Periodic Trends

The usual way this topic is taught is as a set of arrows drawn over a periodic table: radius increases this way, ionisation energy that way, eight arrows in all, learned by rote. It works until a question asks you to compare two elements that are neither in the same row nor the same column, at which point the arrows are silent.

There is a better route, and it is not longer. Almost every periodic trend is the outcome of two quantities pulling against each other:

• how strongly the nucleus pulls on the outermost electrons, and
• how far away those electrons are.

Get those two right for any pair of elements and you can derive the arrow instead of recalling it. The rest of this page is about making the first quantity concrete, because the second is just the shell number.

Effective nuclear charge, calculated

An outer electron in a chlorine atom does not feel a pull of +17. Sixteen other electrons stand between it and the nucleus, cancelling much of that charge. What is left is the effective nuclear charge, Zeff:

Zeff = Z − S

where S is the screening constant. Getting S exactly requires solving the whole atom, but John Slater published a set of empirical rules in 1930 that get remarkably close, and running them once makes the whole topic click.

Slater's rules, for an outer s or p electron: other electrons in the same shell contribute 0.35 each, electrons in the shell one below contribute 0.85 each, and everything deeper contributes a full 1.00.

Sodium, 1s² 2s² 2p⁶ 3s¹, screening the 3s electron. Nothing else is in shell 3. Shell 2 holds eight electrons at 0.85, giving 6.80. Shell 1 holds two at 1.00, giving 2.00.

S = 6.80 + 2.00 = 8.80
Zeff = 11 − 8.80 = 2.20

Chlorine, 1s² 2s² 2p⁶ 3s² 3p⁵, screening one of the 3p electrons. Six other electrons share shell 3, at 0.35 each: 2.10. Shell 2 gives 6.80 again, shell 1 gives 2.00.

S = 2.10 + 6.80 + 2.00 = 10.90
Zeff = 17 − 10.90 = 6.10

That is the whole story of a period in two calculations. Crossing from sodium to chlorine adds six protons but only six electrons to the same shell, and same-shell electrons screen each other badly — 0.35 apiece rather than the 0.85 or 1.00 that inner electrons manage. So the pull on the outer electrons nearly triples while the shell they occupy does not change. Everything gets smaller, harder to ionise and more electron-hungry from left to right, and this is why.

Down a group, the pull does not change at all

Run the same calculation for potassium, 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹. Shell 3 holds eight electrons at 0.85 for 6.80; shells 1 and 2 hold ten at 1.00 for 10.00.

S = 16.80
Zeff = 19 − 16.80 = 2.20

Exactly sodium's value. Repeat it for rubidium and you get 2.20 again. Adding a full shell of electrons adds almost exactly as much screening as the new protons add charge, so the outermost electron of every alkali metal feels essentially the same pull.

This is the cleanest possible demonstration that group trends are about distance, not about charge. Potassium's outer electron is further out than sodium's, in a shell of higher n, and that alone accounts for potassium being larger, easier to ionise and more reactive. Nothing about the nuclear pull has changed.

The one alkali metal that breaks the pattern is lithium, which comes out at 1.30 because it has no shell two levels down to contribute a full 1.00 each. Lithium's chemistry is correspondingly odd, and that is not a coincidence.

Slater's numbers are approximations, and better ones exist

Slater's rules are a 1930 fit, not a calculation from first principles, and they should be presented as such.

Values derived from real atomic wavefunctions — the Clementi–Raimondi set from 1963 is the standard reference — differ noticeably. They give sodium's 3s electron a Zeff of about 2.51 rather than 2.20, and chlorine's 3p about 6.12 rather than 6.10. Slater happens to be very close for chlorine and several per cent out for sodium.

Use Slater's rules for reasoning and for exam answers, since that is what courses teach. Do not treat the numbers as measurements. What survives the discrepancy is the pattern — roughly constant down a group, sharply rising across a period — and the pattern is what the trends depend on.

Three trends with their own treatment

The three best-known consequences each have enough depth to need a page of their own, and this one deliberately does not duplicate them:

• Atomic radius — including the awkward fact that atoms have no edge, so the quantity being trended has to be defined before it can be measured.
• Ionisation energy — including the two places where period 2 dips against the trend, and what successive ionisations reveal.
• Electronegativity — including the three competing scales that disagree about the numbers.

The trend that is not a straight line

Not every property varies smoothly, and melting point across period 3 is the standard counterexample. In degrees Celsius: sodium 98, magnesium 650, aluminum 660, silicon 1,414, phosphorus 44, sulfur 115, chlorine −102, argon −189.

The value climbs by a factor of fourteen and then collapses by a factor of thirty in a single step. No amount of reasoning about effective nuclear charge produces that shape, because melting point is not a property of isolated atoms at all — it is a property of the structure the element forms.

• Sodium, magnesium and aluminum are metals, and their melting points climb as each contributes more electrons to the bonding.
• Silicon holds the peak because its melting point is a bond-breaking energy rather than a separation energy. Breaking bonds costs far more than pulling whole molecules apart, and the height of the peak is the size of that gap.
• Phosphorus, sulfur and chlorine are small molecules — P₄, S₈, Cl₂ — held to each other only by weak intermolecular attraction. Melting separates molecules rather than breaking bonds, and costs almost nothing. Sulfur beats phosphorus only because S₈ is bigger than P₄.
• Argon is single atoms with the weakest attractions of all.

The lesson generalises: whenever a property depends on how atoms are arranged rather than on the atoms themselves, expect a discontinuity at the point where the structure type changes.

Electron affinity, where fluorine loses to chlorine

Electron affinity is the energy change when a gaseous atom gains an electron. Broadly it becomes more exothermic across a period, for the same Zeff reason as everything else — but it is far less regular than ionisation energy, and two features are worth knowing.

Chlorine beats fluorine. Chlorine releases about 349 kJ/mol on gaining an electron; fluorine only about 328. Fluorine should win on every argument about nuclear pull, and loses because it is so small that the incoming electron is forced into a compact shell already crowded with seven others. The repulsion costs more than the extra attraction gains. The same reversal appears at the top of every group in that corner of the table.

The sign convention is genuinely inconsistent between sources. Some textbooks define electron affinity as the energy released, and quote chlorine as +349. Others define it as an enthalpy change, ΔH, and quote −349. Both are in wide use, and a question that gives you a bare number without a sign convention is ambiguous. State which you are using.

Group 2 and group 18 elements have effectively zero or unfavourable electron affinities, because adding an electron would mean starting a new subshell or a new shell entirely.

From metals to non-metals, and the oxides in between

Metallic character increases going down and to the left, and the boundary running diagonally through boron, silicon, arsenic and tellurium marks where elements stop clearly being one thing or the other.

The most systematic way to see the change is in the oxides across period 3. Sodium oxide and magnesium oxide are basic. Aluminum oxide is amphoteric — it reacts as a base toward strong acids and as an acid toward strong bases, which is exactly what a borderline element should do. Silicon dioxide is weakly acidic, and the oxides of phosphorus and sulfur are strongly acidic.

That progression from basic through amphoteric to acidic is a single continuous consequence of the element's grip on electrons, and it is the clearest bridge between periodic position and the behaviour described under acids and bases.

Answering a diagonal comparison

The question that defeats memorised arrows is the one comparing, say, magnesium with gallium — different period, different group, arrows pointing opposite ways.

The reliable approach is to name the two effects and decide which is larger. Moving down usually wins, because adding an entire shell changes the distance more than the extra protons change the pull. But "usually" is doing real work in that sentence, and where the two effects roughly cancel, the elements end up chemically similar in ways the table's layout does not advertise. Lithium resembles magnesium; beryllium resembles aluminum; boron resembles silicon. These diagonal relationships are not curiosities — lithium and magnesium both form nitrides directly, and lithium's carbonate breaks down in a furnace where its heavier group-mates' do not.

If a question sets up a diagonal comparison, say which effect you think dominates and why. An answer that reasons and lands slightly off will usually score better than one that guesses correctly and explains nothing.