Modern periodic law

The modern periodic law. The physical and chemical properties of elements are a periodic function of their atomic number ($Z$), not their atomic mass. This one substitution — mass out, atomic number in — is the entire content of the "modern" revision of Mendeléev's law, and it is worth being precise about why it works rather than just memorising it.

Why atomic number is the right variable. Atomic number equals the number of protons in the nucleus of an atom, and for a neutral atom it also equals the number of electrons. As $Z$ increases by one across a period, exactly one electron is added, and the Aufbau principle fixes where that electron goes — filling shells and subshells in a definite, repeating order. Chemical behaviour — valence, the tendency to gain or lose electrons, reactivity, bonding pattern — is governed almost entirely by the outermost (valence) electrons. Since the valence-shell pattern itself repeats periodically as $Z$ increases (a new principal shell begins after every noble gas), every property that depends on it must repeat periodically too. Atomic mass, by contrast, is not a clean single-electron-at-a-time count: it depends on the number of neutrons as well, and neutron number does not track chemical behaviour at all — which is exactly why mass-based ordering occasionally goes wrong.

Resolving Mendeléev's clashes. Mendeléev ordered by atomic mass, so wherever mass order and proton-count order disagree, his table put the wrong element first. Argon ($Z = 18$, mass $\approx 39.9$) is heavier than potassium ($Z = 19$, mass $\approx 39.1$) even though it has one fewer proton; ordering by mass would place Ar after K, but ordering by atomic number places Ar correctly before K — matching Ar's noble-gas inertness against K's vigorous alkali-metal reactivity. The same clash recurs for cobalt ($Z = 27$, mass $\approx 58.9$) and nickel ($Z = 28$, mass $\approx 58.7$): Co is slightly lighter by neutron count quirks yet has one more proton, and atomic-number order again gives the chemically correct sequence. Every one of Mendeléev's stubborn exceptions disappears the moment the ordering variable is changed from mass to atomic number — this is the single biggest reason the modern law replaced the historical one.

From the law to the table. Because properties repeat periodically in $Z$, arranging elements in rows of increasing atomic number automatically produces columns of chemically similar elements — the long form of the periodic table. A new period (horizontal row) begins each time a new principal shell starts filling; a group (vertical column) collects elements that reach the same valence-shell pattern, so they share similar reactivity. The modern table has seven periods and eighteen groups, and elements sort further into $s$, $p$, $d$, and $f$ blocks by which subshell receives the last electron added — a classification carried forward in the companion article on blocks, groups and periods.

This is a purely descriptive, classification-based law rather than an equation, so the reasoning that carries the exam marks is causal, not algebraic.

Cause. Atomic number is a count of protons, and for a neutral atom that count also fixes the number of electrons and, via the Aufbau principle, exactly which orbitals those electrons occupy.

Effect. Chemical behaviour is decided almost entirely by the valence-shell electron pattern, so as $Z$ rises one unit at a time, that pattern cycles through a repeating sequence — and every property riding on it (valence, atomic size trends, metallic or non-metallic character, reactivity) cycles with it.

Contrast. Atomic mass adds a second, chemically irrelevant ingredient — neutron count, which varies between isotopes of the same element and does not track any electron pattern. Ordering by mass therefore sometimes gets the sequence wrong (Ar/K, Co/Ni), while ordering by the true chemical driver, atomic number, never does.

Consequence for isotopes. Isotopes of one element share the same atomic number even though their masses differ, so the modern law automatically places every isotope in a single position — something Mendeléev's mass-based scheme could never cleanly do.

Question. Using the modern periodic law, explain why tellurium ($Z = 52$, atomic mass $\approx 127.6$) is correctly placed before iodine ($Z = 53$, atomic mass $\approx 126.9$) in the periodic table, even though Te is heavier than I.

Step 1. Identify the chemical families first, independent of any ordering scheme. Iodine is a reactive non-metal that forms the $\text{I}^-$ ion and belongs with fluorine and chlorine — the halogens (Group 17). Tellurium behaves like selenium — a chalcogen (Group 16).

Step 2. Check what mass-based ordering would do. Since I (mass $\approx 126.9$) is lighter than Te (mass $\approx 127.6$), Mendeléev's scheme would list iodine first — placing a halogen ahead of a chalcogen in violation of each element's actual family.

Step 3. Apply the modern law instead. Te has $Z = 52$ and I has $Z = 53$; since $52 < 53$, atomic-number ordering places Te before I automatically, with no forcing required, and this order lands each element in its correct group — Te in Group 16, I in Group 17.

Step 4. Conclude. Atomic mass gives the wrong sequence here for the same reason it fails for Ar/K and Co/Ni: it carries neutron-count noise that has nothing to do with chemistry. Atomic number gives the chemically consistent order, which is exactly the anomaly the modern periodic law was designed to fix.

Competitive stretch

If asked to generalise: whenever an element with more protons happens to have a lower average atomic mass than its neighbour (because of a lighter mix of isotopes), a mass-ordered table misplaces it. The modern law is immune to this because it never looks at mass at all — only at $Z$, which is fixed and unambiguous for every element regardless of which isotopes happen to be abundant on Earth.

• Stating the law as "a periodic function of atomic mass" — that is Mendeléev's older, superseded version; the modern law is defined on atomic number.
• Treating atomic number and atomic mass as interchangeable "roughly the same thing" — they usually increase together, which is precisely why the Ar/K, Co/Ni and Te/I cases (where they disagree) are the ones examiners ask about.
• Forgetting that isotopes share one atomic number — a student who still thinks in terms of mass may wrongly expect each isotope to need its own slot in the table.
• Assuming the modern law also fixed hydrogen's dual position (resembling both alkali metals and halogens); it did not — that ambiguity is a separate, still-open feature of hydrogen's chemistry, not something atomic-number ordering resolves.

Ask the tutor: if the Ar/K or Te/I anomaly still feels confusing, ask the AI tutor to walk through the proton-versus-neutron distinction with a few more element pairs.