The s, p, d and f Blocks

The periodic table looks like an awkward shape that somebody had to memorise. It is not. It is four rectangles set side by side, and their widths are 2, 6, 10 and 14.

Those four numbers are the electron capacities of the s, p, d and f subshells, and they are where the entire outline of the table comes from — the two narrow columns on the left, the six wide ones on the right, the ten-wide slab in the middle and the fourteen-wide strip marooned at the bottom. Nothing about the shape is arbitrary once you see that.

Four rectangles, widths 2, 6, 10 and 14

An element's block is named for the subshell that receives its last electron as you build the atom up in filling order.

• The s-block is groups 1 and 2, plus helium: two columns, because an s subshell holds two electrons.
• The p-block is groups 13 to 18: six columns, matching the three p orbitals at two electrons each.
• The d-block is groups 3 to 12: ten columns, from five d orbitals.
• The f-block is the detached strip of lanthanides and actinides: fourteen columns, from seven f orbitals.

Where those capacities come from — counting the allowed orientations of each subshell — is worked through under orbitals and subshells. The point here is that the capacities were established from atomic theory and the table's shape then matched them, which is one of the better pieces of evidence that the theory is describing something real.

Why the d-block starts two rows late

If subshells filled in the order 1, 2, 3, 4, the d-block would begin in period 3, and it does not — the first transition metals appear in period 4. The f-block is displaced further still, appearing first in period 6.

The rule behind the offset is worth learning in this compact form: the nd subshell fills during period n+1, and the nf subshell fills during period n+2. So 3d fills in period 4, 4d in period 5, 4f in period 6, and 5f in period 7.

This is a direct consequence of the filling order, in which 4s comes before 3d and 6s before 4f. The gap opens because the energy of a subshell depends on both its shell number and its shape, and a diffuse d orbital in a low shell can sit above a compact s orbital in a higher one. The electron configuration guide sets out the ordering and how to apply it.

The offset also explains the blank space at the top of the d-block and the f-block. There is no period-3 transition metal not because the table is missing entries but because 3d has not started filling yet at that point in the sequence.

Period lengths are just the widths added up

Period lengths look like a sequence to memorise: 2, then 8 twice over, then 18 twice, then 32 twice. They are addition.

• Period 1 contains only an s subshell: 2.
• Periods 2 and 3 contain s and p: 2 + 6 = 8.
• Periods 4 and 5 add a d subshell: 2 + 10 + 6 = 18.
• Periods 6 and 7 add an f subshell as well: 2 + 14 + 10 + 6 = 32.

Each length appears twice because a new subshell type becomes available every second period, and that is the whole explanation for why the table widens in steps rather than smoothly.

Reading a configuration off a coordinate

Blocks turn the table into a lookup table for electron configurations. Three pieces of information — the period, the block, and how far into the block the element sits — give the outermost part of the configuration directly.

Tin. Period 5, p-block, second column of the p-block, which is group 14. Second column of p means p², and the period gives the shell number: it ends in 5p². Written out, tin is [Kr] 4d¹⁰ 5s² 5p².

Zirconium. Period 5, d-block, second column. The d subshell in period 5 is 4d, one shell behind, so zirconium ends in 4d², and the full form is [Kr] 4d² 5s².

The shell-number rule is the part people get wrong: within a d-block element the d subshell carries a number one lower than the period, and within an f-block element two lower. Period 6's f-block elements are filling 4f.

This works for the overwhelming majority of elements. It fails for about twenty of them, where the ground state is not what the filling order predicts, and those anomalies cluster in the d-block and f-block for reasons of subshell stability.

The f-block is detached to save paper

The lanthanides and actinides are printed below the table with a gap, which suggests they are somehow separate. They are not. They belong in periods 6 and 7, between the s-block and the d-block, and every element in the table is in a single continuous sequence of atomic number.

The 32-column "long form" of the table shows them where they belong. Nobody prints it, because a table 32 columns wide is unusable on a page or a wall. The familiar 18-column version is a formatting compromise, and the two are the same table.

It is a compromise with a cost. Generations of students have inferred that the f-block elements are exotic or unimportant, when they include the metals inside every strong permanent magnet, every energy-efficient lamp phosphor, and the fuel of every nuclear reactor.

Is group 3 lanthanum or lutetium?

There is a real, unresolved disagreement about what belongs in group 3 beneath scandium and yttrium, and it has run since 1982.

One camp puts lanthanum and actinium there, with the f-block beginning at cerium. The other puts lutetium and lawrencium there, with the f-block beginning at lanthanum.

The configuration argument favours lutetium. Lanthanum's ground state is [Xe] 5d¹ 6s² — it has no f electron at all, which is peculiar for the first element of the f-block. Lutetium has a completely filled 4f¹⁴ and a single 5d electron, which is exactly what a d-block element should look like. Trends in atomic radius and other properties across group 3 are also smoother with lutetium in place.

The counter-argument is chemical: lanthanum's behaviour resembles scandium's and yttrium's more closely than lutetium's does, and the periodic table has always been organised around chemical similarity first.

IUPAC appointed a task group, chaired by Eric Scerri, to settle it. Its analysis has favoured the lutetium arrangement, but no formal recommendation has been adopted, and published tables disagree with one another today. Many hedge by printing "La–Lu" and "Ac–Lr" across the disputed cells, which is a way of declining to answer.

Helium is an s-block element in the wrong column

Helium is 1s². By configuration it is unambiguously an s-block element, and its place is above beryllium at the top of group 2.

It is printed above neon instead, because it behaves like a noble gas — inert, monatomic, with a full outer shell. That is the table choosing observed chemistry over electron configuration, and it is the only place where it does so this openly.

An alternative layout, Charles Janet's left-step table from 1928, organises strictly by filling order and does place helium above beryllium. It is more logical, it makes the block structure perfectly regular, and essentially nobody uses it — because a table that puts the least reactive element in a column of reactive metals fails at the job a periodic table is for.

Hydrogen presents the same tension without a settled answer. Its 1s¹ configuration says group 1, its chemistry says it is not an alkali metal, and different publishers place it above group 1, above group 17, in both places, or floating unattached.

Are zinc, cadmium and mercury transition metals?

The d-block and the transition metals are usually treated as the same set, and by IUPAC's own definition they are not.

A transition element is defined as one whose atom has a partially filled d subshell, or which can form a cation with a partially filled d subshell. Zinc, cadmium and mercury have d¹⁰ in the atom and d¹⁰ in every common ion they form. On that definition, group 12 is in the d-block but is not transition.

The chemistry supports the exclusion. These three are colourless in solution, form few complexes of the kind their neighbours specialise in, and show a single oxidation state where iron and manganese show half a dozen — all consequences of a full d subshell.

There is one loose end. Mercury(IV) fluoride, in which mercury would have an incomplete d subshell and would therefore qualify as a transition metal, was reported in 2007 from a low-temperature matrix experiment. Attempts to reproduce it have not succeeded, and its existence remains contested.