CHEMISTRY · LESSON 03 OF 12

Periodic table

Electron configurations follow from filling orbitals in order of energy. The periodic table groups elements with similar outer electrons, and effective nuclear charge explains the trends in size, ionisation energy and electronegativity.

What this lesson explains

The periodic table is chemistry’s map. From an element’s position you can predict its outer electrons, the ions it forms, how reactive it is, whether it is a metal, and what kind of bonds it makes. These predictions guide material selection, corrosion behaviour and reaction design in chemical engineering.

Before you begin

Quantum numbers and subshells

Shell n contains subshells s, p, d, … with 1, 3, 5, … orbitals (see Quantum theory). Each orbital holds two electrons.

Noble-gas shorthand

Write the preceding noble gas in brackets for the core: Na = [Ne]3s¹.

The idea, made visible

Electrons fill orbitals from the lowest energy upward (the Aufbau principle): 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, … Each orbital holds at most two electrons with opposite spins (Pauli exclusion principle). Within a subshell of equal-energy orbitals, electrons occupy separate orbitals with parallel spins before pairing (Hund’s rule).

The valence electrons (outermost shell) govern chemistry. Elements in the same group have the same valence configuration — for example ns¹ for the alkali metals — and therefore similar properties. The table’s blocks show which subshell is being filled: s, p, d or f.

Across a period Z_eff rises: atoms shrink and hold electrons more tightly. Down a group a new shell is added: atoms grow and lose outer electrons more easily.

The key to the trends is effective nuclear charge Z_eff: the positive charge an outer electron actually feels, less than Z because inner electrons shield it. Across a period, Z increases while the added electrons are in the same shell and shield each other poorly, so Z_eff increases: the atoms become smaller and hold their electrons more tightly. Down a group, a new, larger shell is added each period, so atoms get bigger and outer electrons are easier to remove.

So atomic radius decreases across a period and increases down a group; ionisation energy (energy to remove an electron) and electronegativity (pull on bonding electrons) increase across and decrease down. Small exceptions have clear reasons: ionisation energy drops from Be to B (the 2p electron is higher in energy than 2s) and from N to O (pairing repulsion in O’s 2p).

Ions: cations are smaller than their atoms (fewer electrons, sometimes a whole shell removed); anions are larger. When transition metals form ions they lose their 4s electrons before 3d: Fe is [Ar]3d⁶4s², Fe²⁺ is [Ar]3d⁶.

Period 3: first ionisation energy and atomic radius
element	configuration	IE₁ (kJ/mol)	radius (pm)
Na	[Ne]3s¹	496	186
Mg	[Ne]3s²	738	160
Al	[Ne]3s²3p¹	578	143
Si	[Ne]3s²3p²	787	118
P	[Ne]3s²3p³	1012	110
S	[Ne]3s²3p⁴	1000	103
Cl	[Ne]3s²3p⁵	1251	99
Ar	[Ne]3s²3p⁶	1521	71

The general rise has two dips: Mg → Al (the 3p electron is higher in energy and slightly shielded by 3s) and P → S (the fourth 3p electron is paired and repelled). Radii are approximate and differ between sources depending on how they are defined.

Key terms

Electron configuration: The distribution of electrons among orbitals, e.g. O: 1s²2s²2p⁴.
Valence electrons: Electrons in the outermost shell (for main-group elements: the ns and np electrons).
Effective nuclear charge Z_eff: The net positive charge felt by an electron after shielding by other electrons; roughly Z − (number of core electrons) for valence electrons.
Ionisation energy (IE): Energy required to remove an electron from a gaseous atom or ion: X(g) → X⁺(g) + e⁻. Successive IEs increase.
Electronegativity: The ability of an atom in a molecule to attract bonding electrons (Pauling scale: F = 3.98 highest).
Paramagnetic / diamagnetic: Having unpaired electrons (attracted by a magnetic field) / all electrons paired (weakly repelled).

The formulas and what they mean

Symbols, meanings and units
Symbol	Meaning	Unit
nℓ^x	x electrons in subshell ℓ of shell n (e.g. 2p⁴)	—
Z_eff	effective nuclear charge	proton charges
IE₁, IE₂	first, second ionisation energies	kJ/mol
χ	electronegativity	no unit

Filling order

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p …

Conditions and limits: Ground states of most atoms. Exceptions include Cr ([Ar]3d⁵4s¹) and Cu ([Ar]3d¹⁰4s¹).

Capacity

s: 2, p: 6, d: 10, f: 14 electrons

Conditions and limits: Each orbital holds 2 electrons of opposite spin (Pauli).

Valence effective charge (estimate)

Z_eff ≈ Z − (core electrons)

Conditions and limits: A rough guide for comparing main-group atoms; refined models (Slater’s rules) are beyond this topic.

Ion formation, transition metals

remove ns before (n − 1)d

Conditions and limits: Fe → Fe²⁺: remove the two 4s electrons.

Why it works: Why a large jump in ionisation energy reveals the valence electrons

Magnesium ([Ne]3s²) has IE₁ = 738, IE₂ = 1451 and IE₃ = 7733 kJ/mol.

IE₁ and IE₂ remove the two 3s valence electrons.
Each removal is harder because the ion becomes more positive.
IE₃ must remove an electron from the 2p core, much closer to the nucleus with far less shielding.
A new, inner shell.
So IE₃ is about five times IE₂.
The jump marks the end of the valence shell.

This is why magnesium forms Mg²⁺ but never Mg³⁺ in chemical reactions.

A first worked example

Writing configurations and predicting trends

Count the electrons (Z for a neutral atom; adjust for charge).
Fill subshells in the Aufbau order, respecting capacities; use noble-gas shorthand.
For orbital diagrams, apply Hund’s rule; count unpaired electrons.
For cations of transition metals, remove the ns electrons first.
For trends, compare positions: same period → Z_eff argument; same group → number of shells argument. Mention known exceptions.

Configuration and unpaired electrons of oxygen

Problem. Write the ground-state configuration of oxygen (Z = 8) and find the number of unpaired electrons.

1s² 2s² 2p⁴.
Fill 1s, 2s, then 2p with the remaining four electrons.
2p has three orbitals: put one electron in each, then pair the fourth: ↑↓ ↑ ↑.
Hund’s rule.

Result: 1s²2s²2p⁴, with 2 unpaired electrons (oxygen atoms are paramagnetic).

What it means: A 2p³ configuration (nitrogen) would have 3 unpaired electrons.

A different case

A transition-metal ion

Problem. Write configurations for Fe (Z = 26) and Fe³⁺.

Fe: [Ar]3d⁶4s².
18 core electrons + 8.
Fe³⁺: remove the two 4s electrons, then one 3d: [Ar]3d⁵.
Remove ns before (n − 1)d.

Result: Fe = [Ar]3d⁶4s²; Fe³⁺ = [Ar]3d⁵.

What it means: Writing Fe³⁺ as [Ar]3d³4s² is a common error; the 4s electrons go first.

More worked cases

Each case below uses a different skill. Every step and result is shown.

Electrons needed for a noble-gas configuration

Problem. An atom has shell arrangement 2, 8, 7. How many electrons must it gain to complete an octet? Which element and ion is it?

Outer shell has 7; an octet needs 8: gain 1.
Main-group atoms tend to reach 8 valence electrons.
Total electrons 17 ⇒ chlorine; ion Cl⁻.
Z = 17.

Result: Gains 1 electron to form Cl⁻ (configuration of argon).

What it means: Halogens (group 17) form 1− ions; alkali metals (2, 8, 1 etc.) form 1+ ions.

Compare sizes and ionisation energies

Problem. Arrange Na, Mg and K in order of increasing atomic radius, and of increasing first ionisation energy.

Na and Mg are in period 3; Mg has higher Z_eff, so Mg is smaller than Na.
Across a period.
K is below Na (an extra shell), so K is larger than Na.
Down a group.
Ionisation energy follows the reverse order.
Smaller atoms hold electrons more tightly.

Result: Radius: Mg < Na < K. First ionisation energy: K < Na < Mg (419 < 496 < 738 kJ/mol).

What it means: This is why potassium reacts with water more violently than sodium.

Isoelectronic ions

Problem. Order O²⁻, F⁻, Na⁺ and Mg²⁺ by size.

All have 10 electrons (the neon configuration).
Same electron count.
Their proton numbers are 8, 9, 11, 12: more protons pull the same electrons closer.
Higher nuclear charge, smaller ion.

Result: Mg²⁺ < Na⁺ < F⁻ < O²⁻ (smallest to largest).

What it means: For isoelectronic species, size decreases as Z increases.

Common misunderstandings

Misunderstanding: Filling 3d before 4s for neutral atoms, or removing 3d before 4s for ions.
Correct idea: Fill 4s before 3d; ionise 4s before 3d.
Misunderstanding: Pairing electrons before filling each orbital of a subshell singly.
Correct idea: Hund’s rule: singly first, parallel spins.
Misunderstanding: “Atoms get bigger across a period because they have more electrons.”
Correct idea: They get smaller: the added electrons are in the same shell while Z_eff increases.
Misunderstanding: Treating trends as rules with no exceptions.
Correct idea: Be/B and N/O ionisation dips, and Cr/Cu configurations, are the standard exceptions.

Keep in mind

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p …Filling order
s: 2, p: 6, d: 10, f: 14 electronsCapacity
Z_eff ≈ Z − (core electrons)Valence effective charge (estimate)
remove ns before (n − 1)dIon formation, transition metals

Scope of this lesson

Quantitative shielding (Slater’s rules), lanthanides and actinides, and detailed transition-metal chemistry are beyond this topic.

Next: Chemical bonding. Atoms bond by transferring electrons (ionic) or sharing them (covalent). Lewis structures count the electrons; VSEPR turns electron domains into shapes; shape and electronegativity decide polarity.

Original study text. Sources and credits.

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