Periodicity and atomic number

Line up all the elements by atomic number and something remarkable happens: their properties repeat in a rhythm. Sodium and potassium, sitting one below the other, both react violently with water and both form 1+ ions — while sodium's neighbour chlorine, one square to the right, behaves nothing like it. This repeating rhythm is periodicity, and the Modern Periodic Table is simply that rhythm made visible: 18 columns (groups) and 7 rows (periods) built from one fact about every atom — how its electrons are arranged in shells. Once you can write an element's shell arrangement, the whole table opens up: its period, its group, its valency, even whether it is a metal or a non-metal fall out from that arrangement alone, with no need to memorise a separate fact for each of a hundred-plus elements.

The core insight

An element's period equals its number of occupied electron shells and its group follows its valence-electron count, so the entire structure of the periodic table — and an element's valency — is read directly off its electron distribution, filled shell by shell using the 2n22n^2 rule.

The core idea

The law that replaced atomic mass. Early tables (Mendeleev's) were built on atomic mass and ran into trouble — some elements had to be placed out of mass order to keep similar elements together. The Modern Periodic Law fixes this: the physical and chemical properties of elements are a periodic function of their atomic number, ZZ, not their atomic mass. Atomic number counts protons in the nucleus, and in a neutral atom, protons equal electrons, so ZZ also fixes the electron count you must arrange.

The grid itself. The table has 18 groups (columns) and 7 periods (rows), with elements placed in strict order of increasing ZZ. Two structural facts do all the work:

  • Period number = number of occupied electron shells. An atom using shells K and L only sits in Period 2; one using K, L, M sits in Period 3.
  • Group number determines the valence-electron pattern. Group 1 elements carry 1 valence electron, Group 2 carries 2, and Groups 13–18 carry 3 through 8 valence electrons respectively (helium, in Group 18, is the one exception, with only 2).

Filling the shells. Electrons occupy shells labelled K, L, M, N outward from the nucleus, innermost first, and each shell has a maximum capacity given by the 2n22n^2 rule, where nn is the shell number:

Maximum electrons in shell n=2n2\text{Maximum electrons in shell } n = 2n^2

where: nn is the shell's position counting outward from the nucleus (n=1n = 1 for K, 22 for L, 33 for M, 44 for N), and the result is the largest number of electrons that shell can hold. Up to atomic number 20, this gives K →2\to 2, L →8\to 8, and M treated as filling to 8 before N begins (even though 2n22n^2 for M would allow 18, that extra capacity is not used until heavier elements beyond this syllabus).

From shells to valency. Atoms are most stable with a full outer shell — 8 electrons (or 2, for a lone K shell), the same arrangement noble gases already have. Valency is how many electrons an atom must lose, gain, or share to reach that stable count. An atom close to empty in its outer shell (1, 2, or 3 valence electrons) tends to lose them, forming a positive ion (electrovalency); one close to full (5, 6, or 7 valence electrons) tends to gain the few it lacks, forming a negative ion; atoms roughly in the middle, or non-metals bonding with each other, share electrons instead (covalency). This single idea — "move toward 8" — sorts elements into metals (electron-losers, left and centre of the table), non-metals (electron-gainers, upper right), metalloids (borderline, e.g. silicon), and noble gases (Group 18, already at 8, and so almost entirely unreactive).

Figure
Three atoms drawn as concentric shells showing sodium with one outer electron losing it chlorine with seven outer electrons gaining one and neon with a full outer shell of eight staying unreactive
Shell arrangement decides valency — the drive toward 8 in the outer shell 11p Sodium 2 8 1 loses 1 electron, forms Na+ 17p Chlorine 2 8 7 gains 1 electron, forms Cl minus 10p Neon 2 8 outer shell already full, unreactive
Derivation ABuilding the K L M N shell capacities from the 2n squared rule

The goal is to derive, purely by substituting shell numbers into the 2n22n^2 rule, the actual maximum electron counts of the K, L, M and N shells that you use every time you write an electron distribution — and to see why the familiar 2, 8, 8 pattern used up to atomic number 20 is not an arbitrary list to memorise but the direct output of one formula applied four times.

Step 1. Take the K shell, the one nearest the nucleus, where n=1n = 1. Substituting into 2n22n^2 gives 2(1)2=2×1=22(1)^2 = 2 \times 1 = 2. So the K shell holds at most 2 electrons — this is why every element from lithium onward starts its distribution with "2," and why helium (with exactly 2 electrons) is already a complete, unreactive noble gas.

Step 2. Take the L shell, n=2n = 2. Substituting gives 2(2)2=2×4=82(2)^2 = 2 \times 4 = 8. The L shell holds at most 8. Combined with Step 1, the first ten electrons fill K then L completely (2+8=102 + 8 = 10), which is exactly the electron count of neon — the second noble gas, and the point at which both the K and L shells are full.

Step 3. Take the M shell, n=3n = 3. Substituting gives 2(3)2=2×9=182(3)^2 = 2 \times 9 = 18, the true maximum for that shell. But at Class 10 level, elements are only tracked up to Z=20Z = 20, and chemically the M shell already behaves as "closed" once it reaches 8 electrons (matching the K and L pattern of an outer octet) — so for these elements the M shell is filled only to 8 before the next shell begins, and the full capacity of 18 is reserved for elements beyond this syllabus.

Step 4. Take the N shell, n=4n = 4, giving 2(4)2=2×16=322(4)^2 = 2 \times 16 = 32 as its eventual maximum — far beyond what is needed here. For Z=19Z = 19 (potassium) and Z=20Z = 20 (calcium), only 1 or 2 electrons enter the N shell once K, L and M(as 8) are full, because a single outer electron in a fresh shell is more stable than forcing the ninth electron into the already octet-like M shell. This is exactly why potassium's distribution is 2, 8, 8, 1 and not 2, 8, 9. Check: summing each element's full distribution must always return its atomic number — for potassium, 2+8+8+1=192 + 8 + 8 + 1 = 19, matching Z=19Z = 19 exactly, confirming the shell-by-shell filling is consistent.

Worked example

Question: Write the electron distribution of potassium (Z = 19), state its period, group, and valency, and predict the type of ion it forms.

Step 1. Potassium has atomic number 19, so a neutral atom has 19 electrons to place in shells.

Step 2. Fill shells innermost first, using the capacities derived above. K shell: fill 2, leaving 19−2=1719 - 2 = 17. L shell: fill 8, leaving 17−8=917 - 8 = 9. M shell (capped at 8 for this syllabus): fill 8, leaving 9−8=19 - 8 = 1. N shell: the last 1 electron goes here, since M is already treated as full at 8.

Step 3. The distribution is 2, 8, 8, 1. As a check, 2+8+8+1=192 + 8 + 8 + 1 = 19, matching Z exactly.

Step 4. Four shells (K, L, M, N) are occupied, so potassium sits in Period 4 — one row below sodium, which has the same outer pattern of 1 valence electron but only three shells.

Step 5. The outermost (N) shell carries 1 electron, matching the Group 1 pattern, so potassium is in Group 1, directly below sodium and lithium — explaining why all three react vigorously with water in the same way.

Step 6. With just 1 valence electron, potassium loses it far more easily than it could gain 7 to complete an octet, giving a valency of 1 and forming the cation K⁺, exactly analogous to Na⁺.

Competitive stretch

Compare potassium (2, 8, 8, 1) with calcium, Z = 20. Following the same filling, calcium's distribution is 2, 8, 8, 2 (2+8+8+2=202+8+8+2=20), placing it in Period 4 (four shells) and Group 2 (2 valence electrons), with valency 2, forming Ca²⁺ — the same group-2 chemistry already seen for magnesium (2, 8, 2) one period up, confirming that group membership, not period, is what fixes an element's characteristic valency.

Common traps

  • Confusing atomic number with atomic mass — the Modern Periodic Law is defined strictly on atomic number (protons), which is why Mendeleev's mass-based table needed exceptions that the modern one does not.
  • Force-filling the M shell to its full 2n22n^2 capacity of 18. Up to Z=20Z = 20, treat M as capped at 8, exactly like K and L reaching their outer-octet limit, with any extra electrons starting a new N shell.
  • Mixing up period and group: period counts occupied shells; group is read from the valence-electron pattern of the outermost shell.
  • Assuming valency always equals the valence electron count. Oxygen has 6 valence electrons but a valency of 2, because it is easier to gain 2 electrons (reaching 8) than to lose 6.

Ask the tutor: If shell-filling or reading period, group, and valency from a distribution still feels shaky, ask the AI tutor to work through Z = 11, 14, and 20 with you until the pattern is automatic.

Why does the M shell get capped at 8 electrons here when 2n squared clearly gives 18 for n equals 3?

The formula's raw answer, 18, is correct in general, but it only becomes relevant for elements past atomic number 20 that this syllabus does not cover. For elements up to Z = 20, the M shell behaves chemically as if it is "full" once it reaches 8, matching the stable-octet pattern already seen in K and L. So potassium and calcium put their extra electron(s) into a fresh N shell rather than continuing to add to M. Treat the 2, 8, 8 pattern as the rule at this level, and reserve the full 2n22n^2 value of 18 for later study.

If group number comes from valence electrons, why does helium (Group 18, only 2 electrons) not follow the same 8-electron pattern as neon or argon?

Helium is the one built-in exception. It has just one shell (K), which is already full at its own maximum of 2 electrons — not 8. Because a full, stable outer shell is what defines a noble gas, helium counts as complete and unreactive with only 2 valence electrons, so it is grouped with the other noble gases (Group 18) despite not having 8. Every other Group 18 element (neon, argon, and so on) does have the full 8.

How can I tell from an electron distribution alone whether an element forms a positive or a negative ion?

Look at how close the outer-shell electron count is to 8 (or to 2, for a single K shell). If there are only 1, 2, or 3 electrons in the outer shell, it is much easier for the atom to lose them than to gain 5, 6, or 7 more, so it forms a positive ion (a metal). If there are 5, 6, or 7 electrons, it is easier to gain the few electrons needed to reach 8, so it forms a negative ion (a non-metal). An outer shell of exactly 8 (or 2) means the atom is already stable and tends not to form ions at all — a noble gas.

Before this

Where this leads