 e-]
    B --> C[Fill 2s up to 2 e-]
    C --> D[Fill 2p up to 6 e- using Hund]
    D --> E[Fill 3s, then 3p with Hund]
    E --> F[Fill 4s up to 2 e-]
    F --> G[Fill 3d up to 10 e- using Hund]
    G --> H[Special: Cr is 3d5 4s1, Cu is 3d10 4s1]
    H --> I[Fill 4p, 5s, 4d, 5p in order]
    I --> J[Done at electron Z]

The traditional Madelung rule (used at university to predict filling order) states: orbitals fill in order of increasing $n + \ell$n+ℓ, and within the same $n + \ell$n+ℓ, the lower-$n$n one fills first. This gives 1s (n + ℓ = 1) < 2s (2) < 2p, 3s (3) < 3p, 4s (4) < 3d, 4p, 5s (5) < 4d, 5p, 6s (6).. — exactly the A-Level filling order. You do not need to know the rule by name, but recognising the pattern (s before next-period s before previous-period d) helps when constructions get long.

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Hund's rule and orbital box diagrams

When electrons fill degenerate orbitals (e.g. the three 2p orbitals), they singly occupy each orbital with parallel spins before pairing. This minimises electron-electron repulsion (the two electrons in different orbitals avoid each other in space).

Orbital "box" diagram for nitrogen (Z = 7, configuration 1s² 2s² 2p³):

Nitrogen (Z = 7): 1s² 2s² 2p³ ↑↓ 1s ↑↓ 2s ↑ ↑ ↑ 2p (Hund: singly with parallel spin)

Oxygen (Z = 8): 1s² 2s² 2p⁴ ↑↓ 1s ↑↓ 2s ↑↓ ↑ ↑ 2p (one pair, two singly filled)

Iron (Z = 26): [Ar] 3d⁶ 4s² 3d sub-shell (filled left-to-right by Hund, then pair): ↑↓ ↑ ↑ ↑ ↑ 4s: ↑↓ — drawn after 3d for ions (3d is lower)

The diagram makes the Pauli (paired arrows must be antiparallel) and Hund (singly filled before pairing) rules visually clear.

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Full electron configurations Z = 1 → 36

Z	Element	Configuration
1	H	1s¹
2	He	1s²
3	Li	1s² 2s¹
4	Be	1s² 2s²
5	B	1s² 2s² 2p¹
6	C	1s² 2s² 2p²
7	N	1s² 2s² 2p³
8	O	1s² 2s² 2p⁴
9	F	1s² 2s² 2p⁵
10	Ne	1s² 2s² 2p⁶
11	Na	1s² 2s² 2p⁶ 3s¹
12	Mg	1s² 2s² 2p⁶ 3s²
13	Al	[Ne] 3s² 3p¹
14	Si	[Ne] 3s² 3p²
15	P	[Ne] 3s² 3p³
16	S	[Ne] 3s² 3p⁴
17	Cl	[Ne] 3s² 3p⁵
18	Ar	[Ne] 3s² 3p⁶
19	K	[Ar] 4s¹
20	Ca	[Ar] 4s²
21	Sc	[Ar] 3d¹ 4s²
22	Ti	[Ar] 3d² 4s²
23	V	[Ar] 3d³ 4s²
24	Cr	[Ar] 3d⁵ 4s¹ (anomaly)
25	Mn	[Ar] 3d⁵ 4s²
26	Fe	[Ar] 3d⁶ 4s²
27	Co	[Ar] 3d⁷ 4s²
28	Ni	[Ar] 3d⁸ 4s²
29	Cu	[Ar] 3d¹⁰ 4s¹ (anomaly)
30	Zn	[Ar] 3d¹⁰ 4s²
31	Ga	[Ar] 3d¹⁰ 4s² 4p¹
35	Br	[Ar] 3d¹⁰ 4s² 4p⁵
36	Kr	[Ar] 3d¹⁰ 4s² 4p⁶

Convention: for filled atoms write sub-shells in shell-number order (3d before 4s). For ions where 4s electrons have been removed, this matters even more — see below.

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The chromium and copper anomalies

Two first-row transition metals violate the simple Aufbau rule:

• Cr (Z = 24): expected [Ar] 3d⁴ 4s², actual [Ar] 3d⁵ 4s¹.
• Cu (Z = 29): expected [Ar] 3d⁹ 4s², actual [Ar] 3d¹⁰ 4s¹.

In both cases an electron has been promoted from 4s into 3d to achieve a half-filled or filled d sub-shell. Why? At AS-level we say: "a half-filled or completely-filled d sub-shell offers extra stability". At deeper level this stability arises from the favourable exchange energy of parallel-spin electrons in degenerate orbitals (Cr) and the symmetric closed-shell stability of d¹⁰ (Cu). These are the only first-row anomalies; later in the d-block (e.g. Mo, Ag, Au) similar promotions occur and the explanation generalises.

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Cation configurations — the 4s-out-first rule

When a transition metal forms a cation, 4s electrons are removed before 3d electrons. The reason: once 3d is partly populated, the 3d orbitals become lower in energy than 4s (the order reverses). Therefore the highest-energy electrons in a filled or partly-filled transition-metal atom sit in 4s, and these are the first to be ionised.