Electronic Structure and Periodic Properties

This is Unit Five of Chemistry, Part Two: orbitals, configurations and periodic trends. Part One ended with the four quantum numbers. This part uses them — first to describe what an orbital actually looks like, then to fill an atom's orbitals in order, and finally to explain the periodic table's trends. The through-line for that last stretch is a single mechanism: effective nuclear charge, the pull an outer electron actually feels once inner electrons have shielded part of it. Every trend here — radius, ionisation energy, electron affinity — is a consequence of it, which means they are derivable rather than facts to memorise separately. By the end you will be able to say why an orbital holds at most two electrons; say what an orbital diagram shows that configuration notation cannot; say what sets an element's block; say what drives every trend in this unit; and say what a sharp jump in successive ionisation energies marks.

Three entries. What the probability region actually looks like for each subshell type, and the pattern of nodes running through all of them — which is what makes the more complicated shapes an extension rather than a new rule.

A sphere.

Chem 0834 The s Orbital Shape

Every s orbital, with l equal to zero, has a spherical probability region centred on the nucleus — the simplest shape at every shell. The 1s orbital is a single sphere; the 2s is a larger sphere with an internal node. A larger n's s orbital is not merely a bigger sphere: it gains internal nodes as n increases.

Two lobes.

Chem 0836 The p Orbital Shape

Every p orbital, with l equal to one, has a two-lobed, dumbbell-shaped region split by a node at the nucleus, oriented along one of three axes. The three 2p orbitals point along the x, y and z axes, each shaped as two lobes with a node between. That node sits at the nucleus, meaning there is zero probability of finding the electron precisely there.

More lobes.

Chem 0838 The d and f Orbitals

The d orbitals, l equal to two, and f orbitals, l equal to three, have more complex multi-lobed regions than s or p, with more nodes as l rises. A d subshell holds five orbitals and an f subshell seven, each set by an ml value. Their lobe counts follow the same nodal pattern s and p already show — there is no new rule to learn.

Three entries, and between them they determine every ground-state configuration. One sets how many electrons an orbital can hold, one sets the order orbitals are filled in, and one sets how electrons distribute within a set of equal-energy orbitals.

Why only two.

Chem 0844 The Pauli Exclusion Principle

The Pauli exclusion principle states that no two electrons in one atom share the same complete set of four quantum numbers. Two electrons in the same orbital already share n, l and ml, so they must carry opposite spin values. That is what limits every orbital to two electrons — once n, l and ml are fixed, only two spin values remain.

Lowest first.

Chem 0847 The Aufbau Principle

The Aufbau principle states that electrons fill an atom's orbitals from the lowest available energy upward as more electrons are added. Building carbon's six electrons fills 1s, then 2s, then two of the three 2p orbitals in increasing energy order. Filling order tracks energy rather than shell number — the 4s orbital fills before 3d despite its lower principal quantum number.

Spread out first.

Chem 0850 Hund's Rule

Hund's rule states that electrons fill degenerate orbitals singly, with parallel spins, before any orbital in that set takes a second electron. Nitrogen's three 2p electrons each occupy a separate 2p orbital with parallel spin rather than pairing up in fewer orbitals. Pairing electrons early, before every orbital in the set holds one, violates the arrangement the rule predicts.

Four entries. The compact notation chemists use, the diagram that carries information the notation cannot, the split between the electrons that react and the ones that do not, and then the procedure applying all three filling rules at once.

Subshell by subshell.

Chem 0853 Electron Configuration Notation

Electron configuration notation lists each occupied subshell as its principal quantum number, the subshell letter, and a superscript electron count, in filling order. Oxygen's configuration, 1s2 2s2 2p4, shows two electrons in 1s, two in 2s and four in 2p, for eight in total. Those superscripts are electron counts, not exponents — never multiplied or raised to a power.

Boxes and arrows.

Chem 0856 Orbital Diagrams

An orbital diagram represents each orbital as a box and each electron as an arrow, with arrow direction showing spin, adding detail the notation lacks. Nitrogen's 2p diagram shows three boxes each holding one upward arrow, matching Hund's rule. Configuration notation cannot show which orbitals in a subshell hold unpaired electrons — only a diagram shows that.

Which ones react.

Chem 0859 Core Electrons Versus Valence Electrons

Valence electrons occupy an atom's outermost shell, while core electrons fill the complete inner shells beneath, matching a noble gas's configuration. Sodium's configuration, written as neon in brackets followed by 3s1, shows ten core electrons abbreviated and one valence electron. Chemical reactivity is governed chiefly by valence electrons, since core electrons are shielded from most chemical interactions by the shells outside them.

All three rules at once.

Chem 0862 Writing an Electron Configuration

Writing a ground-state configuration means filling orbitals in Aufbau order, respecting Pauli's two-electron limit and Hund's rule in any degenerate subshell, until every electron matching the atomic number is placed. Phosphorus, atomic number fifteen, fills 1s2 2s2 2p6, then 3s2, then places its last three singly across the three 3p orbitals — giving 1s2 2s2 2p6 3s2 3p3, whose superscripts sum to fifteen. Pairing two 3p electrons before each orbital holds one violates Hund's rule even though the total still comes out right.

Two entries. What the periodic table's four blocks actually record about an element's configuration, and the handful of elements that fill their orbitals in a different order than the rules predict.

Which block, and why.

Chem 0865 Electron Configuration and Periodic Table Blocks

The periodic table's s, p, d and f blocks group elements whose highest-energy electron, added last by Aufbau, occupies that subshell type. Aluminium sits in the p block because its last-added electron occupies a 3p orbital. An element's block is set by which subshell that last-added electron enters, not by which subshells appear anywhere in its full configuration.

A few depart.

Chem 0868 Exceptions to the Aufbau Filling Order

A few elements fill orbitals in a way that departs from the Aufbau sequence, favouring a half-filled or fully filled d subshell over the predicted order. Some transition metals place one fewer electron in the s subshell than plain Aufbau order predicts, shifting it into d instead. These are a recognised feature of certain transition metals rather than evidence that Aufbau is unreliable elsewhere.

Nine entries closing the unit. One mechanism first — the pull an outer electron actually feels — and then five trends that all follow from it, a structural note on a sixth property, and the capstone that shows why the mechanism alone is not quite enough.

What the electron feels.

Chem 0875 Effective Nuclear Charge (Zeff)

Effective nuclear charge is the net positive charge an outer electron feels, after inner electrons partially shield it from the full nuclear charge. An outer electron in a heavier atom feels less than the full charge, since core electrons cancel part of the pull. Effective nuclear charge is the mechanism behind every periodic trend that follows — those trends are its consequence.

Smaller across, larger down.

Chem 0878 Atomic Radius Trend

Atomic radius decreases across a period as rising effective nuclear charge pulls electrons inward, and increases down a group as added shells outweigh that pull. Across a period, added protons raise the effective charge faster than shielding rises, drawing the outermost electrons closer. Radius does not track atomic number alone — within a period, more protons shrink the atom rather than expand it.

Losing an electron.

Chem 0881 Ionic Radius: Cations

A cation is smaller than its parent atom, since removing an electron leaves fewer electrons for the same nuclear charge to pull inward. Aluminium's neutral atom has a larger radius than the Al three-plus ion, since losing three electrons exposes a smaller core to a less shielded pull. The smaller radius comes from a changed electron-to-proton balance, not from the nucleus losing protons.

Gaining one.

Chem 0883 Ionic Radius: Anions

An anion is larger than its parent atom, since adding an electron raises electron-electron repulsion without any added nuclear charge to offset it. A sulfur atom's radius is smaller than the S two-minus anion's, since two added electrons spread negative charge over more space. The larger radius comes from added repulsion at fixed charge, not from a new proton entering the nucleus.

Cost of removal.

Chem 0886 First Ionization Energy Trend

First ionisation energy rises across a period as effective nuclear charge increases, and falls down a group as the removed electron sits farther out. Removing an electron from a small, high-charge atom on a period's right takes more energy than from a larger, lower-charge atom. A few systematic dips interrupt the across-period rise, tied to subshell arrangements, without overturning the underlying trend.

A sudden jump.

Chem 0889 Successive Ionization Energies and the Core-Electron Jump

Each successive ionisation energy is larger than the last, with a sharp jump once removal reaches a core electron rather than a valence one. Sodium's second ionisation energy far exceeds its first, because the first removes its single valence electron and the second reaches into the core. A large jump between successive values marks the boundary between valence and core rather than being a quirk of the element.

Gaining, energetically.

Chem 0892 Electron Affinity Trend

Electron affinity is the energy change when a gaseous atom gains an electron, growing more negative across a period as effective nuclear charge increases. A halogen's high effective charge attracts an added electron strongly, releasing energy and giving a strongly negative affinity. A more negative electron affinity means a stronger pull on the electron, not a measure of reluctance to accept one.

Named, not yet developed.

Chem 0895 Electronegativity, Named Structurally

Electronegativity is an atom's tendency to attract shared electrons in a bond — related to, but distinct from, the electron affinity of an unbonded atom. Unlike electron affinity, it is only meaningfully defined for an atom already bonded to another. This entry names it structurally; its full periodic trend and its role in bond polarity belong to Unit Six's bonding material.

Magnesium against aluminium.

Chem 0900 Capstone: Predicting a Periodic Trend from Electron Configuration and Zeff

Magnesium is neon-core 3s2 and aluminium neon-core 3s2 3p1, so aluminium has one more proton and one more electron. The added proton raises effective nuclear charge and predicts a slightly smaller atom, which the radius trend bears out. But first ionisation energy runs the other way: magnesium's electron leaves a filled 3s subshell while aluminium's leaves a lone 3p electron sitting higher in energy and shielded by the 3s pair beneath it — so aluminium's is measured lower. Predicting from effective nuclear charge alone, without checking which subshell the outermost electron occupies, misses exactly this exception.

Five things to carry out of this part, and out of the unit. An orbital holds at most two electrons because of the Pauli exclusion principle: no two electrons in an atom share all four quantum numbers, and two electrons in the same orbital already share n, l and ml — so only the two spin values are left to distinguish them, and a third electron would have nothing left to differ by. An orbital diagram shows which orbitals within a subshell hold unpaired electrons, which configuration notation cannot: writing nitrogen as 2p3 tells you the count but not that all three sit singly with parallel spins, as Hund's rule requires. An element's block is set by which subshell its last-added electron enters under Aufbau order — not by which subshells appear anywhere in its configuration, which is why aluminium is a p-block element despite having filled s subshells. Every periodic trend in this unit is driven by effective nuclear charge, the net pull an outer electron feels once inner electrons have shielded part of the nucleus: radius, ionisation energy and electron affinity are all consequences of it rather than separate facts. And a sharp jump between successive ionisation energies marks the boundary between valence and core — once removal reaches a core electron the cost rises steeply, which is why sodium's second ionisation energy far exceeds its first. Unit Six takes up chemical bonding and molecular geometry.