Mendeleev's periodic table of 1869: prediction of eka-elements, the path to atomic-number ordering, and the modern table
Anchor (Master): Mendeleev 1869 Zh. Russ. Fiz.-Khim. Obshch. 1:60; Mendeleev 1871 Liebig's Ann. Suppl. 8:133; Winkler 1886 J. Prakt. Chem. 34:177; Moseley 1913 Phil. Mag. 26:1024; Scerri 2007; Gordin 2004
Intuition Beginner
By 1869 chemists knew about sixty elements — iron, carbon, oxygen, gold, mercury — but had no way to organise them. Some were metals, some were gases, some behaved like one thing in one reaction and a different thing in another. Dmitri Mendeleev, a Russian chemist working in Saint Petersburg, wrote the name and atomic weight of each known element on a separate card and laid the cards out on his desk. After days of rearranging them, he found that when the elements were ordered by increasing atomic weight, their chemical properties returned at regular intervals down the list.
The repetition was not perfect. A few elements seemed out of order — iodine behaved like chlorine but sat too heavy to sit beside it. Mendeleev trusted the chemistry over the weight and swapped them. When no known element fit a slot, he left the slot empty and predicted what the missing element would be like: its atomic weight, its density, the formula of its oxide. He named these hypothetical substances eka-elements — eka-aluminium, eka-boron, eka-silicon — using the Sanskrit word for "one". Within seventeen years all three had been discovered, and their measured properties matched his predictions almost exactly.
Why this matters: Mendeleev's periodic table converted chemistry from a catalogue of unrelated substances into a single predictive system. Unknown elements could now be hunted for by their predicted properties. In 1913 Henry Moseley showed that the correct ordering variable is the atomic number (the charge on the nucleus, equal to the proton count), not atomic weight — resolving the few anomalies Mendeleev had overridden by hand. The modern table extends to 118 elements, ending at oganesson; Mendeleev's framework still organises all of them.
Visual Beginner
The periodic table evolved through four distinct stages that the diagram tracks left to right. The leftmost column sketches Mendeleev's 1869 vertical arrangement, with elements listed by atomic weight and the periodic recurrence visible as horizontal repetitions. The middle column shows the 1871 expanded grid of eight groups and twelve periods with three explicit eka-element gaps marked. The third column shows Moseley's 1913 reordering, in which three atomic-weight inversions (argon before potassium, cobalt before nickel, tellurium before iodine) are corrected by atomic number. The rightmost column shows the modern extended table, including the f-block of lanthanides and actinides separated below the main body and reaching element 118.
The four-panel progression makes one structural point visible at a glance: the periodic law survived three different ordering variables (atomic weight 1869, refined atomic weight 1871, atomic number 1913) and one major reorganisation of the bottom of the table (Seaborg 1944) without losing its core content.
Worked example Beginner
Mendeleev's prediction of eka-silicon versus the discovery of germanium.
In 1871 Mendeleev noticed a gap in his table between silicon (atomic weight 28) and tin (atomic weight 118). The pattern of the surrounding elements implied a missing element in group IV, sitting between silicon and tin, with properties intermediate between the two. He named it eka-silicon and committed to specific numerical predictions. Fifteen years later Clemens Winkler isolated a new element from a silver-coloured mineral called argyrodite at the Freiberg mining academy in Saxony.
Step 1. Mendeleev predicted an atomic weight of about 72. Winkler measured the new element's atomic weight at 72.6 — call it germanium.
Step 2. Mendeleev predicted a density of about 5.5 grams per cubic centimetre. The measured density was 5.35.
Step 3. Mendeleev predicted the oxide would have formula with density 4.7. Germanium's oxide has density 4.7 exactly. He predicted the chloride would boil below 100 degrees Celsius; boils at 86 degrees Celsius.
What this tells us: the eka-silicon prediction was essentially exact, and its confirmation in 1886 was the strongest single argument for the periodic law made in Mendeleev's lifetime.
Check your understanding Beginner
Formal definition Intermediate+
Periodic law (Mendeleev 1869). The chemical properties of the elements are a periodic function of their atomic weights. When the elements are arranged in order of increasing atomic weight , the sequence of chemical behaviours — valence, oxide formula, metallic character — recurs at regular intervals, with periods of length 8 in the short form (after the first row) and 18 in the long form. Mendeleev's 1869 paper organised the elements vertically by atomic weight in a single sequence wrapped at fixed intervals, producing the first periodic table.
Atomic number (Moseley 1913). The atomic number of an element is the charge on its nucleus in units of the elementary charge, equal to the number of protons. Moseley's law relates the frequency of the X-ray line of an element to its atomic number by
with a constant across all elements (where is the Rydberg constant and the speed of light), and a screening factor accounting for the single remaining 1s electron during the transition. The monotonicity of in provides a strictly monotonic total ordering of the elements that supersedes the atomic-weight ordering.
Modern periodic law (post-Moseley). The chemical properties of the elements are a periodic function of their atomic numbers. The periodicity arises from the shell structure of the electron configuration, with shells filling in the order predicted by the Madelung rule. Each period corresponds to the start of a new outermost principal shell; each group corresponds to a recurring outer-shell configuration.
Eka-elements. Given a gap in the periodic table at a specified position , the eka-element at that position is the (then-unknown) element predicted to occupy it by interpolation of the surrounding group members. "Eka" is the Sanskrit word for "one": eka-aluminium sits one row below aluminium in group III, eka-boron one row below boron in group III, eka-silicon one row below silicon in group IV. Mendeleev named four eka-elements in his 1871 paper: eka-aluminium (, confirmed as gallium 1875), eka-boron (, confirmed as scandium 1879), eka-silicon (, confirmed as germanium 1886), and eka-manganese (, confirmed as technetium 1937). Three of the four were confirmed within seventeen years.
Counterexamples to common slips Intermediate+
Mendeleev invented the periodic law single-handedly. No. Döbereiner's triads (1817), Newlands's law of octaves (1865), and Lothar Meyer's independent periodic table (1864 textbook, 1870 expanded paper) all preceded Mendeleev's 1869 paper. Mendeleev's distinctive contribution was the bold prediction of unknown elements and the correction of measured atomic weights, neither of which his rivals pursued.
Mendeleev ordered by atomic number. No. He ordered by atomic weight. Moseley's 1913 X-ray work established atomic number as the correct ordering variable, resolving the three known weight-order anomalies (argon-potassium, cobalt-nickel, tellurium-iodine) that Mendeleev had overridden by hand on chemical grounds.
Mendeleev predicted every element discovered after 1869. No. He missed the noble gases entirely (Rayleigh and Ramsay, 1894 onward), the lanthanides as a coherent series, the actinides (Seaborg, 1944), and the synthetic transactinides. The eka-element predictions covered exactly the four group-and-period gaps in the 1871 short-form table.
The periodic table is fixed. No. Seaborg's 1944 actinide concept reorganised the bottom of the table by relocating thorium, protactinium, and uranium out of groups IV-VI and into a separate f-block. The modern table extends to element 118 (oganesson, synthesised 2002, named 2016), and the precise placement of hydrogen and the heaviest superheavy elements remains under discussion.
The eka-element predictions followed from quantum theory. No. Mendeleev had no quantum theory to draw on; he reasoned by chemical analogy with neighbouring elements in the same group. Quantum-mechanical justification (electron shells, Madelung filling, Aufbau) arrived with Bohr 1923 and Pauli 1925, half a century after the periodic law.
Key result: the eka-silicon prediction and confirmation Intermediate+
Theorem (Mendeleev 1871; Winkler 1886). Given the 1871 periodic table's gap in group IV between silicon (atomic weight 28) and tin (atomic weight 118), the predicted properties of eka-silicon (Es) and the measured properties of germanium (Ge), isolated by Winkler from argyrodite in 1886, agree to within experimental error on every quantitative prediction made.
Argument. Mendeleev's 1871 prediction was constructed by chemical analogy with the surrounding elements. The group IV elements above silicon are carbon (12) and silicon (28); below silicon sit tin (118) and lead (207). The arithmetic midpoint between silicon and tin lies near atomic weight 73; Mendeleev committed to 72 on chemical grounds (the geometry of the table's group-IV column). The dark-grey-metal character was inherited from silicon's and tin's shared tendency toward semimetallic oxides of formula . The oxide density of 4.7 was interpolated between (2.65) and (6.95). The chloride was predicted by analogy with (boiling point 57 degrees Celsius) and (boiling point 114 degrees Celsius), giving a predicted boiling point below 100 degrees Celsius.
Winkler's measurements on the new element from argyrodite (later identified as , although the formula was unknown to him at the time) gave: atomic weight 72.6 (predicted 72; relative error 0.8 percent); density 5.35 grams per cubic centimetre (predicted 5.5; relative error 3 percent); dark-grey metallic appearance (predicted dark-grey metal); oxide formula (predicted ; identical stoichiometry); oxide density 4.7 (predicted 4.7; exact agreement); chloride formula (predicted ; identical stoichiometry); chloride boiling point 86 degrees Celsius (predicted below 100 degrees Celsius; within range). Every quantitative prediction was confirmed within fifteen years of its being made.
The result is decisive because it cannot be dismissed as lucky guessing. The probability of six independent quantitative predictions (atomic weight, density, oxide stoichiometry, oxide density, chloride stoichiometry, chloride boiling-point range) all landing within their predicted envelopes by chance is negligibly small. The only reasonable conclusion is that the periodic-law structure Mendeleev identified is real, and that the eka-silicon prediction is the strongest single piece of evidence for it produced in Mendeleev's lifetime.
Bridge. The eka-silicon confirmation builds toward 16.01.01 periodic trends quantified, where the same group-IV interpolation reappears as the systematic variation of atomic radius, ionisation energy, and electronegativity down the carbon-silicon-germanium-tin-lead column. The foundational reason the prediction was forced is that group membership in the periodic table fixes both the valence and the typical oxide and chloride stoichiometries, and this is exactly the structural fact that generalises to every other eka-element confirmation (gallium 1875 for eka-aluminium, scandium 1879 for eka-boron) and to the modern superheavy-element programme at GSI Darmstadt, JINR Dubna, and RIKEN. Putting these together identifies the periodic table as the first predictive theoretical framework in chemistry, and the bridge is between the descriptive taxonomy of the early nineteenth century and the atomic-number-ordered quantum-mechanical framework that crystallised with Moseley 1913 and Bohr's 1923 Aufbau principle.
Exercises Intermediate+
Historiographical debates Master
Debate 1 (priority: Mendeleev versus Meyer). Lothar Meyer published an independent periodic table in 1864 (in his textbook Die modernen Theorien der Chemie) and a more developed version in 1870 (Liebig's Ann. 187, 300) after seeing Mendeleev's 1869 paper. Meyer's table covered fewer elements and made no predictions of unknown elements. The question of priority is factual (Meyer 1864 precedes Mendeleev 1869), but the question of significance favours Mendeleev: his willingness to commit publicly to specific predictions and atomic-weight corrections is what converted the periodicity from an observational regularity into a falsifiable scientific theory. The Davy Medal was awarded jointly to Mendeleev and Meyer by the Royal Society in 1882; the historiographic consensus since the 1960s is that both discovered the periodicity but only Mendeleev discovered its predictive content [Scerri2007].
Debate 2 (the role of prediction versus accommodation). The philosopher and historian of science Stephen Brush argued in a 1996 paper ("The Reception of Mendeleev's Periodic Law in America and Britain", Isis 87) that the eka-element predictions were not, in fact, the primary reason the periodic law was accepted by chemists. Brush's evidence is that the major Anglo-American textbooks of the 1870s adopted the periodic table on the basis of its organisational clarity rather than on the basis of predictions that had not yet been confirmed. The counterargument, developed by Eric Scerri in "The Periodic Table: Its Story and Its Significance" (2007), is that the German and Russian chemical communities took the predictions seriously from 1871 onward and that the textbook lag in Britain reflects institutional inertia rather than methodological judgement. The current consensus is that predictions mattered differently in different national communities, and that the reception of the periodic law cannot be reduced to a single narrative of confirmational success.
Debate 3 (was the periodic law a "law" before Moseley?). Before Moseley, the periodic law was an empirical regularity with three known exceptions (the atomic-weight inversions). Some historians and philosophers argue that it should be called a "periodic principle" until 1913, with Moseley's atomic-number reordering elevating it to a genuine law without exceptions. The opposing view, defended by Scerri, is that the 1869 formulation already constituted a law because it made novel predictions; the Moseley reformulation changed the independent variable but did not change the law's empirical content. The disagreement turns on whether "law" requires strict monotonicity in the ordering variable or only requires novel predictive success.
Debate 4 (Mendeleev's anti-atomic-theory stance). Mendeleev was sceptical of atomism throughout his career and rejected the periodic table's atomic-number reinterpretation when it was first proposed. He held that atomic weights were empirical measurements and that atomic numbers required an unverifiable hypothesis about subatomic structure. The historiographic puzzle is that the periodic table is now universally regarded as evidence for atomism, but its originator regarded it as consistent with a chemistry-first, anti-speculative methodology. Gordin's "A Well-Ordered Thing" (2004) reads Mendeleev's anti-atomism as a deliberate methodological choice in the Russian empiricist tradition, not as an intellectual failure [Gordin2004]; Scerri's 2007 monograph gives the more conventional reading that Mendeleev was simply wrong about atomism, even though he was right about the periodic law.
Debate 5 (the eka-element predictions: lucky or systematic?). The eka-element predictions are sometimes dismissed as numerological interpolations that happened to work. This reading is not supported by the historical evidence: Mendeleev constructed the predictions by careful chemical analogy with neighbouring elements in the same group, and the predictions included qualitative claims (the dark-grey-metallic appearance, the oxide stoichiometry, the chloride volatility) that could not have been obtained by arithmetic interpolation alone. The systematic character of the predictions is shown by their failure mode: eka-manganese (technetium, ) was not discovered until 1937 because no stable isotope exists, but Mendeleev's predicted properties for it were essentially correct when Perrier and Segrè finally isolated the element in a Berkeley cyclotron. A lucky guess would not survive a seventy-year delay.
Synthesis. The priority debate over Mendeleev versus Meyer builds toward 33.04.02 pending chemistry's revolution from phlogiston to Lavoisier, where the same methodological pattern reappears as the conversion of descriptive chemistry into a predictive theoretical science. The foundational reason the periodic table became the organising structure of chemistry is that Mendeleev alone committed to specific falsifiable predictions, and this is exactly the structural fact that generalises across every subsequent theoretical revolution in chemistry (the octet rule of main-group chemistry, the 18-electron rule of 16.05.04 ferrocene and the metallocenes, the Aufbau principle of quantum chemistry). Putting these together with the Brush-Scerri debate on prediction versus accommodation identifies the periodic table as the first successful theoretical prediction in modern chemistry, and the bridge is between the descriptive taxonomy of the early nineteenth century (Döbereiner triads, Newlands octaves) and the atomic-number-ordered, quantum-mechanically grounded framework that crystallised with Moseley 1913 and Bohr's 1923 Aufbau principle. The pattern recurs in the actinide reorganisation of 1944 and in the modern superheavy-element programme at GSI Darmstadt, JINR Dubna, and RIKEN, identifying the periodic law as a living theoretical structure rather than a closed 1869 achievement.
Full argument set Master
Proposition 1 (Mendeleev's eka-silicon prediction is uniquely determined by the local structure of the periodic table). In any periodic table satisfying the periodic-law regularity on the elements known in 1871 — specifically, that elements in the same group share valence and principal oxide stoichiometry — the gap in group IV between silicon (, atomic weight 28) and tin (, atomic weight 118) is uniquely filled by an element whose properties interpolate the group-IV column.
Proof. Group IV by definition contains elements whose principal valence is 4 and whose principal oxide has formula and chloride . Carbon (12), silicon (28), titanium (48), zirconium (91), tin (118), and lead (207) are observed members. The chemical evidence available to Mendeleev — namely the recurrence of the oxide formula and the chloride formula down the column, and the systematic trend in oxide densities from 2.65 () to 6.95 () — constrains the missing element to (a) have valence 4, (b) form and as its principal compounds, and (c) have an atomic weight between 28 and 118.
Within these constraints, the atomic weight is approximately determined by linear interpolation: the average of 28 (Si) and 118 (Sn) is 73; the average of 14 (C) and 118 (Sn) is 66; the average of 28 (Si) and 207 (Pb) is 117.5. Mendeleev's published prediction of 72 falls within this range. The density of the oxide is determined by linear interpolation between (2.65) and (6.95): the midpoint is 4.8; Mendeleev committed to 4.7. The boiling point of is interpolated between (57 degrees Celsius) and (114 degrees Celsius): the midpoint is 85.5 degrees Celsius; Mendeleev committed to "below 100 degrees Celsius". Every quantitative prediction is constrained to within a narrow range by the local structure of the table.
The unique-determination claim follows from the conjunction of these constraints. The missing element must have valence 4 (group-IV membership); it must form oxide and chloride (group-IV chemistry); it must have an atomic weight between 28 and 118 (position between Si and Sn); it must have density between 2.33 (Si) and 7.27 (Sn); it must have an oxide with density between 2.65 and 6.95; it must have a chloride boiling between 57 and 114 degrees Celsius. The product of these constraints is a small region of property-space, and Mendeleev's specific numerical predictions land inside it. The 1886 confirmation by Winkler, with measured values atomic weight 72.6, density 5.35, oxide density 4.7, chloride boiling point 86 degrees Celsius, falls inside the same region.
Proposition 2 (Moseley's law removes the atomic-weight inversions). If Moseley's law holds for the X-ray lines, then ordering by is identical to ordering by , and the three known atomic-weight inversions (argon-potassium, cobalt-nickel, tellurium-iodine) become correctly ordered without overriding the chemical data.
Proof. By Moseley's law, , which is strictly monotone increasing in for . Therefore ordering by is identical to ordering by . The atomic weight, by contrast, is where is the proton mass, the neutron mass, and the neutron count; isotopic composition varies across the table, so is not strictly monotone in .
For argon (, measured , mostly ) and potassium (, measured , mostly ), the heavier isotope of the lighter element is more abundant than the lighter isotope of the heavier element, producing the observed weight inversion. The same effect, with different isotopic compositions, produces the cobalt-nickel () and tellurium-iodine () inversions.
Under the Moseley reordering, argon () precedes potassium () by the strict monotonicity of in , regardless of ; cobalt () precedes nickel (); tellurium () precedes iodine (). Every previously overridden pair is correctly placed by the X-ray data itself, with no need for chemical-overriding corrections. The 1913 reformulation placed the periodic law on a strictly monotonic variable for the first time.
Connections Master
Periodic trends quantified
16.01.01. Builds toward this chapter anchor, where the systematic variation of atomic radius, ionisation energy, electron affinity, and electronegativity down a group or across a period is given quantitative form. The foundational bridge is that Mendeleev's qualitative 1869 periodicity is precisely the regularity that16.01.01measures and tabulates; the eka-element predictions become the historical test case for the quantitative trends, and the Moseley reordering makes the trends monotone in for the first time. Putting these together identifies the periodic law as the structural backbone of all of inorganic chemistry.Chemistry's revolution: phlogiston to Lavoisier
33.04.02pending. Provides the immediate historical predecessor in the history-of-science sequence: Lavoisier's 1789 reform of chemistry established the conceptual framework of elements as irreducible substances with measurable weights that Mendeleev's 1869 table then organised. The central insight is that the periodic law is the second of the two great nineteenth-century systematisations of chemistry (the first being Dalton's atomic theory of 1808, treated in the same unit), and the bridge is between the chemical-revolution context of33.04.02pending and the predictive synthesis of 1869.Ferrocene and the sandwich compounds
16.05.04. Generalises the periodic-table logic into transition-metal organometallic chemistry: the 18-electron rule that organises ferrocene, ruthenocene, and the metallocenes is the d-block analogue of the noble-gas closed-shell pattern that organises Mendeleev's main-group columns. The foundational bridge is that the periodic law's group structure persists across the d-block, with group membership (group 8 for iron, group 9 for cobalt, group 10 for nickel) determining the metal's electron count and therefore the metallocene's stability. The pattern recurs across the entire organometallic chapter.Molecular orbital theory
14.05.01. Provides the quantum-mechanical foundation that ultimately explains why the periodic structure exists: the shell-and-subshell filling order () emerges from the MO theory of multi-electron atoms, and the periodicity of chemical properties reflects the recurrence of similar outer-shell configurations at regular intervals in . The central insight is that Mendeleev's empirical periodic law and the MO-theoretic Aufbau principle are two descriptions of the same underlying structure, and the bridge is between Mendeleev's 1869 observational discovery and the 1923-25 quantum-mechanical explanation by Bohr, Pauli, and Schrödinger's school.
Historical & philosophical context Master
Mendeleev's 1869 paper "Sootnoshenie svoistv s atomnym vesom elementov" [Mendeleev1869] was submitted to the Journal of the Russian Chemical Society on 6 March 1869 (Old Style) and printed as the seventh paper in the journal's first volume, on pages 60-77. The paper's central claim — that the chemical properties of the elements are a periodic function of their atomic weights — had been approached independently by Newlands in 1865 and by Lothar Meyer in 1864, but Mendeleev's formulation was the first to leave explicit gaps for missing elements and to commit publicly to their predicted properties in the 1871 expansion [Mendeleev1871]. The 1871 paper contained the four eka-element predictions whose confirmation by Lecoq de Boisbaudran (gallium, 1875), Nilson (scandium, 1879), and Winkler (germanium, 1886) secured the periodic law's acceptance; the fourth, eka-manganese, was confirmed as technetium by Perrier and Segrè in 1937.
The atomic-number reordering that resolved the periodic law's known weight-inversion anomalies is due to Moseley's 1913 paper in the Philosophical Magazine [Moseley1913], which measured the X-ray frequencies of thirty-eight elements and showed that their square root is linear in an integer label identified with the nuclear charge. The Davy Medal had been jointly awarded to Mendeleev and Meyer in 1882; the 1905 Copley Medal to Mendeleev alone made no mention of the priority dispute. The twentieth-century extension of the table to element 118 began with Seaborg's actinide concept of 1944 and continued with the heavy-ion-fusion synthesis programmes at Berkeley, Darmstadt (GSI), Dubna (JINR), and RIKEN; the most recent confirmed element, oganesson (), was synthesised at Dubna in 2002 and named in 2016.
Bibliography Master
Mendeleev, Dmitri I. "Sootnoshenie svoistv s atomnym vesom elementov" [The relation between the properties of the elements and their atomic weights]. Zhurnal Russkago Fiziko-Khimicheskago Obshchestva 1 (1869): 60–77.
Mendeleev, Dmitri I. "Die periodische Gesetzmässigkeit der Elemente" [The periodic law of the elements]. Liebig's Annalen der Chemie und Pharmacie, Supplementband 8 (1871): 133–229.
Meyer, Lothar. Die modernen Theorien der Chemie und ihre Bedeutung für die chemische Statik. Breslau: Trewendt, 1864.
Newlands, John A. R. "On the Law of Octaves." Chemical News 12 (1865): 83.
Lecoq de Boisbaudran, Paul-Émile. "Caractères chimiques du gallium." Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences 81 (1875): 493–495.
Nilson, Lars Fredrik. "Sur l'ytterbine, terre nouvelle de M. Marignac." Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences 88 (1879): 642–647.
Winkler, Clemens. "Germanium, Ge, ein neues, nichtmetallisches Element." Journal für Praktische Chemie 34 (1886): 177–229.
Rayleigh, Lord (John William Strutt), and William Ramsay. "Argon, a New Constituent of the Atmosphere." Philosophical Transactions of the Royal Society of London, Series A 186 (1895): 187–241.
Moseley, Henry G. J. "The High-Frequency Spectra of the Elements." Philosophical Magazine 26, no. 156 (1913): 1024–1034.
Seaborg, Glenn T. "The Chemical and Radioactive Properties of the Heavy Elements." Chemical & Engineering News 23, no. 23 (1945): 2190–2193.
Brush, Stephen G. "The Reception of Mendeleev's Periodic Law in America and Britain." Isis 87, no. 4 (1996): 595–628.
Scerri, Eric R. The Periodic Table: Its Story and Its Significance. Oxford: Oxford University Press, 2007.
Gordin, Michael D. A Well-Ordered Thing: Dmitrii Mendeleev and the Shadow of the Periodic Table. New York: Basic Books, 2004.
Strathern, Paul. Mendeleev's Dream: The Quest for the Elements. New York: St. Martin's Press, 2000.