Elements—Old Vertex Sourced

notes
science
mathematics
llm
elements
Properties of the elements in charts and tables.
Author

Stephen J. Mildenhall

Published

2025-08-10

Modified

2025-08-18

Mendeleev (1834-1907) imagined at work on the periodic table.

Mendeleev (1834-1907) imagined at work on the periodic table.

1 Data

The charts and tables in this post use data from the Vertex Printable Period Table of Elements, which provides a comprehensive Excel database of elements and a very nice, easily customized, period table layout. Commentary and estimates of discovery year for ancient elements provided by GPT5. Alas, about when I finished the post I learned about the Mendeleev Python package, see Section 5.

1.1 Discovery Year

The discovery year data is adjusted according to Table 1.

Table 1: Adjusted discovery year.
Element Known Since / Discovery Details Year (approx.)
Carbon Charcoal by ~3750 BC; diamond by ~2500 BC 3750 BC
Sulfur Documented use in Egypt by ~2000 BC 2000 BC
Iron Meteoric iron ~4000 BC; smelted ~1500 BC 4000 BC
Copper Use by ~8000 BC; smelting by ~5000 BC, Bronze Age ~3500 BC 8000 BC
Tin Bronze tool-making ~3500 BC 3500 BC
Silver Known by ~5000 BC 5000 BC
Antimony Artifact ~3000 BC; isolation in alchemical era 3000 BC
Arsenic Isolated by Albertus Magnus (~1250 AD) 1250 AD
Gold Known in prehistoric times (~2500 BC) 2500 BC
Mercury Used from cinnabar in Egypt & China by ~1500 BC 1500 BC
Lead Smelting in Anatolia/Mesopotamia by ~3500 BC 3500 BC
Bismuth Distinguished as separate element by Claude-François Geoffroy (1753) 1753 AD
Zinc Known/used by medieval times (~1374 AD) 1374 AD

2 Charts

Coloring is by block (s, p, d, f) with paler colors for higher periods. Vertical lines separate the blocks.

2.1 Atomic weight

Atomic weight (more precisely, relative atomic mass) is the weighted average mass of an element’s naturally occurring isotopes, measured relative to one-twelfth of the mass of a carbon-12 atom. It is dimensionless (a ratio), but in practice often written in unified atomic mass units (u), where 1 u ≈ 1.660 539 × 10⁻²⁷ kg. The value reflects both the number of protons and neutrons in the nucleus and the proportions of each isotope found in nature, which means it can vary slightly depending on the source of the element—chlorine, for example, has an atomic weight of about 35.45 because it is roughly 75 % chlorine-35 and 25 % chlorine-37. Some elements, especially those with only one stable isotope (e.g., fluorine-19, beryllium-9), have atomic weights that are essentially fixed, while others with large isotope variations (e.g., lithium, boron) may be given as ranges by IUPAC. For radioactive elements with no stable isotopes, an atomic weight is not fixed and is often based on the most stable isotope or the isotope most commonly used in research.

Figure 1: Atomic weight.

2.2 Density

Density is the mass per unit volume of a substance, typically expressed for elements in kilograms per cubic metre (kg·m⁻³) or grams per cubic centimetre (g·cm⁻³). For solids and liquids, density depends on both the mass of individual atoms and how closely they are packed in the crystal or molecular structure. In the periodic table, metals tend to have higher densities than nonmetals because their atoms are both heavier and packed tightly in metallic lattices. Osmium and iridium are the densest known elements under standard conditions (both around 22.6 g·cm⁻³), while lithium, the least dense metal, has a density of just 0.534 g·cm⁻³—light enough to float on water. Nonmetals vary widely: solid carbon (graphite) is about 2.27 g·cm⁻³, while gaseous elements like helium have densities in the thousandths of a g·cm⁻³ at room temperature. Density can also change significantly with temperature and pressure; for example, metals expand slightly when heated, lowering their density, while gases follow the ideal gas law and decrease in density more sharply with rising temperature at constant pressure.

See Section 4 for estimates of density based on atomic weight, crystal structure and atomic radius.

Figure 2: Density (g/cm3).

2.3 Melting and boiling points

When plotted across the periodic table, melting and boiling points reveal distinct trends and striking anomalies. Metals in the middle of the transition series, such as tungsten, have exceptionally high melting points (tungsten’s is the highest of all, 3422 °C), while noble gases like helium remain liquefied only near absolute zero (helium’s boiling point is the lowest known, −268.93 °C). Carbon is unusual in that at atmospheric pressure it does not melt but sublimates directly to gas at about 3900 K, giving it one of the highest sublimation points of any element. Gallium is another oddity—its melting point is just 29.76 °C, meaning it can melt in the palm of your hand, yet its boiling point is a much higher 2400 °C, an unusually wide liquid range for a metal. The alkali metals show a steady increase in both melting and boiling points up a group, while the halogens progress from gases to solids with rising boiling points as atomic mass increases. Mercury is a notable liquid metal at room temperature, with a melting point of −38.83 °C and a relatively low boiling point of 356.73 °C. These extremes—whether in refractory metals, cryogenic gases, or unusual phase behavior—mark the boundaries of elemental physical properties.

Figure 3: Melting point.
Figure 4: Boiling point.

2.4 Ionization energy and electron affinity

These are complementary measures, but not strict opposites.

  • Ionization energy, Figure 5, measures how much energy you must put in to remove an electron from a neutral atom.
  • Electron affinity Figure 6, measures how much energy is released (or absorbed) when you add an electron to a neutral atom.

High ionization energy usually goes with a strongly negative electron affinity (atoms both hold on to electrons tightly and want more—e.g., fluorine, chlorine). Low ionization energy often accompanies small or even positive electron affinity (atoms lose electrons easily and don’t strongly attract extras—e.g., alkali metals, noble gases).

But the relationship isn’t perfectly mirrored because the processes involve different initial and final states, and subshell structure can skew the trends.

Ionization energy

Ionization energy is the amount of energy required to remove the most loosely bound electron from a neutral atom in its gaseous state, producing a singly charged positive ion. It is usually expressed in electronvolts (eV, shown here) or kilojoules per mole (kJ·mol⁻¹). When plotted by element, first ionization energy shows a strong periodic trend: it generally increases across a period from left to right, reflecting the growing nuclear charge that holds electrons more tightly, and decreases down a group as outer electrons are farther from the nucleus and more shielded by inner shells. The noble gases sit at the top of each period, with helium having the highest value of all (24.59 eV, 2372 kJ·mol⁻¹), while alkali metals like cesium and francium have the lowest, reflecting how easily they lose their single valence electron. Notable irregularities occur in elements like boron and oxygen, where subshell structure slightly lowers the expected value. These variations reflect the interplay of nuclear charge, electron shielding, and subshell stability.

Figure 5: Ionization energy (eV).

Electron affinity

Electron affinity is the change in energy when a neutral atom in the gaseous state gains an electron to form a negative ion. It is usually expressed in electronvolts (eV, shown here) or kilojoules per mole (kJ·mol⁻¹); by convention, a negative value means energy is released (exothermic), while a positive value means energy is required (endothermic). Across a period from left to right, electron affinity generally becomes more negative as atoms have a stronger tendency to complete their valence shell—halogens are the most extreme, with chlorine releasing about −3.6 eV (−349 kJ·mol⁻¹) when gaining an electron. Noble gases have positive electron affinities because adding an electron would start a new shell, which is energetically unfavorable. Down a group, the trend is less regular than for ionization energy: while increasing atomic size generally makes electron gain less favorable, subshell configurations cause exceptions, such as oxygen’s slightly less negative value than sulfur’s, due to electron–electron repulsion in its compact 2p shell. These variations highlight the balance between nuclear attraction, electron shielding, and subshell stability in determining how readily an atom will accept an extra electron.

Figure 6: Electron Affinity (kJ/mol)/

2.5 Radii

An element’s radius can be defined in several different ways, depending on how the atom is bonded or measured, and each definition captures a different aspect of its size.

  • Metallic radius (Figure 7) is half the distance between the nuclei of two adjacent atoms in a pure metallic crystal; it is most relevant for metals and is typically larger than other definitions because metallic bonding allows atoms to be packed but still delocalized.
  • Covalent radius (Figure 8) is half the distance between the nuclei of two atoms joined by a single covalent bond; it applies mainly to nonmetals and covalently bonded solids and tends to be smaller than the metallic radius for the same element.
  • Atomic radius (Figure 9) is often a more general term—sometimes used for the covalent value, sometimes defined from theoretical models like the Bohr radius for hydrogen. Figure 9 shows the metallic radius for metals and the covalent radius otherwise.
  • Van der Waals radius (Figure 10) measures half the distance between two non-bonded atoms when they are in closest contact (e.g., in neighboring molecules in a crystal or liquid); it is the largest of these radii, since it represents the “personal space” an atom keeps when no bond is present.

When plotted across the periodic table, all radii decrease from left to right within a period due to increasing nuclear charge, and increase down a group as additional electron shells are added. Differences between these four radii reflect the type of interaction being measured—tightly bound in covalent bonds, more spread out in metallic lattices, and most expansive when only weak van der Waals forces act.

Figure 7: Metallic Radius (pm).
Figure 8: Covalent radius (pm).
Figure 9: Atomic Radius (pm).
Figure 10: Van der Waals Radius (pm).

2.6 Electro-negativity

Electronegativity is a dimensionless measure of how strongly an atom attracts shared electrons in a chemical bond. It is not a directly measurable physical quantity but is derived from other data, most famously by Linus Pauling, whose Pauling scale remains the most widely used. Other scales, like Mulliken or Allred–Rochow, use ionization energy and electron affinity or electrostatic arguments to produce similar trends. On the Pauling scale, values range from about 0.7 (cesium and francium, very weak attraction) to 4.0 (fluorine, the strongest). Across a period from left to right, electronegativity increases due to rising nuclear charge and smaller atomic radii, making the nucleus’s pull on bonding electrons stronger. Down a group, it decreases as added electron shells increase shielding and distance from the nucleus. Noble gases are usually omitted because they rarely form covalent bonds, though some heavier ones can. Extremes include fluorine (highest), oxygen (second highest), and cesium/francium (lowest). Electronegativity is related to both ionization energy and electron affinity—atoms with high values for both tend to have high electronegativity—but because it deals with shared electrons in bonds rather than isolated atoms, the correlation is not exact.

Figure 11: Electro-negativity (Pauling).

2.7 Thermal conductivity

Thermal conductivity is a measure of how efficiently a material transfers heat, usually expressed in watts per meter per kelvin (W·m⁻¹·K⁻¹). For elements, it largely depends on how mobile the electrons or lattice vibrations (phonons) are in carrying thermal energy. Metals, with their “sea” of delocalized electrons, generally have the highest thermal conductivities—silver holds the record at about 429 W·m⁻¹·K⁻¹, closely followed by copper and gold—while nonmetals vary widely depending on structure. Diamond (a form of carbon) is exceptional, with the highest known thermal conductivity of any bulk material (~2200 W·m⁻¹·K⁻¹) due to its rigid, perfectly ordered covalent lattice and strong covalent bonds. At the other extreme, elements like sulfur, phosphorus, and the noble gases have extremely low conductivities, as they rely solely on phonon transport through relatively weakly bound structures. Trends in the periodic table are less regular than for properties like ionization energy, since conductivity depends not only on bonding type but also on crystal structure, defects, and isotopic composition.

Figure 12: Thermal Conductivity, W/(m K)

2.8 Electrical resistivity

Electrical resistivity measures how strongly a material opposes the flow of electric current, with units of ohm-meters (Ω·m). It is the inverse of electrical conductivity, so low resistivity means high conductivity. Among the elements, silver has the lowest resistivity (~1.59 × 10⁻⁸ Ω·m), followed closely by copper and gold, which is why these metals dominate in electrical wiring and contacts. Most metals have low resistivities because their delocalized conduction electrons can move freely through the metallic lattice. In contrast, nonmetals and metalloids such as sulfur, phosphorus, and silicon have much higher resistivities—ranging from semiconducting values in silicon (~10⁻³ to 10³ Ω·m, depending on doping) to extremely high, effectively insulating values in materials like sulfur or diamond (>10¹² Ω·m). Temperature strongly affects resistivity: in pure metals it increases with temperature due to greater scattering of electrons by lattice vibrations, while in semiconductors it decreases as more charge carriers become available. Extreme cases include superconductors, which have effectively zero resistivity below their critical temperature.

Figure 13: Electrical Resistivity (Ωm)

3 Tables

3.1 Basic Facts

Table 2: Phase, type, electron configuration, group, and crystal structure by element.
Name Symbol Atomic Number Phase at STP Type Electron Configuration Group 2 Crystal Structure
Hydrogen H 1 Gas Non Metal 1s1 IA hex
Helium He 2 Gas Noble Gas 1s2 VIIIA
Lithium Li 3 Solid Alkali Metal [He] 2s1 IA BCC
Beryllium Be 4 Solid Alkaline Earth Metal [He] 2s2 IIA HCP
Boron B 5 Solid Metalloids [He] 2s2 2p1 IIIA rhom.
Carbon C 6 Solid Non Metal [He] 2s2 2p2 IVA hex
Nitrogen N 7 Gas Non Metal [He] 2s2 2p3 VA hex
Oxygen O 8 Gas Non Metal [He] 2s2 2p4 VIA §cubic
Fluorine F 9 Gas Halogen [He] 2s2 2p5 VIIA §cubic
Neon Ne 10 Gas Noble Gas [He] 2s2 2p6 VIIIA FCC
Sodium Na 11 Solid Alkali Metal [Ne] 3s1 IA BCC
Magnesium Mg 12 Solid Alkaline Earth Metal [Ne] 3s2 IIA HCP
Aluminum Al 13 Solid Poor Metal [Ne] 3s2 3p1 IIIA FCC
Silicon Si 14 Solid Metalloids [Ne] 3s2 3p2 IVA cubic
Phosphorus P 15 Solid Non Metal [Ne] 3s2 3p3 VA §
Sulfur S 16 Solid Non Metal [Ne] 3s2 3p4 VIA FCO
Chlorine Cl 17 Gas Halogen [Ne] 3s2 3p5 VIIA BCO
Argon Ar 18 Gas Noble Gas [Ne] 3s2 3p6 VIIIA FCC
Potassium K 19 Solid Alkali Metal [Ar] 4s1 IA BCC
Calcium Ca 20 Solid Alkaline Earth Metal [Ar] 4s2 IIA FCC
Scandium Sc 21 Solid Transition Metal [Ar] 3d1 4s2 IIIB HCP
Titanium Ti 22 Solid Transition Metal [Ar] 3d2 4s2 IVB HCP
Vanadium V 23 Solid Transition Metal [Ar] 3d3 4s2 VB BCC
Chromium Cr 24 Solid Transition Metal [Ar] 3d5 4s1 VIB BCC
Manganese Mn 25 Solid Transition Metal [Ar] 3d5 4s2 VIIB §cubic
Iron Fe 26 Solid Transition Metal [Ar] 3d6 4s2 VIIIB BCC
Cobalt Co 27 Solid Transition Metal [Ar] 3d7 4s2 VIIIB HCP
Nickel Ni 28 Solid Transition Metal [Ar] 3d8 4s2 VIIIB FCC
Copper Cu 29 Solid Transition Metal [Ar] 3d10 4s1 IB FCC
Zinc Zn 30 Solid Transition Metal [Ar] 3d10 4s2 IIB §hex
Gallium Ga 31 Solid Poor Metal [Ar] 3d10 4s2 4p1 IIIA §BCO
Germanium Ge 32 Solid Metalloids [Ar] 3d10 4s2 4p2 IVA §cubic
Arsenic As 33 Solid Metalloids [Ar] 3d10 4s2 4p3 VA rhom.
Selenium Se 34 Solid Non Metal [Ar] 3d10 4s2 4p4 VIA §hex
Bromine Br 35 Liquid Halogen [Ar] 3d10 4s2 4p5 VIIA BCO
Krypton Kr 36 Gas Noble Gas [Ar] 3d10 4s2 4p6 VIIIA FCC
Rubidium Rb 37 Solid Alkali Metal [Kr] 5s1 IA BCC
Strontium Sr 38 Solid Alkaline Earth Metal [Kr] 5s2 IIA FCC
Yttrium Y 39 Solid Transition Metal [Kr] 4d1 5s2 IIIB HCP
Zirconium Zr 40 Solid Transition Metal [Kr] 4d2 5s2 IVB HCP
Niobium Nb 41 Solid Transition Metal [Kr] 4d4 5s1 VB BCC
Molybdenum Mo 42 Solid Transition Metal [Kr] 4d5 5s1 VIB BCC
Technetium Tc 43 Synthetic Transition Metal [Kr] 4d5 5s2 VIIB HCP
Ruthenium Ru 44 Solid Transition Metal [Kr] 4d7 5s1 VIIIB HCP
Rhodium Rh 45 Solid Transition Metal [Kr] 4d8 5s1 VIIIB FCC
Palladium Pd 46 Solid Transition Metal [Kr] 4d10 VIIIB FCC
Silver Ag 47 Solid Transition Metal [Kr] 4d10 5s1 IB FCC
Cadmium Cd 48 Solid Transition Metal [Kr] 4d10 5s2 IIB §hex
Indium In 49 Solid Poor Metal [Kr] 4d10 5s2 5p1 IIIA §tetra.
Tin Sn 50 Solid Poor Metal [Kr] 4d10 5s2 5p2 IVA §tetra.
Antimony Sb 51 Solid Metalloids [Kr] 4d10 5s2 5p3 VA §rhom.
Tellurium Te 52 Solid Metalloids [Kr] 4d10 5s2 5p4 VIA hex
Iodine I 53 Solid Halogen [Kr] 4d10 5s2 5p5 VIIA BCO
Xenon Xe 54 Gas Noble Gas [Kr] 4d10 5s2 5p6 VIIIA FCC
Cesium Cs 55 Solid Alkali Metal [Xe] 6s1 IA BCC
Barium Ba 56 Solid Alkaline Earth Metal [Xe] 6s2 IIA BCC
Lanthanum La 57 Solid Rare Earth Metal [Xe] 5d1 6s2 Lanthanides §hex
Cerium Ce 58 Solid Rare Earth Metal [Xe] 4f1 5d1 6s2 Lanthanides FCC
Praseodymium Pr 59 Solid Rare Earth Metal [Xe] 4f3 6s2 Lanthanides §hex
Neodymium Nd 60 Solid Rare Earth Metal [Xe] 4f4 6s2 Lanthanides §hex
Promethium Pm 61 Synthetic Rare Earth Metal [Xe] 4f5 6s2 Lanthanides HCP
Samarium Sm 62 Solid Rare Earth Metal [Xe] 4f6 6s2 Lanthanides §hex
Europium Eu 63 Solid Rare Earth Metal [Xe] 4f7 6s2 Lanthanides BCC
Gadolinium Gd 64 Solid Rare Earth Metal [Xe] 4f7 5d1 6s2 Lanthanides HCP
Terbium Tb 65 Solid Rare Earth Metal [Xe] 4f9 6s2 Lanthanides HCP
Dysprosium Dy 66 Solid Rare Earth Metal [Xe] 4f10 6s2 Lanthanides HCP
Holmium Ho 67 Solid Rare Earth Metal [Xe] 4f11 6s2 Lanthanides HCP
Erbium Er 68 Solid Rare Earth Metal [Xe] 4f12 6s2 Lanthanides HCP
Thulium Tm 69 Solid Rare Earth Metal [Xe] 4f13 6s2 Lanthanides HCP
Ytterbium Yb 70 Solid Rare Earth Metal [Xe] 4f14 6s2 Lanthanides FCC
Lutetium Lu 71 Solid Rare Earth Metal [Xe] 4f14 5d1 6s2 Lanthanides HCP
Hafnium Hf 72 Solid Transition Metal [Xe] 4f14 5d2 6s2 IVB HCP
Tantalum Ta 73 Solid Transition Metal [Xe] 4f14 5d3 6s2 VB BCC
Tungsten W 74 Solid Transition Metal [Xe] 4f14 5d4 6s2 VIB BCC
Rhenium Re 75 Solid Transition Metal [Xe] 4f14 5d5 6s2 VIIB HCP
Osmium Os 76 Solid Transition Metal [Xe] 4f14 5d6 6s2 VIIIB HCP
Iridium Ir 77 Solid Transition Metal [Xe] 4f14 5d7 6s2 VIIIB FCC
Platinum Pt 78 Solid Transition Metal [Xe] 4f14 5d9 6s1 VIIIB FCC
Gold Au 79 Solid Transition Metal [Xe] 4f14 5d10 6s1 IB FCC
Mercury Hg 80 Liquid Transition Metal [Xe] 4f14 5d10 6s2 IIB §rhom.
Thallium Tl 81 Solid Poor Metal [Hg] 6p1 IIIA HCP
Lead Pb 82 Solid Poor Metal [Hg] 6p2 IVA FCC
Bismuth Bi 83 Solid Poor Metal [Hg] 6p3 VA §rhom.
Polonium Po 84 Solid Metalloids ? [Hg] 6p4 VIA §cubic
Astatine At 85 Solid Metalloids [Hg] 6p5 VIIA
Radon Rn 86 Gas Noble Gas [Hg] 6p6 VIIIA
Francium Fr 87 Solid Alkali Metal [Rn] 7s1 IA
Radium Ra 88 Solid Alkaline Earth Metal [Rn] 7s2 IIA BCC
Actinium Ac 89 Solid Rare Earth Metal [Rn] 6d1 7s2 Actinides FCC
Thorium Th 90 Solid Rare Earth Metal [Rn] 6d2 7s2 Actinides FCC
Protactinium Pa 91 Solid Rare Earth Metal [Rn] 5f2 6d1 7s2 Actinides §tetra
Uranium U 92 Solid Rare Earth Metal [Rn] 5f3 6d1 7s2 Actinides BCO
Neptunium Np 93 Synthetic Rare Earth Metal [Rn] 5f4 6d1 7s2 Actinides SO
Plutonium Pu 94 Synthetic Rare Earth Metal [Rn] 5f6 7s2 Actinides §mono.
Americium Am 95 Synthetic Rare Earth Metal [Rn] 5f7 7s2 Actinides HCP
Curium Cm 96 Synthetic Rare Earth Metal [Rn] 5f7 6d 7s2 Actinides HCP
Berkelium Bk 97 Synthetic Rare Earth Metal [Rn] 5f9 7s2 Actinides hex
Californium Cf 98 Synthetic Rare Earth Metal [Rn] 5f10 7s2 Actinides hex
Einsteinium Es 99 Synthetic Rare Earth Metal [Rn] 5f11 7s2 Actinides
Fermium Fm 100 Synthetic Rare Earth Metal [Rn] 5f12 7s2 Actinides
Mendelevium Md 101 Synthetic Rare Earth Metal [Rn] 5f13 7s2 Actinides
Nobelium No 102 Synthetic Rare Earth Metal [Rn] 5f14 7s2 Actinides
Lawrencium Lr 103 Synthetic Rare Earth Metal [Rn] 5f14 7s2 7p1 Actinides
Rutherfordium Rf 104 Synthetic Transition Metal [Rn] 5f14 6d2 7s2 IVB
Dubnium Db 105 Synthetic Transition Metal [Rn] 5f14 6d3 7s2 VB
Seaborgium Sg 106 Synthetic Transition Metal [Rn] 5f14 6d4 7s2 VIB
Bohrium Bh 107 Synthetic Transition Metal [Rn] 5f14 6d5 7s2 VIIB
Hassium Hs 108 Synthetic Transition Metal [Rn] 5f14 6d6 7s2 VIIIB
Meitnerium Mt 109 Synthetic Transition Metal ? [Rn] 5f14 6d7 7s2 ? VIIIB
Darmstadtium Ds 110 Synthetic Transition Metal ? [Rn] 5f14 6d8 7s2 ? VIIIB
Roentgenium Rg 111 Synthetic Transition Metal ? [Rn] 5f14 6d9 7s2 ? IB
Copernicium Cn 112 Synthetic Transition Metal [Rn] 5f14 6d10 7s2 ? IIB
Nihonium Nh 113 Synthetic Post-Transition Metal ? [Rn] 5f14 6d10 7s2 7p1 ? IIIA
Flerovium Fl 114 Synthetic Post-Transition Metal ? [Rn] 5f14 6d10 7s2 7p2 ? IVA
Moscovium Mc 115 Synthetic Post-Transition Metal ? [Rn] 5f14 6d10 7s2 7p3 ? VA
Livermorium Lv 116 Synthetic Post-Transition Metal ? [Rn] 5f14 6d10 7s2 7p4 ? VIA
Tennessine Ts 117 Synthetic Post-Transition Metal ? [Rn] 5f14 6d10 7s2 7p5 ? VIIA
Oganesson Og 118 Synthetic Noble Gas ? [Rn] 5f14 6d10 7s2 7p6 ? VIIIA

Phase at STP

Type

Type is a broad chemical classification of elements, grouping them by their general physical and chemical properties. It’s a way of labelling an element according to where it sits in the periodic table and the kind of bonding and reactivity it usually shows.

Metals

A metal is an element that tends to lose electrons to form positive ions and whose atoms in the solid state are bound by metallic bonding—a lattice of positive atomic cores surrounded by a “sea” of delocalised electrons. This electron cloud gives metals their characteristic properties: high electrical and thermal conductivity, malleability, ductility, and metallic lustre. Most metals have only one to three electrons in their outermost shell, which are relatively weakly bound and easily delocalised; these configurations are common in the s-block (alkali and alkaline earth metals), d-block (transition metals), and lower p-block (post-transition metals). The periodic table position is a strong guide, with metals dominating the left and centre, nonmetals at the upper right, and metalloids along the boundary between them. While outer-shell electron count is a good predictor of metallic behaviour, the decisive factor is the electronic band structure—specifically, whether the valence and conduction bands overlap to allow electrons to move freely. Edge cases exist, such as metalloids that can act metallic under some conditions, or nonmetals like hydrogen that become metallic only at high pressures.

Metals vs. nonmetals vs. metalloids

  • Metals (e.g., iron, copper, aluminum) are generally good conductors of heat and electricity, malleable, and form positive ions (cations) in compounds.
  • Nonmetals (e.g., oxygen, sulfur, chlorine) are poor conductors, often brittle in solid form, and tend to form negative ions (anions) or covalent bonds.
  • Metalloids (e.g., boron, silicon, arsenic) have properties intermediate between metals and nonmetals, often depending on the chemical environment.

Specific subcategories

These are based mostly on position in the periodic table.

  • Alkali metals — Group 1 (except hydrogen): Li, Na, K, Rb, Cs, Fr. Very reactive metals with one valence electron, low melting points, form strong bases with water.

  • Alkaline earth metals — Group 2: Be, Mg, Ca, Sr, Ba, Ra. Reactive metals with two valence electrons, form basic oxides.

  • Transition metals — Groups 3–12 in the “d-block” of the periodic table. Variable oxidation states, form coloured compounds, often good catalysts. The “Transition Metal ?” label in your list likely means uncertain classification, perhaps due to inconsistent data source mapping.

  • Rare earth metals — The lanthanides (La to Lu) and sometimes Sc and Y. Similar reactivity and electron configurations (4f-block), often used in magnets, alloys, and phosphors.

  • Poor metals / Post-transition metals — Metals in the p-block that are softer, lower melting, and poorer conductors than transition metals (e.g., Al, Ga, In, Sn, Tl, Pb, Bi). “Post-transition” is essentially the same concept; the difference in your list may come from merging multiple data sources.

  • Noble gases — Group 18: He, Ne, Ar, Kr, Xe, Rn, Og. Chemically inert under most conditions, full valence shell. “Noble Gas ?” means an uncertain flag in the source data.

  • Halogens — Group 17: F, Cl, Br, I, At, Ts. Reactive nonmetals with seven valence electrons, form salts with metals.

Crystal Structure

Most elements crystallise at ambient conditions into a small set of common crystal structures, each defined by how atoms are arranged in three-dimensional space. These arrangements determine packing density, nearest-neighbour distances, and many physical properties such as density, strength, and conductivity. The most relevant for elemental solids are:

  • Face-centred cubic (FCC) — Atoms are located at each corner of a cube and at the centres of all cube faces. This structure is close-packed, with a packing fraction of 0.74, and each atom has 12 nearest neighbours. Many ductile metals adopt FCC at room temperature, including aluminium, copper, silver, and gold.

  • Body-centred cubic (BCC) — Atoms are located at each cube corner and one atom at the cube’s body centre. This is not close-packed (packing fraction 0.68) and has 8 nearest neighbours. BCC metals such as iron (at room temperature), chromium, and tungsten are typically stronger and harder but less ductile than FCC metals.

  • Hexagonal close-packed (HCP) — Layers of atoms form a hexagonal lattice, with each atom surrounded by 12 nearest neighbours. This is also a close-packed structure (packing fraction 0.74) but has a different stacking sequence from FCC. Metals such as magnesium, titanium, zinc, and cobalt adopt HCP at ambient conditions.

  • Diamond cubic — A variation of the FCC lattice where each atom is covalently bonded to four others in a tetrahedral arrangement. This open structure has a low packing fraction (~0.34) and is characteristic of covalently bonded elements such as carbon (diamond form), silicon, and germanium.

  • Simple cubic (SC) — Atoms occupy only the cube corners, each with 6 nearest neighbours. This has a low packing fraction (0.52) and is rare among elements; polonium is the only one that adopts it at ambient conditions.

These are the main model structures used in elemental crystallography. Some elements adopt more complex forms—rhombohedral (bismuth, antimony), orthorhombic (sulfur), monoclinic (selenium)—but these can’t be treated as close-packed sphere models and usually require experimental lattice constants for accurate property calculations.

Key to table.

Abbrev. Likely meaning Number Examples
HCP Hexagonal close-packed 23 Be, Mg, Ti
FCC Face-centred cubic 20 Al, Cu, Ag
BCC Body-centred cubic 15 Li, Fe, W
§hex Hexagonal (non-close-packed variant or dhcp) 7 Zn, Cd, La
hex Hexagonal (molecular or layered) 6 H, C (graphite)
§cubic Cubic (unspecified, often molecular) 5 O, F, Po
BCO Base-centred orthorhombic 4 Cl, Br, I
§rhom. Rhombohedral 3 Sb, Bi, Hg
rhom. Rhombohedral 2 B, As
§tetra. Tetragonal 2 In, Sn
FCO Face-centred orthorhombic 1 S
cubic Cubic (unspecified type) 1 Si
§ Unknown / unspecified 1 P
§BCO Base-centred orthorhombic (alt. notation) 1 Ga
§tetra Tetragonal (alt. notation) 1 Pb? (check)
SO Simple orthorhombic 1 Np
§mono. Monoclinic 1 Pu
Table 3: Basic numerical characteristics by element.
Name Symbol Atomic Number Atomic Weight Melting Point (°C) Boiling Point (°C) Density (g/cm3) Electron Affinity (kJ/mol) Thermal Conductivity, W/(m K) Electrical Resistivity (Ωm)
Hydrogen H 1 1.01 -259.14 -252.87 0.09 72.80 0.18
Helium He 2 4.00 -268.93 0.18 0.15
Lithium Li 3 6.94 180.54 1,342.00 0.54 59.60 85.00 0.00
Beryllium Be 4 9.01 1,287.00 2,470.00 1.85 190.00 0.00
Boron B 5 10.81 2,075.00 4,000.00 2.46 26.70 27.00 10,000.00
Carbon C 6 12.01 3,550.00 4,027.00 2.26 153.90 140.00 0.00
Nitrogen N 7 14.01 -210.10 -195.79 1.25 7.00 0.03
Oxygen O 8 16.00 -218.30 -182.90 1.43 141.00 0.03
Fluorine F 9 19.00 -219.60 -188.12 1.70 328.00 0.03
Neon Ne 10 20.18 -248.59 -246.08 0.90 0.05
Sodium Na 11 22.99 97.72 883.00 0.97 52.80 140.00 0.00
Magnesium Mg 12 24.30 650.00 1,090.00 1.74 160.00 0.00
Aluminum Al 13 26.98 660.32 2,519.00 2.70 42.50 235.00 0.00
Silicon Si 14 28.09 1,414.00 2,900.00 2.33 133.60 150.00 0.00
Phosphorus P 15 30.97 44.20 280.50 1.82 72.00 0.24 0.00
Sulfur S 16 32.06 115.21 444.72 1.96 200.00 0.20
Chlorine Cl 17 35.45 -101.50 -34.04 3.21 349.00 0.01
Argon Ar 18 39.95 -189.30 -185.80 1.78 0.02
Potassium K 19 39.10 63.38 759.00 0.86 48.40 100.00 0.00
Calcium Ca 20 40.08 842.00 1,484.00 1.55 2.37 200.00 0.00
Scandium Sc 21 44.96 1,541.00 2,830.00 2.98 18.10 16.00 0.00
Titanium Ti 22 47.87 1,668.00 3,287.00 4.51 7.60 22.00 0.00
Vanadium V 23 50.94 1,910.00 3,407.00 6.11 50.60 31.00 0.00
Chromium Cr 24 52.00 1,907.00 2,671.00 7.14 64.30 94.00 0.00
Manganese Mn 25 54.94 1,246.00 2,061.00 7.47 7.80 0.00
Iron Fe 26 55.84 1,538.00 2,861.00 7.87 15.70 80.00 0.00
Cobalt Co 27 58.93 1,495.00 2,927.00 8.90 63.70 100.00 0.00
Nickel Ni 28 58.69 1,455.00 2,913.00 8.91 112.00 91.00 0.00
Copper Cu 29 63.55 1,084.62 2,927.00 8.92 118.40 400.00 0.00
Zinc Zn 30 65.41 419.53 907.00 7.14 120.00 0.00
Gallium Ga 31 69.72 29.76 2,204.00 5.90 28.90 29.00 0.00
Germanium Ge 32 72.64 938.30 2,820.00 5.32 119.00 60.00 0.00
Arsenic As 33 74.92 817.00 614.00 5.73 78.00 50.00 0.00
Selenium Se 34 78.96 221.00 685.00 4.82 195.00 0.52
Bromine Br 35 79.90 -7.30 59.00 3.12 324.60 0.12
Krypton Kr 36 83.80 -157.36 -153.22 3.75 0.01
Rubidium Rb 37 85.47 39.31 688.00 1.53 46.90 58.00 0.00
Strontium Sr 38 87.62 777.00 1,382.00 2.63 5.03 35.00 0.00
Yttrium Y 39 88.91 1,526.00 3,345.00 4.47 29.60 17.00 0.00
Zirconium Zr 40 91.22 1,855.00 4,409.00 6.51 41.10 23.00 0.00
Niobium Nb 41 92.91 2,477.00 4,744.00 8.57 86.10 54.00 0.00
Molybdenum Mo 42 95.94 2,623.00 4,639.00 10.28 71.90 139.00 0.00
Technetium Tc 43 98.00 2,157.00 4,265.00 11.50 53.00 51.00 0.00
Ruthenium Ru 44 101.07 2,334.00 4,150.00 12.37 101.30 120.00 0.00
Rhodium Rh 45 102.91 1,964.00 3,695.00 12.45 109.70 150.00 0.00
Palladium Pd 46 106.42 1,554.90 2,963.00 12.02 53.70 72.00 0.00
Silver Ag 47 107.87 961.78 2,162.00 10.49 125.60 430.00 0.00
Cadmium Cd 48 112.41 321.07 767.00 8.65 97.00 0.00
Indium In 49 114.82 156.60 2,072.00 7.31 28.90 82.00 0.00
Tin Sn 50 118.71 231.93 2,602.00 7.31 107.30 67.00 0.00
Antimony Sb 51 121.76 630.63 1,587.00 6.70 103.20 24.00 0.00
Tellurium Te 52 127.60 449.51 988.00 6.24 190.20 3.00 0.00
Iodine I 53 126.90 113.70 184.30 4.94 295.20 0.45
Xenon Xe 54 131.29 -111.80 -108.00 5.90 0.01
Cesium Cs 55 132.91 28.44 671.00 1.88 45.50 36.00 0.00
Barium Ba 56 137.33 727.00 1,870.00 3.51 13.95 18.00 0.00
Lanthanum La 57 138.91 920.00 3,464.00 6.15 48.00 13.00 0.00
Cerium Ce 58 140.12 798.00 3,360.00 6.69 50.00 11.00 0.00
Praseodymium Pr 59 140.91 931.00 3,290.00 6.64 50.00 13.00 0.00
Neodymium Nd 60 144.24 1,021.00 3,100.00 7.01 50.00 17.00 0.00
Promethium Pm 61 145.00 1,100.00 3,000.00 7.26 50.00 15.00 0.00
Samarium Sm 62 150.36 1,072.00 1,803.00 7.35 50.00 13.00 0.00
Europium Eu 63 151.96 822.00 1,527.00 5.24 50.00 14.00 0.00
Gadolinium Gd 64 157.25 1,313.00 3,250.00 7.90 50.00 11.00 0.00
Terbium Tb 65 158.93 1,356.00 3,230.00 8.22 50.00 11.00 0.00
Dysprosium Dy 66 162.50 1,412.00 2,567.00 8.55 50.00 11.00 0.00
Holmium Ho 67 164.93 1,474.00 2,700.00 8.79 50.00 16.00 0.00
Erbium Er 68 167.26 1,497.00 2,868.00 9.07 50.00 15.00 0.00
Thulium Tm 69 168.93 1,545.00 1,950.00 9.32 50.00 17.00 0.00
Ytterbium Yb 70 173.04 819.00 1,196.00 6.57 50.00 39.00 0.00
Lutetium Lu 71 174.97 1,663.00 3,402.00 9.84 50.00 16.00 0.00
Hafnium Hf 72 178.49 2,233.00 4,603.00 13.31 0.00 23.00 0.00
Tantalum Ta 73 180.95 3,017.00 5,458.00 16.65 31.00 57.00 0.00
Tungsten W 74 183.84 3,422.00 5,555.00 19.25 78.60 170.00 0.00
Rhenium Re 75 186.21 3,186.00 5,596.00 21.02 14.50 48.00 0.00
Osmium Os 76 190.23 3,033.00 5,012.00 22.61 106.10 88.00 0.00
Iridium Ir 77 192.22 2,466.00 4,428.00 22.65 151.00 150.00 0.00
Platinum Pt 78 195.08 1,768.30 3,825.00 21.09 205.30 72.00 0.00
Gold Au 79 196.97 1,064.18 2,856.00 19.30 222.80 320.00 0.00
Mercury Hg 80 200.59 -38.83 356.73 13.53 8.30 0.00
Thallium Tl 81 204.38 304.00 1,473.00 11.85 19.20 46.00 0.00
Lead Pb 82 207.20 327.46 1,749.00 11.34 35.10 35.00 0.00
Bismuth Bi 83 208.98 271.30 1,564.00 9.78 91.20 8.00 0.00
Polonium Po 84 209.00 254.00 962.00 9.20 183.30 0.00
Astatine At 85 210.00 302.00 270.10 2.00
Radon Rn 86 222.00 -71.00 -61.70 9.73 0.00
Francium Fr 87 223.00
Radium Ra 88 226.00 700.00 1,737.00 5.00 19.00 0.00
Actinium Ac 89 227.00 1,050.00 3,200.00 10.07 12.00
Thorium Th 90 232.04 1,750.00 4,820.00 11.72 54.00 0.00
Protactinium Pa 91 231.04 1,572.00 4,000.00 15.37 47.00 0.00
Uranium U 92 238.03 1,135.00 3,927.00 19.05 27.00 0.00
Neptunium Np 93 237.00 644.00 4,000.00 20.45 6.00 0.00
Plutonium Pu 94 244.00 640.00 3,230.00 19.82 6.00 0.00
Americium Am 95 243.00 1,176.00 2,011.00 10.00
Curium Cm 96 247.00 1,345.00 3,110.00 13.51
Berkelium Bk 97 247.00 1,050.00 14.78 10.00
Californium Cf 98 251.00 900.00 15.10
Einsteinium Es 99 252.00 860.00
Fermium Fm 100 257.00 1,527.00
Mendelevium Md 101 258.00 827.00
Nobelium No 102 259.00 827.00
Lawrencium Lr 103 262.00 1,627.00
Rutherfordium Rf 104 261.00
Dubnium Db 105 262.00
Seaborgium Sg 106 266.00
Bohrium Bh 107 264.00
Hassium Hs 108 277.00
Meitnerium Mt 109 268.00
Darmstadtium Ds 110 281.00
Roentgenium Rg 111 272.00
Copernicium Cn 112 285.00
Nihonium Nh 113 286.00
Flerovium Fl 114 289.00
Moscovium Mc 115 290.00
Livermorium Lv 116 292.00
Tennessine Ts 117 294.00
Oganesson Og 118 294.00

3.2 Year Discovered

Table 4: Year discovered by element.
Name Symbol Atomic Number Discoverer Discovery (Year)
Hydrogen H 1 Cavendish, Henry 1766
Helium He 2 Ramsey, Sir William & Cleve, Per Teodor 1895
Lithium Li 3 Arfvedson, Johan August 1817
Beryllium Be 4 Vauquelin, Nicholas Louis 1797
Boron B 5 Davy, Sir Humphry & Thénard, Louis-Jaques & Gay-Lussac, Louis-Joseph 1808
Carbon C 6 unknown 2500 BC
Nitrogen N 7 Rutherford, Daniel 1772
Oxygen O 8 Priestley, Joseph & Scheele, Carl Wilhelm 1774
Fluorine F 9 Moissan, Henri 1886
Neon Ne 10 Ramsay, William & Travers, Morris 1898
Sodium Na 11 Davy, Sir Humphry 1807
Magnesium Mg 12 Black, Joseph 1755
Aluminum Al 13 Oersted, Hans Christian 1825
Silicon Si 14 Berzelius, Jöns Jacob 1824
Phosphorus P 15 Brandt, Hennig 1669
Sulfur S 16 unknown 2000 BC
Chlorine Cl 17 Scheele, Carl Wilhelm 1774
Argon Ar 18 Ramsay, Sir William & Strutt, John (Lord Rayleigh) 1894
Potassium K 19 Davy, Sir Humphry 1807
Calcium Ca 20 Davy, Sir Humphry 1808
Scandium Sc 21 Nilson, Lars Fredrik 1879
Titanium Ti 22 Gregor, William 1791
Vanadium V 23 Del Rio, Andrés Manuel (1801) & Sefström, Nils Gabriel (1830) 1801
Chromium Cr 24 Vauquelin 1797
Manganese Mn 25 Gahn, Johan Gottlieb 1774
Iron Fe 26 unknown 4000 BC
Cobalt Co 27 Brandt, Georg 1735
Nickel Ni 28 Cronstedt, Alex Fredrik 1751
Copper Cu 29 unknown 8000 BC
Zinc Zn 30 unknown 1374
Gallium Ga 31 Lecoq de Boisbaudran, Paul-Émile 1875
Germanium Ge 32 Winkler, Clemens A. 1886
Arsenic As 33 unknown 1250
Selenium Se 34 Berzelius, Jöns Jacob 1817
Bromine Br 35 Balard, Antoine-Jérôme 1826
Krypton Kr 36 Ramsay, Sir William & Travers, Morris 1898
Rubidium Rb 37 Bunsen, Robert Wilhelm & Kirchhoff, Gustav Robert 1861
Strontium Sr 38 Crawford, Adair 1790
Yttrium Y 39 Gadolin, Johan 1789
Zirconium Zr 40 Klaproth, Martin Heinrich 1789
Niobium Nb 41 Hatchet, Charles 1801
Molybdenum Mo 42 Scheele, Carl Welhelm 1778
Technetium Tc 43 Perrier, Carlo & Segrè, Emilio 1937
Ruthenium Ru 44 Klaus, Karl Karlovich 1844
Rhodium Rh 45 Wollaston, William Hyde 1803
Palladium Pd 46 Wollaston, William Hyde 1803
Silver Ag 47 unknown 5000 BC
Cadmium Cd 48 Stromeyer, Prof. Friedrich 1817
Indium In 49 Reich, Ferdinand & Richter, Hieronymus 1863
Tin Sn 50 unknown 3500 BC
Antimony Sb 51 unknown 3000 BC
Tellurium Te 52 Müller von Reichenstein, Franz Joseph 1782
Iodine I 53 Courtois, Bernard 1811
Xenon Xe 54 Ramsay, William & Travers, Morris William 1898
Cesium Cs 55 Kirchhoff, Gustav & Bunsen, Robert 1860
Barium Ba 56 Davy, Sir Humphry 1808
Lanthanum La 57 Mosander, Carl Gustav 1839
Cerium Ce 58 Hisinger, Wilhelm & Berzelius, Jöns Jacob/Klaproth, Martin Heinrich 1803
Praseodymium Pr 59 Von Welsbach, Baron Auer 1885
Neodymium Nd 60 Von Welsbach, Baron Auer 1885
Promethium Pm 61 Marinsky, Jacob A. & Coryell, Charles D. & Glendenin, Lawerence. E. 1944
Samarium Sm 62 Lecoq de Boisbaudran, Paul-Émile 1879
Europium Eu 63 Demarçay, Eugène-Antole 1901
Gadolinium Gd 64 De Marignac, Charles Galissard 1880
Terbium Tb 65 Mosander, Carl Gustav 1843
Dysprosium Dy 66 Lecoq de Boisbaudran, Paul-Émile 1886
Holmium Ho 67 Cleve, Per Theodor 1879
Erbium Er 68 Mosander, Carl Gustav 1842
Thulium Tm 69 Cleve, Per Teodor 1879
Ytterbium Yb 70 De Marignac, Jean Charles Galissard 1878
Lutetium Lu 71 Urbain, Georges 1907
Hafnium Hf 72 Coster, Dirk & De Hevesy, George Charles 1923
Tantalum Ta 73 Ekeberg, Anders Gustav 1802
Tungsten W 74 Elhuyar, Juan José & Elhuyar, Fausto 1783
Rhenium Re 75 Noddack, Walter & Berg, Otto Carl & Tacke, Ida 1925
Osmium Os 76 Tennant, Smithson 1803
Iridium Ir 77 Tennant, Smithson 1803
Platinum Pt 78 Ulloa, Antonio de 1735
Gold Au 79 unknown 2500 BC
Mercury Hg 80 unknown 1500 BC
Thallium Tl 81 Crookes, William 1861
Lead Pb 82 unknown 3500 BC
Bismuth Bi 83 Geoffroy, Claude 1753
Polonium Po 84 Curie, Marie & Pierre 1898
Astatine At 85 Corson, Dale R. & Mackenzie, K. R. 1940
Radon Rn 86 Dorn, Friedrich Ernst 1900
Francium Fr 87 Perey, Marguerite 1939
Radium Ra 88 Curie, Marie & Pierre 1898
Actinium Ac 89 Debierne, André 1899
Thorium Th 90 Berzelius, Jöns Jacob 1829
Protactinium Pa 91 Göhring, Otto & Fajans, Kasimir 1913
Uranium U 92 Klaproth, Martin Heinrich 1789
Neptunium Np 93 McMillan, Edwin M. & Abelson, Philip H. 1940
Plutonium Pu 94 Glenn T. Seaborg, Joseph W. Kennedy, Edward M. McMillan, Arthur C. Wohl 1940
Americium Am 95 Glenn T. Seaborg, Ralph A. James, Leon O. Morgan, Albert Ghiorso 1944
Curium Cm 96 Glenn T. Seaborg, Ralph A. James, Albert Ghiorso 1944
Berkelium Bk 97 Stanley G. Thompson, Glenn T. Seaborg, Kenneth Street, Jr., Albert Ghiorso 1949
Californium Cf 98 Stanley G. Thompson, Glenn T. Seaborg, Kenneth Street, Jr., Albert Ghiorso 1950
Einsteinium Es 99 Albert Ghiorso et. al. 1952
Fermium Fm 100 Albert Ghiorso et. al. 1952
Mendelevium Md 101 Stanley G. Thompson, Glenn T. Seaborg, Bernard G. Harvey, Gregory R. Choppin, Albert Ghiorso 1955
Nobelium No 102 Albert Ghiorso, Glenn T. Seaborg, Torbørn Sikkeland, John R. Walton 1958
Lawrencium Lr 103 Albert Ghiorso, Torbjørn Sikkeland, Almon E. Larsh, Robert M. Latimer 1961
Rutherfordium Rf 104 Scientists at Dubna, Russia (1964)/Albert Ghiorso et. al. (1969) 1964
Dubnium Db 105 Scientists at Dubna, Russia (1967)/Lawrence Berkeley Laboratory (1970) 1967
Seaborgium Sg 106 Albert Ghiorso et. al. 1974
Bohrium Bh 107 Scientists at Dubna, Russia 1976
Hassium Hs 108 Armbruster, Paula & Muenzenberg, Dr. Gottfried 1984
Meitnerium Mt 109 Armbruster, Paula & Muenzenberg, Dr. Gottfried 1982
Darmstadtium Ds 110 Armbruster, Paula & Muenzenberg, Dr. Gottfried 1994
Roentgenium Rg 111 Hofmann, Sigurd et. al. 1994
Copernicium Cn 112 Armbruster, Paula & Muenzenberg, Dr. Gottfried 1996
Nihonium Nh 113 Y. T. Oganessian et. al. 2004
Flerovium Fl 114 Scientists at Dubna, Russia 1998
Moscovium Mc 115 Y. T. Oganessian et. al. 2004
Livermorium Lv 116 Scientists at Dubna, Russia 2001
Oganesson Og 118 Y. T. Oganessian et. al. 2006

4 Density from radius, crystal structure, and atomic weight

This estimation method uses basic crystallographic geometry to approximate an element’s bulk density from its atomic weight, metallic radius, and crystal structure (Section 3.1.3). The key idea is that, if you know how atoms are arranged in a solid and how big they are, you can calculate the size of the repeating unit cell in the crystal lattice. By combining the unit cell’s volume with the number of atoms it contains and the mass per atom (derived from the atomic weight), you get an estimate of the density. Different crystal structures—face-centred cubic (FCC), body-centred cubic (BCC), hexagonal close-packed (HCP), simple cubic (SC), or diamond cubic—have characteristic relationships between the lattice parameter and the atomic radius, as well as fixed numbers of atoms per unit cell. For close-packed metals, a metallic radius and an idealised \(c/a\) ratio are used; for more accurate work, element-specific \(c/a\) values can be substituted for non-ideal structures such as zinc and cadmium.

This is a first-order physical model and, while it works reasonably well for close-packed metals, it is less reliable for elements with non-metallic bonding, low-symmetry structures, or significant open space in the crystal lattice. In such cases—noble gases, molecular solids, graphite, or unusual hcp variants—the actual packing fraction can deviate substantially from the ideal, leading to large errors. The method also depends on using the correct type of radius (metallic, covalent, or van der Waals) for the structure in question. When applied carefully with appropriate inputs, it can match tabulated densities within about 5–10 % for many metals, while providing a clear, geometry-based link between microscopic atomic parameters and macroscopic material properties.

Table 5: Estimating density from atomic radius, crystal structure, and atomic weight.
Symbol Z Atomic Weight Density Crystal Structure Radius Crystal Radius_pm Density_est Error
Li 3 6.94 0.535 BCC 152.00 bcc 167.00 0.402 -24.9%
Be 4 9.01 1.848 HCP 112.00 hcp 112.00 1.883 1.9%
C 6 12.01 2.260 hex nan diamond 77.00 3.547 56.9%
Na 11 22.99 0.968 BCC 186.00 bcc 190.00 0.904 -6.6%
Mg 12 24.30 1.738 HCP 160.00 hcp 160.00 1.742 0.2%
Al 13 26.98 2.700 FCC 143.00 fcc 143.00 2.709 0.3%
Si 14 28.09 2.330 cubic nan diamond 111.00 2.769 18.8%
K 19 39.10 0.856 BCC 227.00 bcc 243.00 0.735 -14.2%
Ca 20 40.08 1.550 FCC 197.00 fcc 197.00 1.539 -0.7%
Ti 22 47.87 4.507 HCP 147.00 hcp 147.00 4.423 -1.9%
V 23 50.94 6.110 BCC 134.00 bcc 134.00 5.709 -6.6%
Cr 24 52.00 7.140 BCC 128.00 bcc 128.00 6.685 -6.4%
Mn 25 54.94 7.470 §cubic 127.00 bcc 127.00 7.232 -3.2%
Fe 26 55.84 7.874 BCC 126.00 bcc 126.00 7.528 -4.4%
Co 27 58.93 8.900 HCP 125.00 hcp 125.00 8.857 -0.5%
Ni 28 58.69 8.908 FCC 124.00 fcc 124.00 9.036 1.4%
Cu 29 63.55 8.920 FCC 128.00 fcc 128.00 8.895 -0.3%
Zn 30 65.41 7.140 §hex 134.00 hcp 134.00 7.021 -1.7%
Ge 32 72.64 5.323 §cubic nan diamond 122.00 5.393 1.3%
Rb 37 85.47 1.532 BCC 248.00 bcc 265.00 1.238 -19.2%
Sr 38 87.62 2.630 FCC 215.00 fcc 215.00 2.588 -1.6%
Y 39 88.91 4.472 HCP 180.00 hcp 180.00 4.475 0.1%
Zr 40 91.22 6.511 HCP 160.00 hcp 160.00 6.538 0.4%
Nb 41 92.91 8.570 BCC 146.00 bcc 146.00 8.049 -6.1%
Mo 42 95.94 10.280 BCC 139.00 bcc 139.00 9.632 -6.3%
Tc 43 98.00 11.500 HCP 136.00 hcp 136.00 11.436 -0.6%
Ru 44 101.07 12.370 HCP 134.00 hcp 134.00 12.331 -0.3%
Ag 47 107.87 10.490 FCC 144.00 fcc 144.00 10.604 1.1%
Cd 48 112.41 8.650 §hex 151.00 hcp 151.00 8.298 -4.1%
Cs 55 132.91 1.879 BCC 265.00 bcc 298.00 1.354 -27.9%
Ba 56 137.33 3.510 BCC 222.00 bcc 217.00 3.624 3.2%
La 57 138.91 6.146 §hex 187.00 hcp 187.00 6.235 1.5%
Eu 63 151.96 5.244 BCC 180.00 bcc 199.00 5.200 -0.8%
Gd 64 157.25 7.901 HCP 180.00 hcp 180.00 7.915 0.2%
Tb 65 158.93 8.219 HCP 177.00 hcp 177.00 8.413 2.4%
Dy 66 162.50 8.551 HCP 178.00 hcp 178.00 8.458 -1.1%
Ho 67 164.93 8.795 HCP 176.00 hcp 176.00 8.880 1.0%
Er 68 167.26 9.066 HCP 176.00 hcp 176.00 9.006 -0.7%
Tm 69 168.93 9.321 HCP 176.00 hcp 175.00 9.253 -0.7%
Yb 70 173.04 6.570 FCC 176.00 fcc 194.00 6.957 5.9%
Lu 71 174.97 9.841 HCP 174.00 hcp 174.00 9.750 -0.9%
Hf 72 178.49 13.310 HCP 159.00 hcp 159.00 13.035 -2.1%
Ta 73 180.95 16.650 BCC 146.00 bcc 146.00 15.677 -5.8%
W 74 183.84 19.250 BCC 139.00 bcc 139.00 18.458 -4.1%
Re 75 186.21 21.020 HCP 137.00 hcp 137.00 21.257 1.1%
Os 76 190.23 22.610 HCP 135.00 hcp 135.00 22.696 0.4%
Au 79 196.97 19.300 FCC 144.00 fcc 144.00 19.363 0.3%
Pb 82 207.20 11.340 FCC 175.00 fcc 175.00 11.349 0.1%
Po 84 209.00 9.196 §cubic nan sc 167.00 9.314 1.3%
Figure 14: Estimating density from atomic radius, crystal structure, and atomic weight: estimated vs. actual. Diagonal line shows actual.

4.1 Other relationships

Here are some other relationships between observables.

Directly from crystal geometry and atomic constants

  • Molar volume \(V_m\) — the volume occupied by one mole of a substance. Formula: \(V_m = M / \rho\), where \(M\) is molar mass in g·mol⁻¹ (mass of one mole of atoms), and \(\rho\) is density in g·cm⁻³. Units are usually cm³·mol⁻¹.

  • Packing fraction — the fraction of space inside a crystal lattice that is actually filled by atoms. Formula: \(f = V_{\text{atoms}} / V_{\text{cell}}\), where \(V_{\text{atoms}}\) is the combined volume of all atoms in the unit cell (from atomic radius), and \(V_{\text{cell}}\) is the volume of the unit cell (from lattice parameters). Ideal close-packed values are 0.74 (FCC, HCP), 0.68 (BCC), and 0.52 (simple cubic).

  • Nearest-neighbor distance \(d_{\text{NN}}\) — the distance between the centers of two atoms that are directly bonded (or touching in the metallic sense). Calculated from the lattice parameter \(a\) and structure: for FCC, \(d_{\text{NN}} = a / \sqrt{2}\); for BCC, \(d_{\text{NN}} = \sqrt{3}a / 2\); for HCP, \(d_{\text{NN}} = a\).

  • Number density \(n\) — the number of atoms per unit volume of the solid. Formula: \(n = N_A \rho / M\), where \(N_A\) is Avogadro’s number (6.022×10²³ mol⁻¹), \(\rho\) is density (kg·m⁻³ or g·cm⁻³), and \(M\) is molar mass in kg·mol⁻¹ or g·mol⁻¹.

Elastic properties

  • Bulk modulus \(K\) — a measure of resistance to uniform compression, in pascals (Pa). Roughly scales with bond strength and inversely with atomic volume (\(K \propto 1 / V_m\)); highest in dense covalent solids and close-packed transition metals.

  • Speed of sound \(v\) — the velocity of mechanical waves through the solid, in m·s⁻¹. Formula: \(v = \sqrt{K / \rho}\) for longitudinal waves in a simple isotropic model, where \(K\) is bulk modulus and \(\rho\) is density.

Derived from periodic table block & radius

  • Cohesive energy \(E_c\) — the energy required to separate a solid into isolated atoms, usually in eV per atom. Correlates with bonding type, crystal structure, and atomic radius: covalent networks and dense metals have the highest \(E_c\).

  • Surface energy \(\gamma\) — the energy per unit area to create a new surface, in J·m⁻². Related to cohesive energy and atomic packing: \(\gamma\) tends to be high for strongly bonded, close-packed solids and low for weakly bound molecular solids.

5 Mendeleev package

The Mendeleev package is a comprehensive source of data.

Documentation

L. M. Mentel, mendeleev - A Python resource for properties of chemical elements, ions and isotopes. , 2014– . Available at: https://github.com/lmmentel/mendeleev.

Table 6: Data available from Mendeleev.
index Hydrogen Carbon Nitrogen Oxygen Neon
atomic_number 1 6 7 8 10
atomic_radius 25 70 65 60 160
block s p p p p
density 0.000 2.200 0.001 0.001 0.001
description Colourless, odourless gaseous chemical element. Lightest and most abundant element in the universe. Present in water and in all organic compounds. Chemically reacts with most elements. Discovered by Henry Cavendish in 1776. Carbon is a member of group 14 of the periodic table. It has three allotropic forms of it, diamonds, graphite and fullerite. Carbon-14 is commonly used in radioactive dating. Carbon occurs in all organic life and is the basis of organic chemistry. Carbon has the interesting chemical property of being able to bond with itself, and a wide variety of other elements. Colourless, gaseous element which belongs to group 15 of the periodic table. Constitutes ~78% of the atmosphere and is an essential part of the ecosystem. Nitrogen for industrial purposes is acquired by the fractional distillation of liquid air. Chemically inactive, reactive generally only at high temperatures or in electrical discharges. It was discovered in 1772 by D. Rutherford. A colourless, odourless gaseous element belonging to group 16 of the periodic table. It is the most abundant element present in the earth's crust. It also makes up 20.8% of the Earth's atmosphere. For industrial purposes, it is separated from liquid air by fractional distillation. It is used in high temperature welding, and in breathing. It commonly comes in the form of Oxygen, but is found as Ozone in the upper atmosphere. It was discovered by Priestley in 1774. Colourless gaseous element of group 18 on the periodic table (noble gases). Neon occurs in the atmosphere, and comprises 0.0018% of the volume of the atmosphere. It has a distinct reddish glow when used in discharge tubes and neon based lamps. It forms almost no chemical compounds. Neon was discovered in 1898 by Sir William Ramsey and M.W. Travers.
dipole_polarizability 4.507 11.300 7.400 5.300 2.661
electron_affinity 0.754 1.262 -1.400 1.461 nan
electronic_configuration 1s [He] 2s2 2p2 [He] 2s2 2p3 [He] 2s2 2p4 [He] 2s2 2p6
evaporation_heat 0.904 nan nan nan 1.740
fusion_heat 0.117 nan nan nan nan
group_id 1 14 15 16 18
lattice_constant 3.750 3.570 4.039 6.830 4.430
lattice_structure HEX DIA HEX CUB FCC
period 1 2 2 2 2
series_id 1 1 1 1 2
specific_heat_capacity 14.304 0.709 1.040 0.918 1.030
symbol H C N O Ne
thermal_conductivity 0.181 1.590 0.026 0.027 nan
vdw_radius 110.000 170 155 152 154
covalent_radius_cordero 31 73 71 66 58.000
covalent_radius_pyykko 32 75 71 63 67
en_pauling 2.200 2.550 3.040 3.440 nan
en_allen 13.610 15.050 18.130 21.360 28.310
jmol_color #ffffff #909090 #3050f8 #ff0d0d #b3e3f5
cpk_color #ffffff #c8c8c8 #8f8fff #f00000 #ff1493
proton_affinity nan nan 342.200 485.200 198.800
gas_basicity nan nan 318.700 459.600 174.400
heat_of_formation 217.998 716.870 472.440 249.229 nan
c6 6.499 46.600 24.200 15.600 6.200
covalent_radius_bragg nan 77 65 65 nan
vdw_radius_bondi 120 170 155 152 154
vdw_radius_truhlar nan nan nan nan nan
vdw_radius_rt 110.000 177 164 158 nan
vdw_radius_batsanov nan 170 160 155 nan
vdw_radius_dreiding 319.500 389.830 366.210 340.460 nan
vdw_radius_uff 288.600 385.100 366 350 324.300
vdw_radius_mm3 162 204 193 182 160
abundance_crust 1,400 200 19 461,000 0.005
abundance_sea 108,000 28 0.500 857,000 0.000
molcas_gv_color #f2f2f2 #555555 #3753bb #f32e42 #b3e3f5
en_ghosh 0.264 0.225 0.265 0.305 0.384
vdw_radius_alvarez 120 177 166 150 158
c6_gb 6.510 47.900 25.700 16.700 6.910
atomic_weight 1.008 12.011 14.007 15.999 20.180
atomic_weight_uncertainty nan nan nan nan 0.001
is_monoisotopic nan nan nan nan nan
is_radioactive 0 0 0 0 0
cas 1333-74-0 7440-44-0 7727-37-9 7782-44-7 7440-01-9
atomic_radius_rahm 154 190 179 171 156
geochemical_class volatile semi-volatile volatile major volatile
goldschmidt_class atmophile atmophile atmophile litophile atmophile
metallic_radius nan nan nan nan nan
metallic_radius_c12 78 86 53 nan nan
covalent_radius_pyykko_double nan 67 60 57 96
covalent_radius_pyykko_triple nan 60 54 53 nan
discoverers Henry Cavendish Known to the ancients Daniel Rutherford Joseph Priestly, Carl Wilhelm Scheele Sir William Ramsey, M.W. Travers
discovery_year 1,766 nan 1,772 1,774 1,898
discovery_location England None Scotland England/Sweden England
name_origin Greek: hydro (water) and genes (generate) Latin: carbo, (charcoal). Greek: nitron and genes, (soda forming). Greek: oxys and genes, (acid former). Greek: neos (new).
sources Commercial quantities are produced by reacting superheated steam with methane or carbon. In lab work from reaction of metals with acid solutions or electrolysis. Made by burning organic compounds with insufficient oxygen. Obtained from liquid air by fractional distillation. Obtained primarily from liquid air by fractional distillation. Small amounts are made in the laboratory by electrolysis of water or heating potassium chlorate (KClO3) with manganese dioxide (MnO2) catalyst. Obtained from production of liquid air as a byproduct of producing liquid oxygen and nitrogen.
uses Most hydrogen is used in the production of ammonia. Also used in balloons and in metal refining. Also used as fuel in rockets. Its two heavier isotopes are: deuterium (D) and tritium (T) used respectively for nuclear fission and fusion. For making steel, in filters, and many more uses. Radiocarbon dating uses the carbon-14 isotope to date old objects. Primarily to produce ammonia and other fertilizers. Also used in making nitric acid, which is used in explosives. Also used in welding and enhanced oil recovery. Used in steel making, welding, and supporting life. Naturally occuring ozone (O3) in the upper atmosphere shields the earth from ultraviolet radiation. Primarily for lighting.
mendeleev_number 105 87 93 99 113
dipole_polarizability_unc 0.000 0.400 0.200 0.200 0.000
pettifor_number 103 95 100 101 2
glawe_number 103 87 88 97 2
molar_heat_capacity 28.836 8.517 29.124 29.378 20.786
en_miedema 5.200 6.240 6.860 nan nan
miedema_molar_volume 1.700 3.260 4.100 nan nan
miedema_electron_density 3.380 5.550 4.490 nan nan
en_gunnarsson_lundqvist 5.740 6.520 6.670 7.670 6.960
en_robles_bartolotti 5.270 6.390 5.780 6.450 6.600
production_concentration nan 46 nan nan nan
relative_supply_risk nan 4.500 nan nan nan
reserve_distribution nan 28 nan nan nan
political_stability_of_top_producer nan 24.100 nan nan nan
political_stability_of_top_reserve_holder nan 56.600 nan nan nan
top_3_producers None 1) China 2) USA 3) India None None None
top_3_reserve_holders None 1) USA 2) Russia 3) China None None None
recycling_rate None None None None None
substitutability None None None None None
price_per_kg 1.390 0.122 0.140 0.154 240
en_mullay 2.080 2.470 2.400 3.150 nan

5.1 Ionization energies

Table 7: Data available from Mendeleev.
atomic_number IE1 IE2 IE3 IE4 IE5
1 13.60
2 24.59 54.42
3 5.39 75.64 122.45
4 9.32 18.21 153.90 217.72
5 8.30 25.15 37.93 259.37 340.23
6 11.26 24.38 47.89 64.49 392.09
7 14.53 29.60 47.45 77.47 97.89
8 13.62 35.12 54.94 77.41 113.90
9 17.42 34.97 62.71 87.17 114.25
10 21.56 40.96 63.42 97.19 126.25
11 5.14 47.29 71.62 98.94 138.40
12 7.65 15.04 80.14 109.27 141.33
13 5.99 18.83 28.45 119.99 153.83
14 8.15 16.35 33.49 45.14 166.77
15 10.49 19.77 30.20 51.44 65.03
16 10.36 23.34 34.86 47.22 72.59
17 12.97 23.81 39.80 53.24 67.68
18 15.76 27.63 40.73 59.58 74.84