Periodicity

The previous lesson gave the rules for putting electrons into orbitals, and this one is what those rules look like with every element laid out side by side. The periodic table is not a filing system for chemical facts, it is the electron configurations of the elements in order of atomic number, folded so that atoms with matching outer configurations share a column. Every trend on it follows from two quantities: the effective nuclear charge $Z_{eff}$ felt by an outer electron, and the principal quantum number $n$ of its shell. $Z_{eff}$ sets how hard the nucleus pulls, $n$ how far out the electron sits, and what follows is an argument about which is winning.

A table that predicted elements nobody had seen

Dmitri Mendeleev was not the first to notice that chemical properties recur, but he was the first to trust the recurrence more than the data. Arranging the known elements by atomic weight in 1869, he found valency and reactivity recurring at intervals, and where the pattern demanded an element no laboratory possessed he left the square empty. A catalogue can only be wrong about what it contains; a theory can be wrong about what it omits.

He went further and specified them. His eka-silicon, the gap below silicon in group 14, was described in 1871 with a mass, a density, an oxide and the volatility of its chloride. Clemens Winkler isolated germanium from argyrodite in 1886.

Property	Eka-silicon, predicted 1871	Germanium, measured 1886
Atomic weight	$72$	$72.3$
Density / g cm⁻³	$5.5$	$5.47$
Oxide	${EsO}_{2}$ , density $4.7$	${GeO}_{2}$ , density $4.70$
Chloride	boils below $100$ degrees Celsius, density $1.9$	boils at $86$ degrees Celsius, density $1.88$

Gallium and scandium had already arrived in 1875 and 1879 with comparable agreement. Predictions of that precision about substances nobody had handled are not what a lucky filing scheme produces. The table was reporting something physical, and that something was electron structure.

Moseley and the ordering variable

Mendeleev's arrangement carried a flaw he could not explain. Strict ordering by atomic weight put tellurium ( $127.6$ ) after iodine ( $126.9$ ), and argon ( $39.9$ ) after potassium ( $39.1$ ), placing each in a group whose chemistry it plainly did not share. He inverted both pairs on chemical grounds, contradicting his own rule and suspecting the weights were simply wrong.

The resolution came in 1913 from Henry Moseley, who bombarded metal targets with electrons and measured the X-rays emitted as an electron fell into a vacancy in the innermost shell. The frequencies did not scale with atomic weight; they obeyed $\sqrt{ν} \propto (Z - σ)$ , with $Z$ an integer stepping up by one along the table and $σ$ near $1$ for the $K$ series, just as a one-electron Bohr calculation predicts.

That integer is the nuclear charge, and Moseley showed it, not mass, orders the elements. Tellurium at $Z = 52$ genuinely precedes iodine at $Z = 53$ ; the weights invert only because tellurium's stable isotopes are neutron-rich. The same argument settled argon and potassium, and cobalt and nickel, and since $Z$ counts without skipping it fixed how many gaps were left to fill.

The shape of the table is orbital filling

Read the table left to right and you are reading the aufbau order out loud. In the two columns on the left the outermost electron enters an $s$ orbital, in the six on the right a $p$ , in the ten in the middle a $d$ , in the detached strip an $f$ . These are the blocks, and their widths are the degeneracies $2 (2 ℓ + 1)$ , doubled by spin: two, six, ten, fourteen.

The period lengths follow. Period 1 offers only $1 s$ and holds two elements; periods 2 and 3 offer $n s$ and $n p$ , so eight each. From period 4 the $(n - 1) d$ set has fallen below $n p$ and slots in after $n s$ , giving $2 + 10 + 6 = 18$ , and period 5 repeats it. Period 6 adds $4 f$ : $2 + 14 + 10 + 6 = 32$ . The sequence $2, 8, 8, 18, 18, 32$ is a census of orbital capacity in filling order.

The $f$ block is pulled out beneath the main body for the width of the page: printed in full the table would be thirty-two columns across, driving the transition metals far from the elements they resemble. That is typography rather than chemistry, and it hides the fact that the lanthanides sit inside period 6, not below it.

Size: atomic and ionic radii

Cross period 2 and each step adds a proton and an electron, the electron joining the same $n = 2$ shell. Electrons in one shell screen each other poorly, so $Z_{eff}$ climbs by roughly $0.65$ per step while $n$ is unchanged, and the shell is reeled in: lithium $152$ pm, beryllium $112$ , boron $85$ , carbon $77$ , nitrogen $75$ , oxygen $73$ , fluorine $71$ . Descend group 1 and $Z_{eff}$ barely moves, since each new inner shell screens almost completely, while $n$ grows: $152$ , $186$ , $227$ , $248$ , $265$ pm to caesium.

Ions restate the argument more violently. Cations shrink because stripping sodium's lone $3 s$ electron removes a whole shell, leaving ${Na}^{+}$ at $102$ pm against the atom's $186$ . Anions expand because adding an electron to chlorine leaves $n$ alone but shares seventeen protons among eighteen electrons, cutting $Z_{eff}$ and swelling the ion to $181$ pm from a covalent radius of $99$ .

An isoelectronic series isolates the effect. $N^{3 -}$ , $O^{2 -}$ , $F^{-}$ , ${Na}^{+}$ , ${Mg}^{2 +}$ and ${Al}^{3 +}$ all hold ten electrons in the same configuration, so $n$ and the shielding are fixed and only $Z$ varies. The radii fall monotonically: $146$ , $140$ , $133$ , $102$ , $72$ , $53$ pm.

One irregularity earns its own name. The $4 f$ electrons added across the lanthanides are diffuse and shield badly, so $Z_{eff}$ creeps up over fourteen consecutive elements and the atoms contract. This lanthanide contraction of some $15$ pm lands on everything after it in period 6. Hafnium ends up the same size as the zirconium above it ( $159$ pm against $160$ , and $71$ against $72$ as $4 +$ ions), so the two are chemically almost inseparable.

Ionisation energy and its two dips

The first ionisation energy is the work needed to remove the least tightly held electron, and by Coulomb's law it scales as $Z_{eff}$ over the orbital radius. It therefore rises across a period and falls down a group, mirroring size. Period 2 runs $520$ , $899$ , $801$ , $1086$ , $1402$ , $1314$ , $1681$ , $2081$ kJ mol⁻¹ to neon, while group 1 falls $520$ , $496$ , $419$ , $403$ , $376$ to caesium.

Two of those numbers go the wrong way, and both are diagnostic. Boron ( $801$ ) is easier to ionise than beryllium ( $899$ ) because beryllium's outermost electron is a $2 s$ and boron's a $2 p$ . The $2 p$ orbital penetrates the $1 s$ core less, so it is screened more effectively and lies higher in energy despite boron's greater nuclear charge. The same group 2 to group 13 dip recurs between magnesium and aluminium, direct evidence that $s$ and $p$ subshells are split.

Oxygen ( $1314$ ) is likewise easier to ionise than nitrogen ( $1402$ ). Nitrogen's $2 p^{3}$ puts one electron in each $2 p$ orbital with parallel spins, as Hund's rule requires. Oxygen's fourth $2 p$ electron finds no empty orbital and must pair, and two electrons in one region repel strongly. That penalty is handed back when the electron leaves, and the same group 15 to group 16 dip appears between phosphorus and sulfur.

Electron affinity, the awkward cousin

Electron affinity is the energy released when a gaseous atom accepts an electron. Broadly it grows across a period with $Z_{eff}$ and shrinks down a group as $n$ grows, so the halogens are the champions while the noble gases and group 2 metals give negative values, meaning an unbound anion. The trend is much rougher than the ionisation trend, because the incoming electron joins a crowded shell and the repulsion can rival the nuclear attraction.

Nitrogen is the clearest case. Its affinity is about $- 7$ kJ mol⁻¹, effectively zero, because the arriving electron must pair up in a half-filled $2 p^{3}$ set and the repulsion nearly cancels the attraction. Carbon, which still has a genuinely empty $2 p$ orbital, releases $122$ kJ mol⁻¹.

Fluorine breaks the naive expectation outright. Sitting above chlorine with the higher $Z_{eff}$ and smaller radius, it ought to be the better acceptor, yet it releases $328$ kJ mol⁻¹ against chlorine's $349$ . Fluorine's $2 p$ shell is so compact that seven electrons are already packed into a tiny volume and an eighth arrives into severe repulsion, while chlorine's roomier $3 p$ shell buys the same pull at a lower crowding cost.

Electronegativity

Electronegativity is not an experimental quantity in the way ionisation energy is. Linus Pauling defined it thermochemically in 1932, noting that a bond between unlike atoms is almost always stronger than the mean of the two homonuclear bonds and attributing the excess $Δ$ to ionic character:

| χ_{A} - χ_{B} | = 0.102 \sqrt{Δ}, Δ = D (AB) - \sqrt{D (AA) D (BB)}

with $Δ$ in kJ mol⁻¹. Only differences are defined, so the scale needs an anchor, and fluorine takes the maximum at $3.98$ , with caesium at $0.79$ and francium near $0.7$ .

Robert Mulliken offered a cleaner justification. An atom that both holds its own electrons tightly and welcomes new ones will draw electron density towards itself in a bond, so $χ_{M} \approx (I + A) / 2$ . Suitably scaled, Mulliken values track Pauling values closely, and both rise across a period and fall down a group for the reasons you now expect.

The caveat matters. Electronegativity belongs to an atom in a molecule rather than to an isolated atom, and it shifts with oxidation state, hybridisation and neighbouring groups: carbon is more electronegative in an $s p$ hybrid than in an $s p^{3}$ one, because more $s$ character means more penetration towards the nucleus. The tabulated numbers are a useful average, not a constant.

Metals, diagonals and the anomalous first row

Metallic character is what low ionisation energy looks like in bulk. An element whose valence electrons are weakly held surrenders them to a delocalised sea, giving lustre, malleability and conduction, so metals crowd the bottom left where $Z_{eff}$ is low and $n$ high, non-metals the top right, and the metalloids run diagonally between them. The oxides trace the same gradient, from basic sodium oxide through amphoteric alumina to acidic sulfur trioxide.

Because $Z_{eff}$ rises rightwards and $n$ downwards, a step right combined with a step down partly cancels the two and leaves charge density roughly unchanged. This is the diagonal relationship. Lithium resembles magnesium more than sodium: both form normal oxides rather than peroxides, both combine directly with $N_{2}$ , and both have carbonates that decompose on heating. Beryllium resembles aluminium: amphoteric oxides, covalent bridged chlorides, passivation by an oxide film.

That diagonal is a symptom of a broader first-row anomaly. Second-period elements have no accessible $d$ orbitals, capping their covalency at four: nitrogen forms ${NF}_{3}$ but never ${NF}_{5}$ , while phosphorus gives ${PF}_{5}$ readily and sulfur ${SF}_{6}$ . They are also small and of high charge density, so their $2 p$ orbitals overlap sideways well and they form strong multiple bonds, which is why nitrogen is a triple-bonded gas while phosphorus catenates into $P_{4}$ and silica builds a single-bonded lattice. Small size also crowds lone pairs and weakens single bonds: F-F is only $158$ kJ mol⁻¹ against Cl-Cl at $242$ , much of the reason fluorine is so aggressive.

Every property here has reduced to one competition, between how hard the nucleus pulls and how far out the electron sits. What it fixes is where electron density goes when two atoms meet: whether one surrenders an electron outright, or whether the two share it evenly or unequally. That is the question lesson 6 takes up, because knowing which way the electrons move is knowing how the atoms bond.