How to Find Any Element's Place in the Periodic Table From One Number

Learning the properties of every element separately would be impossible. Arranged in the right order, though, elements with similar properties line up in columns, and one position tells you a great deal about an element's behaviour.

This part covers how periodic classification developed, finding period and group, naming elements beyond $100$, and the four blocks.

Early schemes grouped elements by atomic mass — triads, then octaves, then Mendeleev's periodic law that properties repeat with atomic mass — and the modern periodic law states that properties are a periodic function of atomic number.

- Dobereiner's triads — in groups of three similar elements, the middle atomic mass is about the average of the other two. For Li, Na, K: $\frac{7+39}{2}=23$, the atomic mass of Na. Only a few triads could be found.
- Newlands' law of octaves — in order of atomic mass, every eighth element resembles the first, like notes of a musical scale; it worked well only for the lighter elements.
- Mendeleev's periodic law — properties are a periodic function of atomic mass. This table grouped elements by similar properties, left gaps for elements not yet known with predicted properties, and sometimes placed a heavier element before a lighter one to keep similar elements together.
- Modern periodic law — X-ray frequencies of elements depend on atomic number, with $\sqrt{\nu }$ increasing steadily with $Z$. Ordering by atomic number removes the anomalies.

Worked example — the anomalies resolved. Argon ($39.9$ u) comes before potassium ($39.1$ u), and tellurium ($127.6$ u) before iodine ($126.9$ u). By atomic mass these look out of order; by atomic number (18 before 19, 52 before 53) they are exactly right.

An everyday example. Arranging students by roll number instead of by height gives one fixed, unambiguous order — just as atomic number does for elements.

The substance. Atomic number, not atomic mass, is the fundamental property that fixes an element's place and chemistry.

**The period equals the principal quantum number of the outermost shell; the group equals the number of valence electrons for s-block elements, $10$ plus the number of $ns$ and $np$ electrons for p-block elements, and the number of $(n-1)d$ plus $ns$ electrons for d-block elements.

Worked examples.

- Chlorine** ($Z=17$): $[\text{Ne}]3s^{2}3p^5$ — outermost shell $n=3$, so period 3; $2+5=7$ valence electrons in the p-block, so **group $10+7=17$
- Strontium** ($Z=38$): $[\text{Kr}]5s^2$ — period 5, group 2
- Iron ($Z=26$): $[\text{Ar}]3d^{6}4s^2$ — period 4; $6+2=8$, so group 8
- Iodine ($Z=53$): $[\text{Kr}]4d^{10}5s^{2}5p^5$ — period 5, group 17

An everyday example. A berth in a train is found by coach number and seat number — period and group work the same way for elements.

The substance. **Helium, $1s^2$, sits in group 18** with the noble gases because its shell is completely filled, even though it has only two electrons.

**Until official names are approved, elements beyond atomic number $100$ get systematic IUPAC names built from a root for each digit followed by "ium", with a three-letter symbol made from the roots' first letters.

Roots:** $0$ nil, $1$ un, $2$ bi, $3$ tri, $4$ quad, $5$ pent, $6$ hex, $7$ sept, $8$ oct, $9$ enn.

Spelling rules: the final "i" of bi and tri is dropped before "ium", and the final "n" of enn is dropped before nil.

Worked examples.

- **$Z=101$: un + nil + un + ium = unnilunium, symbol Unu
- $Z=104$: un + nil + quad + ium = unnilquadium, Unq
- $Z=109$: un + nil + enn + ium = unnilennium, Une
- $Z=113$: un + un + tri + ium = ununtrium, Uut
- $Z=120$: un + bi + nil + ium = unbinilium, Ubn

An everyday example. A newborn baby is often called by a pet name until the naming ceremony — systematic names play the same temporary role for new elements.

The substance. The systematic name depends only on the atomic number**, so any element's temporary name and symbol can be worked out without memorising.

An element belongs to the block of the subshell that receives its last electron: s-block for groups 1 and 2, p-block for groups 13 to 18, d-block for groups 3 to 12, and f-block for the lanthanoids and actinoids.

- s-block ($n{s}^{1-2}$) — reactive metals with low ionisation enthalpies, forming basic oxides; for example sodium and calcium
- p-block ($n{s}^{2}n{p}^{1-6}$) — metals, metalloids and non-metals; group 18 noble gases have full $n{s}^{2}n{p}^6$ shells and are very unreactive
- d-block ($(n-1)d^{1-10}n{s}^{0-2}$) — transition metals: variable oxidation states, coloured ions, and many act as catalysts
- f-block ($(n-2)f^{1-14}$) — inner transition metals: lanthanoids ($4f$) and actinoids ($5f$), the actinoids all radioactive

The s- and p-block elements together are the representative elements.

Worked examples.

- Calcium $[\text{Ar}]4s^2$ — s-block
- Bromine $[\text{Ar}]3d^{10}4s^{2}4p^5$ — p-block
- Copper $[\text{Ar}]3d^{10}4s^1$ — d-block
- Cerium $[\text{Xe}]4f^{1}5d^{1}6s^2$ — f-block

An everyday example. Blue copper sulphate crystals used in school labs owe their colour to a d-block ion, while the glow of a neon sign comes from a p-block noble gas.

The substance. Zinc, cadmium and mercury sit in the d-block but are not typical transition metals, because their d subshells are completely filled.