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The INTERNET Database of Periodic Tables

There are thousands of periodic tables in web space, but this is the only comprehensive database of periodic tables & periodic system formulations. If you know of an interesting periodic table that is missing, please contact the database curator: Mark R. Leach Ph.D.

Use the drop menus below to search & select from the more than 1100 Period Tables in the database:

  Text Search:       

Periodic Table database entries referencing the database curator: Mark Leach, by date added

1808   Dalton's Elements
1950   Modern Periodic Table
2006   Where Should Hydrogen Go?
1993   WebElements: The Periodic Table on The Web
2004   Chemical Thesaurus Periodic Table
2003   Electronegativity Periodic Table
2004   Material Type Periodic Table
2004   Elemental Hydride Types Periodic Table
2004   Elemental Oxidation States
2005   Atomic Radii Periodic Table
2006   Radioactivity Periodic Table
2006   Superconducting Elements
2004   Mass Anomaly Periodic Table
2012   Dates of Discovery of the Elements
2006   Group Numbering Systems
2004   Phase State: Solid, Liquid, Gas at 20°C & 700°C
2005   Extraction from Ore to Pure Element
2004   Organic Chemist's Periodic Table
2004   Inorganic Chemist's Periodic Table
2005   Geologist's Periodic Table
2004   Biologist's Periodic Table
2006   Astronomer's Periodic Table
2005   Student's Periodic Table
2003   Elements by Orbital
2007   Gray's Photographic Periodic Table
1843   Gmelin's System
2006   Various Periodic Tables
2010   Lewis Octet Periodic Table
1831   Daubeny's Teaching Display Board & Wooden Cubes of Atomic Weights
1904   Ramsay's Periodic Arrangement of The Elements
2013   Electronegativity Chart (Leach)
2013   Top 10 Periodic Tables
2005   Chemical Thesaurus Reaction Chemistry Database Periodic Table
2018   Number of Stable Isotopes by Element
2018   First Ionisation Energy to the Standard Form Periodic Table
2012   Atoms, Orbitals & The Periodic Table
2019   Leach's Empirical Periodic Table
1814   Wollaston's Physical Slide Rule of Chemical Equivalents
1813   Wollaston's Synoptic Scale of Chemical Equivalents
1858   Cannizzaro's Letter
1939   Foster's Periodic Arrangement
2019   Vernon's Oxidation Number Periodic Table
2021   Chemogenesis In 700 Seconds
2021   The Periodic Table: Is it Perfect, is it Fractured or is it Broken?


Dalton's Elements

Two pages from John Dalton's A New System of Chemical Philosophy in which he proposed his version of atomic theory based on scientific experimentation (see the scanned book, page 219):

Name Modern Symbol Dalton's Data Modern Values % error
Hydrog. H 1 1 0%
Azote N 5 14 -180%
Carbone C 5 12 -140%
Oxygen O 7 16 -129%
Phosphorus P 9 31 -244%
Sulphur S 13 32.1 -147%
Magnesia Mg 20 24.3 -22%
Lime Ca 24 40.1 -67%
Soda Na 28 23 18%
Potash K 42 39.1 7%
Strontites Sr 46 87.6 -90%
Barytes Ba 68 137.3 -102%
Iron Fe 50 55.8 -12%
Zinc Zn 56 65.4 -17%
Copper Cu 56 63.5 -13%
Lead Pb 90 200.6 -123%
Silver Ag 190 107.9 43%
Gold Au 190 197 -4%
Platina Pt 190 195.1 -3%
Mercury Hg 167 200.6 -20%

By Mark Leach

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The Modern Periodic Table

The modern periodic table is based on quantum numbers and blocks, here.

A periodic table can be constructed by listing the elements by n and l quantum number:

The problem with this mapping is that the generated sequence is not continuous with respect to atomic number atomic number, Z: Check out the sequence Ar to K, 18 to 19.

Named after a French chemist who first published in the formulation in 1929, the Janet or Left-Step Periodic Table uses a slightly different mapping:

While the Janet periodic table is very logical and clear it does not separate metals from non-metals as well as the Mendeleev version, and helium is a problem chemically.

However, it is a simple mapping to go from the Janet or Left-Step periodic table to a modern formulation of Mendeleev's periodic table:


On this page web, "full" f-block included periodic tables are shown wherever possible, as above.

However, the periodic table is usually exhibited in book and on posters in a compressed form with the f-block "rare earths" separated away from the s-block, p-block and d-block elements:

However, the compression used introduces the well known problem known as a "fence post error".

The effect is that:

La and Ac: move from f-block to d-block
Lu and Lr: move from p-block to f-block

Chemically, the elements can be fitted in and classified either way. Many thanks to JD for pointing the situation with the periodic table is a fence post error.

Mark Winter's Web Elements project, here, uses the formulation shown below:

Interestingly, the IUPAC periodic table separates out 15 lanthanides, La-Lu, and 15 actinides, Ac-Lr by leaving gaps in period 3 under Sc & Y:

This corresponds to:

By Mark Leach

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Where Should Hydrogen Go?

There are four possible positions for hydrogen:

By Mark Leach

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WebElements: The Periodic Table on The Web

Mark Winter's WebElements was started in 1993 when it was one of the first websites on the internet.

Mark Leach's Chemogenesis web book uses the WebElements periodic table as its master data source, and it does not attempt to duplicate it.

Abundance of elements (Earth's crust)
Abundance of elements (oceans)
Abundance of elements (sun)
Abundance of elements (Universe)
Abundance of elements (in human body)
Accurate mass of the isotopes
Atomic number
Atomic weight
Biological role
Block in periodic table
Boiling point
Bond enthalpy (diatomics)
Bond length in element
Colour (color)
Covalent radius
Crystal structure
Electrical resistivity

Electronic configuration
Element bond length
Enthalpy of atomization
Enthalpy of fusion
Enthalpy of vaporization
Examples of compounds
Group name numbers
Health hazards
History of the element
Ionic radius
Ionization energy
Isotope data
Key data
Meaning of name
Melting point
Molar volume
Names and symbols
Nuclear data
Origin of name

Oxidation states in compounds
Period in table
Properties of some compounds
Radius (atomic)
Radius (covalent)
Radius (ionic)
Radius (van der Waals)
Radius metallic (12)
Radioactive isotopes
Resistivity (electrical)
Shell structure
Standard atomic weights
Standard state
Structure of element
Thermal conductivity
Van der Waals radius
X-ray crystal structure

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Chemical Thesaurus Periodic Table

Search for chemical reagents, atomic and molecular ions, minerals, isotopes, elemental data, etc., using the periodic table built into The Chemical Thesaurus reaction chemistry database:

By Mark Leach

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Electronegativity Periodic Table

A periodic table showing electronegativity, "The ability of an atom to attract electron density from a covalent bond" (Linus Pauling). Blue elements are electronegative, red elements are electropositive, and purple elements are intermediate. Notice how hydrogen is intermediate in electronegativity between carbon and boron and is positioned above and between these elements:

By Mark Leach

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Material Type Periodic Table

All of the the main group elements are common laboratory reagents or chemical in bottles. They appear as metals, metalloid (semi-metals) and non-metals. Most of the non-metals are molecular materials while most of the metalloids have an extended network-covalent structure.

Elsewhere in the chemogenesis web book, material type is discussed in terms of the Laing Tetrahedron, an analysis that classifies binary materials in terms of four extreme types: metallic, ionic, molecular and network. However, none the chemical elements present as ionic materials, only as metals, molecular (van er Waals) and network materials:

The elements B, C, Si, P, S, Ge, As, Se, Sn, Sb and Te can form allotropes: pure elemental substances that can exist with different crystalline structures from the Wikipedia. Allotropes may be metallic, network or molecular.

By Mark Leach

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Elemental Hydride Types Periodic Table

The main group elemental hydrides are all well known reagent chemicals. The main group hydrides always give the lowest and most common oxidation state, and all chemicals are molecular in the gas phase. The Group I and II hydrides are ionic materials, but they can be vaporised to give the molecular form.

The chemicals present and behave as Lewis acids, Lewis bases or Lewis acid/base complexes, here:

By Mark Leach

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Elemental Oxidation States Periodic Table

The periodic table of fluorides (mainly) shows the range of possible oxidation states. Note that lithium, by way of example, is deemed to have two oxidation states: Li0 (the metal), and Li+ (the lithium ion):

There are a few exceptions and points to note:

By Mark Leach

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Atomic Radii Periodic Table

By Mark Leach

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Radioactivity Periodic Table

A periodic table showing the elements that have no stable isotopes, so that all samples are radioactive:

By Mark Leach

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Superconducting Elements

A periodic table showing which elements become superconducting at low temperature.

By Mark Leach

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Mass Anomaly Periodic Table

Pairs of atoms where atomic mass does not follow atomic number.


Nature's little quirk – due to the intricacies of nuclear chemistry and isotopic abundance – caused no end of difficulties to the developers of the periodic table in the mid-nineteenth century. Scientists could determine atomic mass, but knew nothing of protons or atomic numbers.

The tellurium-iodine anomaly was a particular problem.

By Mark Leach

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Dates of Discovery of the Elements

The Elements and their dates of discovery, taken from this Wikipedia page:

Two charts showing the dates of discovery of the elements, one from the 'time of the ancients' (10,000 BC) to the present day, and the second from 1700 to the present day.

These show that there were two distinct phases for the discovery of the 118 known elements:

Data from: this Wikipedia page.


Discovery of Copper-9000
Discovery of Lead -7000
Discovery of Gold -6000
Discovery of Iron -5000
Discovery of Silver -5000
Discovery of Carbon -3750
Discovery of Tin -3500
Discovery of Sulfur (Sulphur) -2000
Discovery of Mercury -2000
Discovery of Zinc -1000
Discovery of Antimony -800
Discovery of Arsenic -300
Discovery of Phosphorus 1669
Discovery of Cobalt 1735
Discovery of Platinum 1748
Discovery of Nickel 1751
Discovery of Bismuth 1753
Discovery of Hydrogen 1766
Discovery of Oxygen 1771
Discovery of Nitrogen 1772
Discovery of Chlorine 1774
Discovery of Manganese 1774
Discovery of Molybdenum 1781
Discovery of Tellurium 1782
Discovery of Tungsten 1783
Discovery of Zirconium 1789
Discovery of Uranium 1789
Discovery of Titanium 1791
Discovery of Yttrium 1794
Discovery of Beryllium 1798
Discovery of Chromium 1798
Discovery of Niobium 1801
Discovery of Tantalum 1802
Discovery of Palladium 1803
Discovery of Cerium 1803
Discovery of Osmium 1803
Discovery of Iridium 1803
Discovery of Rhodium 1804
Discovery of Sodium 1807
Discovery of Potassium 1807
Discovery of Boron 1808
Discovery of Magnesium 1808
Discovery of Calcium 1808
Discovery of Strontium 1808
Discovery of Barium 1808
Discovery of Iodine 1811
Discovery of Lithium 1817
Discovery of Selenium 1817
Discovery of Cadmium 1817
Discovery of Silicon 1824
Discovery of Aluminium (Aluminum) 1825
Discovery of Bromine 1825
Discovery of Thorium 1829
Discovery of Vanadium 1830
Discovery of Lanthanum 1838
Discovery of Terbium 1842
Discovery of Erbium 1842
Discovery of Ruthenium 1844
Discovery of Cesium 1860
Discovery of Rubidium 1861
Discovery of Thallium 1861
Discovery of Indium 1863
Discovery of Gallium 1875
Discovery of Ytterbium 1878
Discovery of Scandium 1879
Discovery of Samarium 1879
Discovery of Holmium 1879
Discovery of Thulium 1879
Discovery of Gadolinium 1880
Discovery of Praseodymium 1885
Discovery of Neodymium 1885
Discovery of Fluorine 1886
Discovery of Germanium 1886
Discovery of Dysprosium 1886
Discovery of Argon 1894
Discovery of Helium 1895
Discovery of Neon 1898
Discovery of Krypton 1898
Discovery of Xenon 1898
Discovery of Polonium 1898
Discovery of Radium 1898
Discovery of Radon 1899
Discovery of Europium 1901
Discovery of Actinium 1902
Discovery of Lutetium 1906
Discovery of Protactinium 1913
Discovery of Rhenium 1919
Discovery of Hafnium 1922
Discovery of Technetium 1937
Discovery of Francium 1939
Discovery of Astatine 1940
Discovery of Neptunium 1940
Discovery of Plutonium 1940
Discovery of Americium 1944
Discovery of Curium 1944
Discovery of Promethium 1945
Discovery of Berkelium 1949
Discovery of Californium 1950
Discovery of Einsteinium 1952
Discovery of Fermium 1952
Discovery of Mendelevium 1955
Discovery of Lawrencium 1961
Discovery of Nobelium 1966
Discovery of Rutherfordium 1969
Discovery of Dubnium 1970
Discovery of Seaborgium 1974
Discovery of Bohrium 1981
Discovery of Meitnerium 1982
Discovery of Hassium 1984
Discovery of Darmstadtium 1994
Discovery of Roentgenium 1994
Discovery of Copernicium 1996
Discovery of Flerovium 1999
Discovery of Livermorium 2000
Discovery of Oganesson 2002
Discovery of Nihonium2003
Discovery of Moscovium2003
Discovery of Tennessine2010

By Mark Leach

A nice graphic from Compound Interest: (click image to enlarge)

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Group Numbering Systems


Phase State: Solid, Liquid, Gas at 20°C & 700°C

By Mark Leach

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Phase State: Solid, Liquid, Gas at 20°C & 700°C

By Mark Leach

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Extraction from Ore to Pure Element

A periodic table showing how pure elements are extracted:

Highly electropositive elements (Na, K) and electronegative elements (Cl2, F2) can only be obtained by electrolysis.

By Mark Leach

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Organic Chemist's Periodic Table

Organic chemistry is dominated by carbon, hydrogen, oxygen and nitrogen. Other elements are commonly encountered in the organic lab, others less commonly and some... almost never at all...

A less than useful formulation (!):

followed by a slightly more useful organic chemist's periodic table:

By Mark Leach

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Inorganic Chemist's Periodic Table

Every element has a specialist, somewhere, for whom it is the most important element.

By Mark Leach

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Geologist's Periodic Table

Atmophile Elements - noble gases and covalently bonded gaseous molecules. The atoms and molecules are attracted by weak van der Waals forces and so these elements remain gaseous at room temperature.

Lithophile Elements - Those elements which form ionic bonds generally have filled outer electron shells. They typically bond to oxygen in silicates and oxides.

Siderophile Elements - The metals near iron in the periodic table that exhibit metallic bonding, have a weak affinity for oxygen and sulfur and are readily soluble in molten iron. Examples include iron, nickel, cobalt, platinum, gold, tin, and tantalum. These elements are depleted in the earth crust because they have partitioned into the earth's iron core.

Chalcophile Elements - The elements that bond to S, Se, Te, Sb, and As. These bonds are predominantly covalent in character.

As discussed in more detail here.

By Mark Leach

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Biologist's Periodic Tables

A periodic table showing where biologically essential (green), essential trace (purple), toxic (red), radioactive (yellow) and of low – but not zero– biological impact (gray) elements are found. Only highly toxic elements are shown in red. Li (as Li+) is biologically active and is used as an antidepressant.

By Mark Leach

or here:


And a periodic table for biologists from Science Videos:

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Astronomer's Periodic Table

Highly amusing for chemists is the astronomer's periodic table because astronomers consider there to be three types of element:

By Mark Leach

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Student's Periodic Table

Students are expected to know that in all equations hydrogen is molecular should [nearly always] be written as H2. Likewise, nitrogen is N2, oxygen O2, fluorine F2, chlorine Cl2, bromine Br2 and iodine I2. But somehow students are expected to know that molecular sulfur, S8, should be written as S and molecular phosphorus, P4, should be written as P.

By Mark Leach

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Elements by Orbital

From elsewhere in Mark Leach's Chemogenesis webbook:

Madelung's Rule tells us that the orbitals fill in the order n + l (lowest first). This gives the sequence:

Electronic structure can be illustrated adding electrons to boxes (to represent orbitals). This representation shows the Pauli exclusion principle, the aufbau principle and Hund's rule in action.

There are some subtle effects with the d block elements chromium, Cr, and copper, Cu. Hund's rule of maximum multiplicity lowers the energy of the 3d orbital below that of the the 4s orbital, due to the stabilisation achieved with a complete and spherically symmetric set of five 3d orbitals containing five or ten electrons. Thus,

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Gray's Photographic Periodic Table

Theodore Gray's Periodic Table.Com is a live version of what is generally regarded as the most beautiful periodic table to be developed so far. It is a treasure trove of pictures, videos and stories. Explore!

Theo is an enthusiast and a collector, and he uses the power of Mathematica (he is a co-founder of Wolfram Research) to drive his astonishing website. It is Theo's aim to be the number one periodic table resource on the web.

Mark Leach, the database curator writes:

"I find Theo's website and approach to be complementary to the more academic WebElements."

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Gmelin's System

L. Gmelin, Handbuch der chemie, 4th ed., Heidelberg, 1843, vol. 1, p. 457 (Many thanks to Carmen Giunta for the ref. update & link.)

The early and important Gmelin formulation redrawn by Mark Leach with modern element symbols:

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Various Periodic Tables

As discussed on this page of the Chemogenesis webbook, the periodic table is ambiguous as to what it is showing.

Does the PT show the element as the abstract 'basic substance', or gas phase atoms or the material substance?

By Mark Leach

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Lewis Octet Periodic Table

A periodic table showing the outer shell of valence electrons associated with Lewis atoms:

By Mark Leach

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Daubeny's Teaching Display Board & Wooden Cubes of Atomic Weights

The Museum of the History of Science, Oxford, has a display of Charles Daubeny's teaching materials, including a black painted wooden board with "SYMBOLS OF SIMPLE BODIES": showing symbols, atomic weights and names of elements in two columns, and a small pile of cubes with element symbols.

Charles Daubeny and Chemistry at the Old Ashmolean

Charles Daubeny (1795-1867) was appointed Aldrichian Professor of Chemistry at Oxford in 1822. In 1847 he moved from the original laboratory in this basement [in the museum] to a new one built at his own expense at the Botanic Garden. His apparatus went with him and was preserved there. Daubeny actively campaigned for the teaching of science in Oxford and held several professorships in addition to chemistry. He also conducted research on subjects such as photosynthesis.

From the HSM Database (Inventory no. 17504):

DAUBENY'S LIST OF ATOMIC WEIGHTS Wooden panel, black with white lettering, listing in two columns the symbols and names of twenty elements. This lecture board is identical to the table in the third edition (1831) of E. Turner, 'Elements of Chemistry', apart from the atomic weight for bromine. Daubeny wrote a useful 'Introduction to the Atomic Theory' (published in three versions: 1831, 1840, and 1850), the first edition of which also quotes Turner's table. Probably contemporary with this lecture board are the wooden cubes with the symbols for certain elements.

The period from 1810 to 1860 was crucial in the development of the periodic table. Most of the main group and transition elements had been discovered, but their atomic weights and stoichiometries (combining ratios) had not been fully deduced. Oxygen was assumed to have a weight of 6, and consequently carbon is assumed to have a mass of 6.

Daubeny's element symbols and weights – along with the modern mass data – are tabulated:

Symbol Daubeny's Weight Modern Mass Data % error Stoichiometry Error
H 1 1 0%  
C 6 12 -100% factor of 2
O 8 16 -100% factor of 2
Si 8 28.1 -251% factor of 5 (?)
Al 10 27 -170% factor of 3
Mg 12 24.3 -103% factor of 2
N 14 14 0%  
S 16 32.1 -101% factor of 2
P 16 31 -94% factor of 2
Fl 19 19 0%  
Ca 20 40.1 -101% factor of 2
Na 24 23 4%  
Fe 28 55.8 -99% factor of 2
Cl 36 35.5 1%  
K 40 39.1 2%  
Cu 64 63.5 1%  
B 80 79.9 0%  
Pb 104 207 -99% factor of 2
I 124 127 -2%  
Hg 200 200.6 0%  

While quite a number of weights are close to the modern values, many are way out. However, the error is usually a stiotoimetric factor error.


Forty-two wooden cubes numbered 1-42, painted black with symbols for certain elements, compounds or radicals painted in white on the faces, together with the corresponding atomic, molecular or radical weights. The face markings appear in various combinations:

H C P Na Ca° S N K Fe K Na° Cy
1 6 16 24 28 16 14 40 28 48 32 26 48

A typical cube (no. 3) may be represented by the following figure. They present something of an enigma as their faces do not form an obvious pattern. The numbers indicate that there were 42 cubes. In style they are similar to the figures on the panel of atomic weights.

The cubes are listed in Daubeny's 1861 catalogue, p. 11 as: "Wooden cubes for illustrating atomic weight". [See D. R. Oldroyd, The Chemical Lectures at Oxford (1822-1854) of Charles Daubeny, M.D., F.R.S. Notes and Records of the Royal Society, vol. 33 (1979), pp. 217-259.]

This display was spotted by Eric Scerri who was visiting the museum with Mark Leach in 2010.

There is a virtual tour on the museum, and the above display is in the basement.

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Ramsay's Periodic Arrangement of The Elements

From from Scientific American in 1904,, an article by Sir William Ramsay discussing the Periodic Arrangement of The Element:

Redrawn by Mark Leach in 2019:

Thanks to Eric Scerri for the tip!
See the website and Eric's Twitter Feed.

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Electronegativity Chart (Leach)

From Mark R Leach's paper, Concerning electronegativity as a basic elemental property and why the periodic table is usually represented in its medium form, Journal & PDF.

Due to the importance of Pauling's electronegativity scale, as published in The Nature of The Chemical Bond (1960), where electronegativity ranges from Cs 0.7 to F 4.0, all the other electronegativity scales are routinely normalised with respect to Pauling's range.

When the Pauling, Revised Pauling, Mulliken, Sanderson and Allred-Rochow electronegativity scales are plotted together against atomic number, Z, the similarity of the data can be observed. The solid line shows the averaged data:

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Top 10 Periodic Tables

There are more than 1000 periodic tables hosted by the Chemogenesis Webbook Periodic Table database, so it can be a little difficult to find the exceptional ones.

Here we present – in our humble opinionThe ten most significant periodic tables in the database.

We present the best:

Three Excellent, Data Rich Periodic Tables

The first three of our top 10 periodic tables are classic element data repositories.

They all work in the same way: click on the element symbol to get data/information about the selected element. The three are Mark Winter's WebElements, Theo Gray's Photographic Periodic Table & Michael Dayah's Ptable.

<Web Elements>

Photographic Periodic Table


Five Formulations Showing The History & Development

The next five examples deal with history and development Periodic Table. The first is Dalton's 1808 list of elements, next is Mendeleev's 1869 Tabelle I, then Werner's remarkably modern looking 1905 formulation. This is followed by Janet's Left Step formulation and then a discussion of how and why the commonly used medium form PT formulation, is constructed.

<Eight-Group Periodic Table>

Mendeleev's Tabelle I

Werner's 1905 Periodic Table

Janet's Left Step

modern (and commonly employed) periodic table

electronegativity periodic table

An Alternative Formulation

The internet database contains many, many alternative formulations, and these are often spiral and/or three dimensional. These exemplified by the 1965 Alexander DeskTopper Arrangement. To see the variety of formulations available, check out the Spiral & Helical and 3-Dimensional formulations in the database:

Alexander DeskTopper Arrangement

Non-Chemistry PTs

The periodic table as a motif is a useful and commonly used infographic template for arranging many types of object with, from 50 to 150 members.

There are numerous examples in the Non-Chemistry section where dozens of completely random representations can be found:

Non-Chemistry Periodic Table

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Chemical Thesaurus Reaction Chemistry Database Periodic Table

A periodic table front end to the Chemical Thesaurus Reaction Chemistry Database Periodic Table. Clicking on an element gives access to database searches of chemical species and their interactions.

A quote neatly sums up what the ChemThes reaction chemistry database project is trying to achieve:

"The Chemical Thesaurus is a reaction chemistry information system that extends traditional references by providing hyperlinks between related information. The program goes a long way toward meeting its ambitious goal of creating a nonlinear reference for reaction information. With its built-in connections, organizing themes, and multiple ways to sort and view data, The Chemical Thesaurus is much greater than the sum of the data in its database.

"The program does an excellent job of removing the artificial barriers between different subdisciplinary areas of chemistry by presenting a unified vision of inorganic and organic reaction chemistry."

K.R. Cousins, JACS, 123, 35, pp 8645-6 (2001)

Chemical Thesaurus Reaction Chemistry Database

By Mark Leach

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Number of Stable Isotopes by Element

When plotting the number of stable isotopes against element, and against atomic number Z, it is clear that elements with an even atomic number are likely to have more stable isotopes (average 4.9) than elements with an odd atomic number (average 1.3). Click here for the Excel file. There is a Wikipedia page here.

The effect is striking in graphical form:

By Mark Leach

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First Ionisation Energy to the Standard Form Periodic Table

There is debate amongst the cognoscenti about the 'best' representation of the periodic table, and how this 'best' formulation can be explained by [rationalized by] quantum mechanics (QM).

Many feel that the Janet PT formulation, the 'Left Step', is the ideal QM PT, but this formulation does not show periodicity very well, and there are issues with the placement of H, He, Be which spill over into questions about their placement in the standard form PT (the periodic table used in classrooms and textbooks around the world).

However, it is possible to get to the conventional standard form PT directly from the first ionisation energy data, where the 1st ionisation energy is the energy required to convert a gas phase atom (M) into its gas phase positive ion plus electron.

M(g)      →       M+(g)     +     e

The process involves:


Note that a similar logic can be applied to atomic radius and electronegativity data.

However, there are issues about the measurement of atomic radius, because atoms are 'soft at their edges', and gas phase atomic radius is not precisely defined. And, electronegativity is a derived parameter.

By Mark Leach

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Atoms, Orbitals & The Periodic Table

One of several animations and explanations/realisations of quantum physics from Data-Burger, scientific advisor: J. Bobroff, with the support of: Univ. Paris Sud, SFP, Triangle de la Physique, PALM, Sciences à l'Ecole, ICAM-I2CAM.

Mark Leach writes:

"What I particularly like about this video is that it shows the quantum fuzziness of the atoms. This explains/shows how and why induced-dipole/induced-dipole (London force) interactions occur, an important class of van der Waals interaction. At any moment, the electron distribution is not perfectly spherical, which means that there is an instantaneous dipole on the atom. This instantaneous dipole is able to induce a dipole on an adjacent atom, with the effect that the two atoms are attracted when they touch. It is as if atoms are 'sticky' like Velcro.

"This effect explains why the Group 18 noble gas elements are able to form liquids and solids [not He] at low temperatures, and why non-polar molecules, such as P4, S8 and hydrocarbons are able to condense."

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Leach's Empirical Periodic Table

The common/conventional/standard 'medium form' periodic table is based on the 1945 Seaborg formulation, and it is interesting to explore where this formulation – and its 1939 predecessor – come from. (Interestingly, the Werner formulation of 1905 is not cited as a source and there are no other similar formulations in the (this) Periodic Table Database.)

However, it is possible to get to the common/conventional/standard periodic table directly from two readily available data-sets: (1) first ionisation energy of the gas phase atoms, and (2) atomic radius.

The procedure involved plotting the data, rotating 90°, squeezing vertically and smoothing. The points need a little tidying up, and then they can be mapped directly onto the Seaborg formulation periodic table.

The only element which does no obviously 'line-up' with the periodic table is hydrogen, but many modern periodic tables have H floating as it is not obvious if it should be considered to be a Group 1 alkali metal or a Group 17 halogen.


There are advantages and disadvantages to each data set. The 1st ionisation energy data from NIST is known with up to seven significant figures of precision, but the data jumps about at times due to the presence of the s & p-orbitals, which appears to make the data a little noisy. (Actually, this 'noise' is embedded information about the electronic structure of the atoms.) The atomic radius gives smoother data, but as gas phase atoms do not have hard edges calculated (Clementi 1967) rather than experimental values, must be used.

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Wollaston's Physical Slide Rule of Chemical Equivalents

From the Science Museum in the UK collection, the Wollaston slide rule of chemical equivalents:

"Three sliding scales of chemical equivalents, all with same manuscripts marks, published by W Cary, devised by W H Wollaston, a leading chemist and natural philosopher during the early 19th century.

"Positioning the slider with the weight of the substance set against it will show you the weights of other substances which will react with it. This fundamental ordering based on measurement paved the way for the periodic table of the elements"

Wollaston uses a decimal scale in which oxygen is defined as having an atomic weight (relative atomic mass) of 10.00 rather than the modern value of 15.999.

Read more here and here, and an entry concerning chemical slide rules:

Mark Leach writes:

"I have edited the image above, setting the scale to zero:"

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Wollaston's Synoptic Scale of Chemical Equivalents

Philosophical Transactions: A Synoptic Scale of Chemical Equivalents by William Hyde Wollaston, M.D. Sec. R.S., or from here.

It is apparent that chemistry the years 1810 to 1850 was largely concerned with discovering the whole number stoichiometric ratios of atoms in chemical compounds.

Wollaston writes in the text above:

"It is impossible in several instances, where only two combinations of the same ingredients are known, to discover which of the compounds is to be regarded as consisting of a pair of single atoms, and since the decision of these questions is purely theoretical, and by no means necessary to the formation of a table adapted to most practical purposes, I have not been desirous of warping my numbers according to an atomic theory, but have endeavored to make practical convenience my sole guide, and have considered the doctrine of simple multiples, on which that of atoms is founded, merely as a valuable assistant in determining, by simple division, the amount of those quantities that are liable to such definite deviations from the original law of Richter."

"Mr. Dalton in his atomic views of chemical combination appears not to have taken much pains to ascertain the actual prevalence of that law of multiple proportions by which the atomic theory is best supported [however] it is in fact to Mr. Dalton that we are indebted for the first correct observation of such an instance of a simple multiple in the union of nitrous gas with oxygen."

"[I have] computed a series of supposed atoms, I [have] assumed oxygen as the decimal unit of my scale [ie. oxygen = 10], in order to facilitate the estimation of those numerous combinations which it forms with other bodies. Though the present table of Equivalents, I have taken care to make oxygen equally prominent on account of the important part it performs in determining the affinities of bodies by the different proportions in which it is united to them.."

Mark Leach writes:

"When Wollaston's equivalent weights are converted from O = 10.00 to the modern value of O = 15.999, the atomic weight values can be seen to be astonishingly accurate.

"However, the language of the article is quite difficult as the meaning of many of the terms is unclear (to me, at least). For example, in modern usage adding 'ia' to a metal implies the oxide: 'magnesia' is magnesium oxide, MgO. I am not clear if this historical usage is consistent. 'Azote' is nitrogen and 'muriatic acid (dry)' is hydrogen chloride gas. I have only analyses/re-calculated the elements and a couple of common/obvious compounds:"

  Wollaston's data Scaled to O = 15.999 Modern Values % error
H (as H2) 1.32 2.112 2.016 5%
O 10.00 15.999 15.999 ref. value
H2O 11.32 18.111 18.015 1%
C 7.74 12.383 12.011 3%
S 20.00 31.998 32.060 0%
P 17.40 27.838 30.974 -11%
N (as N2) 17.54 28.062 28.014 0%
Cl (as Cl2) 44.10 70.556 70.900 0%
Fe 34.50 55.197 55.845 -1%
Cu 40.00 63.996 63.546 1%
Zn 41.00 65.596 65.380 0%
Hg 125.50 200.787 200.590 0%
Pb 129.50 207.187 207.980 0%
Ag 135.00 215.987 107.870 50%

Interestingly, Wollaston's analysis is far better than Daubeny's 1831 data seen in Oxford.

Read more in an entry concerning chemical slide rules.

Thanks to Nawa for the tip!

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Cannizzaro's Letter

Letter of Professor Stanislao Cannizzaro to Professor S. De Luca: Sketch of a Course of Chemical Philosophy given in the Royal University of Genoa, Il Nuovo Cimento, vol. vii. (1858), pp. 321-366.

Read the full letter/paper, in English translation, here.

Many thanks to Carmen Giunta, Professor of Chemistry Emeritus, Le Moyne College who provided the information about, and link to, Cannizzaro's Letter. See a list of other classic chemistry papers.

Cannizzaro writes:

"I believe that the progress of science made in these last years has confirmed the hypothesis of Avogadro, of Ampère, and of Dumas on the similar constitution of substances in the gaseous state; that is, that equal volumes of these substances, whether simple or compound, contain an equal number of molecules: not however an equal number of atoms, since the molecules of the different substances, or those of the same substance in its different states, may contain a different number of atoms, whether of the same or of diverse nature."

From the Science History of Science Institute:

"In 1858 Cannizzaro outlined a course in theoretical chemistry for students at the University of Genoa,where he had to teach without benefit of a laboratory. He used the hypothesis of a fellow Italian, Amedeo Avogadro, who had died just two years earlier, as a pathway out of the confusion rampant among chemists about atomic weights and the fundamental structure of chemical compounds."

Mark Leach writes:

"Before a periodic table of the chemical elements – which orders the elements by atomic weight and then groups them by property – could be developed it was necessary to know the atomic weight values. However, to deduce the atomic weights was a problem as it was necessary to know the ratios of how the elements combined, the stoichiometry.

"Tables of atomic weight data by Dalton (1808), Wollaston (1813) and Daubeny (1831) show progress, but the 1858 Cannizzaro letter was the first where the atomic weight data is more or less both complete and accurate.

"I have extracted the element atomic weight data from the paper, and given the % error with respect to modern atomic weight/mass data. Only titanium is significantly out! It is clear that Cannizzaro knew that hydrogen, nitrogen, oxygen, chlorine, bromine & iodine existed as diatomic molecules."

Element Symbol Cannizzaro's Weight Modern Weight/Mass % error
Hydrogen H 1 1.008 -0.8%
Boron B 11 10.81 1.7%
Carbon C 12 12.011 -0.1%
Nitrogen N 14 14.007 0.0%
Oxygen O 16 15.999 0.0%
Sodium Na 23 22.99 0.0%
Magnesium Mg 24 24.305 -1.3%
Aluminium Al 27 26.982 0.1%
Silicon Si 28 28.085 -0.3%
Sulphur S 32 32.06 -0.2%
Phosphorus P 32 30.974 3.2%
Chlorine Cl 35.5 35.45 0.1%
Potassium K 39 39.098 -0.3%
Calcium Ca 40 40.078 -0.2%
Chromium Cr 53 51.996 1.9%
Manganese Mn 55 54.938 0.1%
Iron Fe 56 55.845 0.3%
Titanium Ti 56 47.867 14.5%
Copper Cu 63 63.546 -0.9%
Zinc Zn 66 65.38 0.9%
Arsenic As 75 74.922 0.1%
Bromine Br 80 79.904 0.1%
Zirconium Zr 89 91.224 -2.5%
Silver Ag 108 107.87 0.1%
Tin Sn 117.6 118.71 -0.9%
Iodine I 127 126.9 0.1%
Platinum Pt 197 195.08 1.0%
Mercury Hg 200 200.59 -0.3%
Lead Pb 207 207.2 -0.1%
Diatomic Molecule Formula Cannizzaro's Weight Modern Weight/Mass % error
Hydrogen H2 2 2.016 -0.8%
Oxygen O2 32 31.998 0.0%
Sulphur S2 64 64.12 -0.2%
Chlorine Cl2 71 70.9 0.1%
Bromine Br2 160 159.808 0.1%
Iodine I2 254 253.8 0.1%
Molecule Formula Cannizzaro's Weight Modern Weight/Mass % error
Water H2O 18 18.015 -0.1%
Hydrochloric Acid HCl 36.5 36.458 0.1%
Methane CH4 16 16.043 -0.3%
Hydrogen sulphide H2S 34 34.076 -0.2%
Diethyl ether CH3CH2OCH2CH3 74 74.123 -0.2%
Carbon disulphide CS2 76 76.131 -0.2%
Chloroethane CH3CH2Cl 64.5 64.512 0.0%
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Foster's Periodic Arrangement

L.S. Foster, "Why not modernise the textbooks also? I. The periodic table", Journal of Chemical Education, vol. 16, no. 9, pp. 409–412,

Foster writes:

"The [above] modern periodic table is simply an orderly array of the elements with all unnecessary ornamentation omitted, has been found highly satisfactory for instructional purposes.

"The transitional elements, with two unfilled electron shells, are separated from the non-metallic elements.

"The rare-earth elements, defined as those with three incomplete electron shells, are shown to be those of atomic numbers 58 to 70, while La and Lu, which have only two incomplete electron shells are classified as transitional elements.

"Copper, silver, and gold act as transitional elements except when the state of oxidation is one."

René Vernon writes:

Foster couldn't show the coinage metals – with their full d10 complements – as transitional elements, but by adding a broken line around them he was showing they had the capacity to act as if they were.

I tried to work out how he distinguished La & Lu from Ce to Yb. Foster seems to be saying that La 5d1 6s2, has incomplete 5th and 6th (ie. 6p) shells.

Same for Lu 4f14 5d1 6s2 having incomplete 5th and 6th shells. Whereas, for example, Ce 4f1 5d1 6s2 has incomplete 4th, 5th and 6th shells. Presumably this was in the years before the fact that the 4f shell became full at Yb was widely appreciated. So, strictly speaking, group 3a should have read:

On the other hand, Yb3+ has an f13 configuration, so it does meet his three unfilled shells criterion. Had he known, he probably would've put a broken line around Yb to indicate its full f14 complement but that it normally acted as a rare earth, with an incomplete 4f shell; whereas neither La nor Lu have this capacity.

Good to see Foster put so much thought into organising his table, and his experience with using it for instructional purposes.

Van Spronsen does not mention Forster's table. Mazurs has a reference to Foster's table but lumps it in with the other medium-long tables, not appreciating its subtlety.

Mark Leach writes:

This formulation is very much like the XBL 769-10601, Periodic Table Before World War II used by Seaborg and the Manhattan project and is a precursor to the modern periodic table.

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Vernon's Oxidation Number Periodic Table

René Vernon's periodic table showing oxidation number trends.

René writes:

Click image to enlarge

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Chemogenesis In 700 Seconds

The Chemogenesis analysis – by Mark Leach – tells the story of how chemical structure and reactivity emerge from the periodic table of the elements. This video is a rapid dash through the story... which unfolds over many pages of the Chemogenesis Web Book.

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The Periodic Table: Is it Perfect, is it Fractured or is it Broken?

A video from Mark Leach, who writes:

The periodic table is an icon of science. Indeed, all chemical matter is made from periodic table stuff. The periodic table of 118 elements is often presented as being: (a) complete, (b) 'perfectly' described by the application of four quantum numbers with the application of some simple rules and (c) chemical structure & reactivity can be deduced from the periodicity of the Groups & Periods. However, the chemistry of the chemical elements is a little more involved than this. So, where & why does the predictability 'break'?

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What is the Periodic Table Showing? Periodicity

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