IMAT Chemistry · Atomic Structure

Shells, Orbitals and Electron Configurations

Electrons sit in shells, split into s, p, d and f subshells of orbitals; they fill the lowest energy orbitals first, two per orbital, spreading out before pairing.

All Atomic Structure notes

Why this matters

The 2014 paper asked which atomic number gives a configuration ending in p⁵, and the 2025 ministry paper asked how many electrons one orbital can hold and with what spins. Every ion configuration question on the next page also starts here.

Concept 1 of 4: Shells, subshells and orbitals, and how many electrons each holds

Electrons do not orbit like planets. Each one occupies an orbital, a region of space where it is likely to be found, and each orbital holds at most two electrons. Orbitals of the same shape and energy form a subshell, and the subshells of one energy level form a shell.

Definition

A shell (energy level) has a number $n = 1, 2, 3, \dots$ ; higher $n$ means further from the nucleus and higher energy.
Each shell splits into subshells labelled s, p, d, f. Shell $n$ has $n$ kinds of subshell.
An orbital holds at most 2 electrons. s orbitals are spherical; p orbitals are dumbbell-shaped, three of them at right angles.
Shell $n$ holds at most $2n^2$ electrons: 2, 8, 18, 32.

Subshell	Orbitals in it	Maximum electrons	First shell that has it
s	1	2	n = 1
p	3	6	n = 2
d	5	10	n = 3
f	7	14	n = 4

Shell 3 has 3s, 3p and 3d: 1 + 3 + 5 = 9 orbitals, so up to 18 electrons.

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Period 3 has 8 elements, but shell 3 holds 18 electrons

The 3d subshell only starts filling after 4s, in period 4. So the third row of the table stops at 8 elements, while the third shell can eventually hold

2 \times 3^2 = 18

electrons.

Concept 2 of 4: Quantum numbers and the Pauli exclusion principle

Four numbers describe each electron in an atom, like an address: the shell, the subshell, the particular orbital, and the spin. The Pauli principle says no two electrons in an atom share the same full address. Since an orbital fixes the first three numbers, only the spin is left to tell its two electrons apart.

Definition

The Pauli exclusion principle: no two electrons in one atom have the same four quantum numbers.
So an orbital holds at most two electrons, with opposite (antiparallel) spins.
The allowed values depend on each other: $l$ runs from 0 to $n - 1$ , and $m_l$ runs from $-l$ to $+l$ .
The number of $m_l$ values ( $2l + 1$ ) is the number of orbitals in the subshell: 1, 3, 5, 7.

Quantum number	Symbol	Allowed values	What it describes
Principal	$n$	1, 2, 3, ...	The shell: energy and size
Angular momentum (azimuthal)	$l$	0 to $n - 1$ (0 = s, 1 = p, 2 = d, 3 = f)	The subshell: orbital shape
Magnetic	$m_l$	$-l$ to $+l$ , whole numbers	Which orbital: its orientation
Spin	$m_s$	$+\tfrac{1}{2}$ or $-\tfrac{1}{2}$	The direction of the electron's spin

Practice this conceptself-check · 3 quick reps

Two electrons in one orbital have opposite spins

An orbital holds two electrons at most, and they must have antiparallel (opposite) spins, by the Pauli principle. Options with two parallel spins, one electron only, or three or four electrons per orbital are wrong.

Concept 3 of 4: Writing electron configurations with the Aufbau principle and Hund's rule

Electrons go into the lowest energy orbitals available, like water filling the lowest part of a container first. The surprise is that 4s is slightly lower in energy than 3d in an empty atom, so it fills first. Inside a subshell, electrons repel each other, so they spread out one per orbital before any pair up.

Definition

Aufbau principle: fill subshells in order of increasing energy.
Hund's rule: in a set of equal-energy orbitals (a p, d or f subshell), electrons occupy separate orbitals with parallel spins before pairing.
A configuration lists subshells with the electron count as a superscript: $1s^2\,2s^2\,2p^3$ for nitrogen. The superscripts add up to the number of electrons.
Noble-gas shorthand: $[\mathrm{Ne}]$ stands for $1s^2\,2s^2\,2p^6$ and $[\mathrm{Ar}]$ for $1s^2\,2s^2\,2p^6\,3s^2\,3p^6$ .
For d-block atoms, $[\mathrm{Ar}]\,3d^6\,4s^2$ and $[\mathrm{Ar}]\,4s^2\,3d^6$ mean the same thing.

Order of filling

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p

$<$ lower in energy, so filled first

Worked example

Write the ground-state configurations of phosphorus (

Z = 15

) and iron (

Z = 26

), and give the number of unpaired electrons in each.

Practice this conceptself-check · 3 quick reps

4s fills before 3d

After 3p comes 4s, not 3d. Potassium is

[\mathrm{Ar}]\,4s^1

, not

[\mathrm{Ar}]\,3d^1

. The 3d subshell starts filling only at scandium,

Z = 21

Hund's rule: a p⁴ subshell has two unpaired electrons, not four

Three p orbitals take one electron each first; a fourth electron must pair. So

p^4

has 2 unpaired electrons and

p^3

has 3, the most a p subshell can have.

Concept 4 of 4: The chromium and copper exceptions to the filling order

A half-filled or completely filled d subshell is especially stable. For chromium and copper, moving one electron from 4s into 3d reaches one of these arrangements, and the energy gained outweighs the small cost of the move. So their real configurations break the simple filling order by one electron.

Definition

Chromium ( $Z = 24$ ) is $[\mathrm{Ar}]\,3d^5\,4s^1$ : a half-filled 3d subshell and six unpaired electrons.
Copper ( $Z = 29$ ) is $[\mathrm{Ar}]\,3d^{10}\,4s^1$ : a full 3d subshell.
The elements below them in the same groups often show the same pattern (molybdenum, silver, gold).
These are the two exceptions IMAT expects you to know. All other atoms in periods 1 to 4 follow the Aufbau order.

Element	Predicted by the filling order	Actual ground state	Why
Chromium, Z = 24	$[\mathrm{Ar}]\,3d^4\,4s^2$	$[\mathrm{Ar}]\,3d^5\,4s^1$	Half-filled 3d subshell is extra stable
Copper, Z = 29	$[\mathrm{Ar}]\,3d^9\,4s^2$	$[\mathrm{Ar}]\,3d^{10}\,4s^1$	Full 3d subshell is extra stable
Molybdenum, Z = 42	$[\mathrm{Kr}]\,4d^4\,5s^2$	$[\mathrm{Kr}]\,4d^5\,5s^1$	Same pattern as chromium (same group)
Silver, Z = 47	$[\mathrm{Kr}]\,4d^9\,5s^2$	$[\mathrm{Kr}]\,4d^{10}\,5s^1$	Same pattern as copper (same group)

Practice this conceptself-check · 3 quick reps

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Writing electron configurations with the Aufbau principle and Hund's rule
Order of filling
$1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p$

Reference tables (3)

Shells, subshells and orbitals, and how many electrons each holds4 rows

Subshell	Orbitals in it	Maximum electrons	First shell that has it
s	1	2	n = 1
p	3	6	n = 2
d	5	10	n = 3
f	7	14	n = 4

Shell 3 has 3s, 3p and 3d: 1 + 3 + 5 = 9 orbitals, so up to 18 electrons.

Quantum numbers and the Pauli exclusion principle4 rows

Quantum number	Symbol	Allowed values	What it describes
Principal	$n$	1, 2, 3, ...	The shell: energy and size
Angular momentum (azimuthal)	$l$	0 to $n - 1$ (0 = s, 1 = p, 2 = d, 3 = f)	The subshell: orbital shape
Magnetic	$m_l$	$-l$ to $+l$ , whole numbers	Which orbital: its orientation
Spin	$m_s$	$+\tfrac{1}{2}$ or $-\tfrac{1}{2}$	The direction of the electron's spin

The chromium and copper exceptions to the filling order4 rows

Element	Predicted by the filling order	Actual ground state	Why
Chromium, Z = 24	$[\mathrm{Ar}]\,3d^4\,4s^2$	$[\mathrm{Ar}]\,3d^5\,4s^1$	Half-filled 3d subshell is extra stable
Copper, Z = 29	$[\mathrm{Ar}]\,3d^9\,4s^2$	$[\mathrm{Ar}]\,3d^{10}\,4s^1$	Full 3d subshell is extra stable
Molybdenum, Z = 42	$[\mathrm{Kr}]\,4d^4\,5s^2$	$[\mathrm{Kr}]\,4d^5\,5s^1$	Same pattern as chromium (same group)
Silver, Z = 47	$[\mathrm{Kr}]\,4d^9\,5s^2$	$[\mathrm{Kr}]\,4d^{10}\,5s^1$	Same pattern as copper (same group)

Watch out for (4)

Period 3 has 8 elements, but shell 3 holds 18 electrons
→ Shells, subshells and orbitals, and how many electrons each holds
Two electrons in one orbital have opposite spins
→ Quantum numbers and the Pauli exclusion principle
4s fills before 3d
→ Writing electron configurations with the Aufbau principle and Hund's rule
Hund's rule: a p⁴ subshell has two unpaired electrons, not four
→ Writing electron configurations with the Aufbau principle and Hund's rule

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