Atomic radii of the elements (data page)

The atomic radius of a chemical element is the distance from the centre of the nucleus to the outermost shell of the electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bound in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. Under some definitions, the value of the radius may depend on the atom's state and context.[1]

Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease rightward along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group (column). The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii (and of various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory.

Atomic radii

Note: All measurements given are in picometers (pm). For more recent data on covalent radii see Covalent radius.

atomic number symbol name empirical Calculated van der Waals Covalent (single bond) Covalent (triple bond) Metallic
1 H hydrogen 25 53 120 38 no data
2 He helium 120 31 140 32 no data
3 Li lithium 145 167 182 134 no data 152
4 Be beryllium 105 112 153 a 90 85 112
5 B boron 85 87 192 a 82 73
6 C carbon 70 67 170 77 60
7 N nitrogen 65 56 155 75 54
8 O oxygen 60 48 152 73 53
9 F fluorine 50 42 147 71 53
10 Ne neon 160 38 154 69 no data
11 Na sodium 180 190 227 154 no data 186
12 Mg magnesium 150 145 173 130 127 160
13 Al aluminium 125 118 184 a 118 111 143
14 Si silicon 110 111 210 111 102
15 P phosphorus 100 98 180 106 94
16 S sulfur 100 88 180 102 95
17 Cl chlorine 100 79 175 99 93
18 Ar argon 71 71 188 97 96
19 K potassium 220 243 275 196 no data 227
20 Ca calcium 180 194 231 a 174 133 197
21 Sc scandium 160 184 211 a 144 114 162 b
22 Ti titanium 140 176 no data 136 108 147
23 V vanadium 135 171 no data 125 106 134 b
24 Cr chromium 140 166 no data 127 103 128 b
25 Mn manganese 140 161 no data 139 103 127 b
26 Fe iron 140 156 no data 125 102 126 b
27 Co cobalt 135 152 no data 126 96 125 b
28 Ni nickel 135 149 163 121 101 124 b
29 Cu copper 135 145 140 138 120 128 b
30 Zn zinc 135 142 139 131 no data 134 b
31 Ga gallium 130 136 187 126 121 135 c
32 Ge germanium 125 125 211 a 122 114
33 As arsenic 115 114 185 119 106
34 Se selenium 115 103 190 116 107
35 Br bromine 115 94 185 114 110
36 Kr krypton no data 88 202 110 108
37 Rb rubidium 235 265 303 a 211 no data 248
38 Sr strontium 200 219 249 a 192 139 215
39 Y yttrium 180 212 no data 162 124 180 b
40 Zr zirconium 155 206 no data 148 121 160
41 Nb niobium 145 198 no data 137 116 146 b
42 Mo molybdenum 145 190 no data 145 113 139 b
43 Tc technetium 135 183 no data 156 110 136 b
44 Ru ruthenium 130 178 no data 126 103 134 b
45 Rh rhodium 135 173 no data 135 106 134 b
46 Pd palladium 140 169 163 131 112 137 b
47 Ag silver 160 165 172 153 137 144 b
48 Cd cadmium 155 161 158 148 no data 151 b
49 In indium 155 156 193 144 146 167
50 Sn tin 145 145 217 141 132
51 Sb antimony 145 133 206 a 138 127
52 Te tellurium 140 123 206 135 121
53 I iodine 140 115 198 133 125
54 Xe xenon no data 108 216 130 122
55 Cs caesium 260 298 343 a 225 no data 265
56 Ba barium 215 253 268 a 198 149 222
57 La lanthanum 195 195 no data 169 139 187 b
58 Ce cerium 185 158 no data no data 131 181.8 c
59 Pr praseodymium 185 247 no data no data 128 182.4 c
60 Nd neodymium 185 206 no data no data no data 181.4 c
61 Pm promethium 185 205 no data no data no data 183.4 c
62 Sm samarium 185 238 no data no data no data 180.4 c
63 Eu europium 185 231 no data no data no data 180.4 c
64 Gd gadolinium 180 233 no data no data 132 180.4 c
65 Tb terbium 175 225 no data no data no data 177.3 c
66 Dy dysprosium 175 228 no data no data no data 178.1 c
67 Ho holmium 175 226 no data no data no data 176.2 c
68 Er erbium 175 226 no data no data no data 176.1 c
69 Tm thulium 175 222 no data no data no data 175.9 c
70 Yb ytterbium 175 222 no data no data no data 176 c
71 Lu lutetium 175 217 no data 160 131 173.8 c
72 Hf hafnium 155 208 no data 150 122 159
73 Ta tantalum 145 200 no data 138 119 146 b
74 W tungsten 135 193 no data 146 115 139 b
75 Re rhenium 135 188 no data 159 110 137 b
76 Os osmium 130 185 no data 128 109 135 b
77 Ir iridium 135 180 no data 137 107 135.5 b
78 Pt platinum 135 177 175 128 110 138.5 b
79 Au gold 135 174 166 144 123 144 b
80 Hg mercury 150 171 155 149 no data 151 b
81 Tl thallium 190 156 196 148 150 170
82 Pb lead 180 154 202 147 137
83 Bi bismuth 160 143 207 a 146 135
84 Po polonium 190 135 197 a no data 129
85 At astatine no data 127 202 a no data 138
86 Rn radon no data 120 220 a 145 133
87 Fr francium no data no data 348 a no data no data no data
88 Ra radium 215 no data 283 a no data 159 no data
89 Ac actinium 195 no data no data no data 140
90 Th thorium 180 no data no data no data 136 179 b
91 Pa protactinium 180 no data no data no data 129 163 d
92 U uranium 175 no data 186 no data 118 156 e
93 Np neptunium 175 no data no data no data 116 155 e
94 Pu plutonium 175 no data no data no data no data 159 e
95 Am americium 175 no data no data no data no data 173 b
96 Cm curium no data no data no data no data no data 174 b
97 Bk berkelium no data no data no data no data no data 170 b
98 Cf californium no data no data no data no data no data 186+/- 2 b
99 Es einsteinium no data no data no data no data no data 186+/- 2 b
100 Fm fermium no data no data no data no data no data no data
101 Md mendelevium no data no data no data no data no data no data
102 No nobelium no data no data no data no data no data no data
103 Lr lawrencium no data no data no data no data no data no data
104 Rf rutherfordium no data no data no data no data 131 no data
105 Db dubnium no data no data no data no data 126 no data
106 Sg seaborgium no data no data no data no data 121 no data
107 Bh bohrium no data no data no data no data 119 no data
108 Hs hassium no data no data no data no data 118 no data
109 Mt meitnerium no data no data no data no data 113 no data
110 Ds darmstadtium no data no data no data no data 112 no data
111 Rg roentgenium no data no data no data no data 118 no data
112 Cn copernicium no data no data no data no data 130 no data
113 Nh nihonium no data no data no data no data no data no data
114 Fl flerovium no data no data no data no data no data no data
115 Mc moscovium no data no data no data no data no data no data
116 Lv livermorium no data no data no data no data no data no data
117 Ts tennessine no data no data no data no data no data no data
118 Og oganesson no data no data no data no data no data no data

See also

Notes

  • The radius of an atom is not a uniquely defined property and depends on the definition. Data derived from other sources with different assumptions cannot be compared.
  • † to an accuracy of about 5 pm
  • (a) These radii are taken from M. Mantina, A.C. Chamberlin, R. Valero, C.J. Cramer, and D.G. Truhlar, J. Phys. Chem. 2009, 113, 5806.
  • (b) 12 coordinate
  • (c) gallium has an anomalous crystal structure
  • (d) 10 coordinate
  • (e) uranium, neptunium and plutonium have irregular structures

References

  1. ^ Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th ed.). Wiley. p. 1385. ISBN 978-0-471-84997-1.

Data is as quoted at http://www.webelements.com/ from these sources:

Atomic radius (empirical)

Atomic radius (calculated)

Van der Waals radius

Covalent radii (single bond)

More recent data can be found in Covalent radius. The above values are based on

  • R.T. Sanderson (1962). Chemical Periodicity. New York, USA: Reinhold.
  • L.E. Sutton, ed. (1965). "Supplement 1956–1959, Special publication No. 18". Table of interatomic distances and configuration in molecules and ions. London, UK: Chemical Society.
  • J.E. Huheey; E.A. Keiter & R.L. Keiter (1993). Inorganic Chemistry : Principles of Structure and Reactivity (4th ed.). New York, USA: HarperCollins. ISBN 0-06-042995-X.
  • W.W. Porterfield (1984). Inorganic chemistry, a unified approach. Reading Massachusetts, USA: Addison Wesley Publishing Co. ISBN 0-201-05660-7.
  • A.M. James & M.P. Lord (1992). Macmillan's Chemical and Physical Data. MacMillan. ISBN 0-333-51167-0.

Triple-bond covalent radii

Metallic radius

Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 978-0-08-037941-8.

Atomic radius

The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding shells of electrons. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Three widely used definitions of atomic radius are: Van der Waals radius, ionic radius, and covalent radius.

Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bonding in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. The value of the radius may depend on the atom's state and context.Electrons do not have definite orbits, or sharply defined ranges. Rather, their positions must be described as probability distributions that taper off gradually as one moves away from the nucleus, without a sharp cutoff. Moreover, in condensed matter and molecules, the electron clouds of the atoms usually overlap to some extent, and some of the electrons may roam over a large region encompassing two or more atoms.

Under most definitions the radii of isolated neutral atoms range between 30 and 300 pm (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm), and less than 1/1000 of the wavelength of visible light (400–700 nm).

For many purposes, atoms can be modeled as spheres. This is only a crude approximation, but it can provide quantitative explanations and predictions for many phenomena, such as the density of liquids and solids, the diffusion of fluids through molecular sieves, the arrangement of atoms and ions in crystals, and the size and shape of molecules.Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group (column). The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii (and of various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory. The atomic radii decrease across the Periodic Table because as the atomic number increases, the number of protons increases across the period, but the extra electrons are only added to the same quantum shell. Therefore, the effective nuclear charge towards the outermost electrons increases, drawing the outermost electrons closer. As a result, the electron cloud contracts and the atomic radius decreases.

Covalent radius

The covalent radius, rcov, is a measure of the size of an atom that forms part of one covalent bond. It is usually measured either in picometres (pm) or angstroms (Å), with 1 Å = 100 pm.

In principle, the sum of the two co equal the covalent bond length between two atoms, R(AB) = r(A) + r(B). Moreover, different radii can be introduced for single, double and triple bonds (r1, r2 and r3 below), in a purely operational sense. These relationships are certainly not exact because the size of an atom is not constant but depends on its chemical environment. For heteroatomic A–B bonds, ionic terms may enter. Often the polar covalent bonds are shorter than would be expected on the basis of the sum of covalent radii. Tabulated values of covalent radii are either average or idealized values, which nevertheless show a certain transferability between different situations, which makes them useful.

The bond lengths R(AB) are measured by X-ray diffraction (more rarely, neutron diffraction on molecular crystals). Rotational spectroscopy can also give extremely accurate values of bond lengths. For homonuclear A–A bonds, Linus Pauling took the covalent radius to be half the single-bond length in the element, e.g. R(H–H, in H2) = 74.14 pm so rcov(H) = 37.07 pm: in practice, it is usual to obtain an average value from a variety of covalent compounds, although the difference is usually small. Sanderson has published a recent set of non-polar covalent radii for the main-group elements, but the availability of large collections of bond lengths, which are more transferable, from the Cambridge Crystallographic Database has rendered covalent radii obsolete in many situations.

List of data references for chemical elements

Values for many properties of the elements, together with various references, are collected on these data pages.

Metallic bonding

Metallic bonding is a type of chemical bonding that rises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. It may be described as the sharing of free electrons among a structure of positively charged ions (cations). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and luster.Metallic bonding is not the only type of chemical bonding a metal can exhibit, even as a pure substance. For example, elemental gallium consists of covalently-bound pairs of atoms in both liquid and solid state—these pairs form a crystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is mercurous ion (Hg2+2).

Outline of chemistry

The following outline is provided as an overview of and topical guide to chemistry:

Chemistry – science of atomic matter (matter that is composed of chemical elements), especially its chemical reactions, but also including its properties, structure, composition, behavior, and changes as they relate the chemical reactions. Chemistry is centrally concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds.

Van der Waals radius

The van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state.

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