Determination of Ionic Radii
The distance between two ions in an ionic crystal can be determined by X-ray crystallography, which gives the lengths of the sides of the unit cell of a crystal. For example, the length of each edge of the unit cell of sodium chloride is found to be 564.02 pm. Each edge of the unit cell of sodium chloride may be considered to have the atoms arranged as Na+∙∙∙Cl-∙∙∙Na+, so the edge is twice the Na-Cl separation. Therefore, the distance between the Na+ and Cl- ions is half of 564.02 pm, which is 282.01 pm. However, although X-ray crystallography gives the distance between ions, it doesn't indicate where the boundary is between those ions, so it doesn't directly give ionic radii.
Landé estimated ionic radii by considering crystals in which the anion and cation have a large difference in size, such as LiI. The lithium ions are so much smaller than the iodide ions that the lithium fits into holes within the crystal lattice, allowing the iodide ions to touch. That is, the distance between two neighboring iodides in the crystal is assumed to be twice the radius of the iodide ion, which was deduced to be 214 pm. This value can be used to determine other radii. For example, the inter-ionic distance in RbI is 356 pm, giving 142 pm for the ionic radius of Rb+. In this way values for the radii of 8 ions were determined.
Wasastjerna estimated ionic radii by considering the relative volumes of ions as determined from electrical polarizability as determined by measurements of refractive index. These results were extended by Victor Goldschmidt Both Wasastjerna and Goldschmidt used a value of 132 pm for the O2- ion.
Pauling used effective nuclear charge to proportion the distance between ions into anionic and a cationic radii. His data gives the O2- ion a radius of 140 pm.
A major review of crystallographic data led to the publication of revised ionic radii by Shannon. Shannon gives different radii for different coordination numbers, and for high and low spin states of the ions. To be consistent with Pauling's radii, Shannon has used a value of rion(O2−) = 140 pm; data using that value are referred to as "effective" ionic radii. However, Shannon also includes data based on rion(O2−) = 126 pm; data using that value are referred to as "Crystal" ionic radii. Shannon states that "it is felt that crystal radii correspond more closely to the physical size of ions in a solid." The two sets of data are listed in the two tables below.
Number | Name | Symbol | 3– | 2– | 1– | 1+ | 2+ | 3+ | 4+ | 5+ | 6+ | 7+ | 8+ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | Lithium | Li | 90 | ||||||||||
4 | Beryllium | Be | 59 | ||||||||||
5 | Boron | B | 41 | ||||||||||
6 | Carbon | C | 30 | ||||||||||
7 | Nitrogen | N | 132 (4) | 30 | 27 | ||||||||
8 | Oxygen | O | 126 | ||||||||||
9 | Fluorine | F | 119 | 22 | |||||||||
11 | Sodium | Na | 116 | ||||||||||
12 | Magnesium | Mg | 86 | ||||||||||
13 | Aluminum | Al | 67.5 | ||||||||||
14 | Silicon | Si | 54 | ||||||||||
15 | Phosphorus | P | 58 | 52 | |||||||||
16 | Sulfur | S | 170 | 51 | 43 | ||||||||
17 | Chlorine | Cl | 167 | 26 (3py) | 41 | ||||||||
19 | Potassium | K | 152 | ||||||||||
20 | Calcium | Ca | 114 | ||||||||||
21 | Scandium | Sc | 88.5 | ||||||||||
22 | Titanium | Ti | 100 | 81 | 74.5 | ||||||||
23 | Vanadium | V | 93 | 78 | 72 | 68 | |||||||
24 | Chromium ls | Cr | 87 | 75.5 | 69 | 63 | 58 | ||||||
24 | Chromium hs | Cr | 94 | ||||||||||
25 | Manganese ls | Mn | 81 | 72 | 67 | 47 (4) | 39.5 (4) | 60 | |||||
25 | Manganese hs | Mn | 97 | 78.5 | |||||||||
26 | Iron ls | Fe | 75 | 69 | 72.5 | 39 (4) | |||||||
26 | Iron hs | Fe | 92 | 78.5 | |||||||||
27 | Cobalt ls | Co | 79 | 68.5 | |||||||||
27 | Cobalt hs | Co | 88.5 | 75 | 67 | ||||||||
28 | Nickel ls | Ni | 83 | 70 | 62 ls | ||||||||
28 | Nickel hs | Ni | 74 | ||||||||||
29 | Copper | Cu | 91 | 87 | 68 ls | ||||||||
30 | Zinc | Zn | 88 | ||||||||||
31 | Gallium | Ga | 76 | ||||||||||
32 | Germanium | Ge | 87 | 67 | |||||||||
33 | Arsenic | As | 72 | 60 | |||||||||
34 | Selenium | Se | 184 | 64 | 56 | ||||||||
35 | Bromine | Br | 182 | 73 (4sq) | 45 (3py) | 53 | |||||||
37 | Rubidium | Rb | 166 | ||||||||||
38 | Strontium | Sr | 132 | ||||||||||
39 | Yttrium | Y | 104 | ||||||||||
40 | Zirconium | Zr | 86 | ||||||||||
41 | Niobium | Nb | 86 | 82 | 78 | ||||||||
42 | Molybdenum | Mo | 83 | 79 | 75 | 73 | |||||||
43 | Technetium | Tc | 78.5 | 74 | 70 | ||||||||
44 | Ruthenium | Ru | 82 | 76 | 70.5 | 52 (4) | 50 (4) | ||||||
45 | Rhodium | Rh | 80.5 | 74 | 69 | ||||||||
46 | Palladium | Pd | 73 (2) | 100 | 90 | 75.5 | |||||||
47 | Silver | Ag | 129 | 108 | 89 | ||||||||
48 | Cadmium | Cd | 109 | ||||||||||
49 | Indium | In | 94 | ||||||||||
50 | Tin | Sn | 83 | ||||||||||
51 | Antimony | Sb | 90 | 74 | |||||||||
52 | Tellurium | Te | 207 | 111 | 70 | ||||||||
53 | Iodine | I | 206 | 109 | 67 | ||||||||
54 | Xenon | Xe | 62 | ||||||||||
55 | Caesium | Cs | 181 | ||||||||||
56 | Barium | Ba | 149 | ||||||||||
57 | Lanthanum | La | 117.2 | ||||||||||
58 | Cerium | Ce | 115 | 101 | |||||||||
59 | Praseodymium | Pr | 113 | 99 | |||||||||
60 | Neodymium | Nd | 143 (8) | 112.3 | |||||||||
61 | Promethium | Pm | 111 | ||||||||||
62 | Samarium | Sm | 136 (7) | 109.8 | |||||||||
63 | Europium | Eu | 131 | 108.7 | |||||||||
64 | Gadolinium | Gd | 107.8 | ||||||||||
65 | Terbium | Tb | 106.3 | 90 | |||||||||
66 | Dysprosium | Dy | 121 | 105.2 | |||||||||
67 | Holmium | Ho | 104.1 | ||||||||||
68 | Erbium | Er | 103 | ||||||||||
69 | Thulium | Tm | 117 | 102 | |||||||||
70 | Ytterbium | Yb | 116 | 100.8 | |||||||||
71 | Lutetium | Lu | 100.1 | ||||||||||
72 | Hafnium | Hf | 85 | ||||||||||
73 | Tantalum | Ta | 86 | 82 | 78 | ||||||||
74 | Tungsten | W | 80 | 76 | 74 | ||||||||
75 | Rhenium | Re | 77 | 72 | 69 | 67 | |||||||
76 | Osmium | Os | 77 | 71.5 | 68.5 | 66.5 | 53 (4) | ||||||
77 | Iridium | Ir | 82 | 76.5 | 71 | ||||||||
78 | Platinum | Pt | 94 | 76.5 | 71 | ||||||||
79 | Gold | Au | 151 | 99 | 71 | ||||||||
80 | Mercury | Hg | 133 | 116 | |||||||||
81 | Thallium | Tl | 164 | 102.5 | |||||||||
82 | Lead | Pb | 133 | 91.5 | |||||||||
83 | Bismuth | Bi | 117 | 90 | |||||||||
84 | Polonium | Po | 108 | 81 | |||||||||
85 | Astatine | At | 76 | ||||||||||
87 | Francium | Fr | 194 | ||||||||||
88 | Radium | Ra | 162 (8) | ||||||||||
89 | Actinium | Ac | 126 | ||||||||||
90 | Thorium | Th | 108 | ||||||||||
91 | Protactinium | Pa | 116 | 104 | 92 | ||||||||
92 | Uranium | U | 116.5 | 103 | 90 | 87 | |||||||
93 | Neptunium | Np | 124 | 115 | 101 | 89 | 86 | 85 | |||||
94 | Plutonium | Pu | 114 | 100 | 88 | 85 | |||||||
95 | Americium | Am | 140 (8) | 111.5 | 99 | ||||||||
96 | Curium | Cm | 111 | 99 | |||||||||
97 | Berkelium | Bk | 110 | 97 | |||||||||
98 | Californium | Cf | 109 | 96.1 | |||||||||
99 | Einsteinium | Es | 92.8 |
Number | Name | Symbol | 3– | 2– | 1– | 1+ | 2+ | 3+ | 4+ | 5+ | 6+ | 7+ | 8+ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | Lithium | Li | 76 | ||||||||||
4 | Beryllium | Be | 45 | ||||||||||
5 | Boron | B | 27 | ||||||||||
6 | Carbon | C | 16 | ||||||||||
7 | Nitrogen | N | 146 (4) | 16 | 13 | ||||||||
8 | Oxygen | O | 140 | ||||||||||
9 | Fluorine | F | 133 | 8 | |||||||||
11 | Sodium | Na | 102 | ||||||||||
12 | Magnesium | Mg | 72 | ||||||||||
13 | Aluminum | Al | 53.5 | ||||||||||
14 | Silicon | Si | 40 | ||||||||||
15 | Phosphorus | P | 44 | 38 | |||||||||
16 | Sulfur | S | 184 | 37 | 29 | ||||||||
17 | Chlorine | Cl | 181 | 12 (3py) | 27 | ||||||||
19 | Potassium | K | 138 | ||||||||||
20 | Calcium | Ca | 100 | ||||||||||
21 | Scandium | Sc | 74.5 | ||||||||||
22 | Titanium | Ti | 86 | 67 | 60.5 | ||||||||
23 | Vanadium | V | 79 | 64 | 58 | 54 | |||||||
24 | Chromium ls | Cr | 73 | 61.5 | 55 | 49 | 44 | ||||||
24 | Chromium hs | Cr | 80 | ||||||||||
25 | Manganese ls | Mn | 67 | 58 | 53 | 33 (4) | 25.5 (4) | 46 | |||||
25 | Manganese hs | Mn | 83 | 64.5 | |||||||||
26 | Iron ls | Fe | 61 | 55 | 58.5 | 25 (4) | |||||||
26 | Iron hs | Fe | 78 | 64.5 | |||||||||
27 | Cobalt ls | Co | 65 | 54.5 | |||||||||
27 | Cobalt hs | Co | 74.5 | 61 | 53 hs | ||||||||
28 | Nickel ls | Ni | 69 | 56 | 48 ls | ||||||||
28 | Nickel hs | Ni | 60 | ||||||||||
29 | Copper | Cu | 77 | 73 | 54 ls | ||||||||
30 | Zinc | Zn | 74 | ||||||||||
31 | Gallium | Ga | 62 | ||||||||||
32 | Germanium | Ge | 73 | 53 | |||||||||
33 | Arsenic | As | 58 | 46 | |||||||||
34 | Selenium | Se | 198 | 50 | 42 | ||||||||
35 | Bromine | Br | 196 | 59 (4sq) | 31 (3py) | 39 | |||||||
37 | Rubidium | Rb | 152 | ||||||||||
38 | Strontium | Sr | 118 | ||||||||||
39 | Yttrium | Y | 90 | ||||||||||
40 | Zirconium | Zr | 72 | ||||||||||
41 | Niobium | Nb | 72 | 68 | 64 | ||||||||
42 | Molybdenum | Mo | 69 | 65 | 61 | 59 | |||||||
43 | Technetium | Tc | 64.5 | 60 | 56 | ||||||||
44 | Ruthenium | Ru | 68 | 62 | 56.5 | 38 (4) | 36 (4) | ||||||
45 | Rhodium | Rh | 66.5 | 60 | 55 | ||||||||
46 | Palladium | Pd | 59 (2) | 86 | 76 | 61.5 | |||||||
47 | Silver | Ag | 115 | 94 | 75 | ||||||||
48 | Cadmium | Cd | 95 | ||||||||||
49 | Indium | In | 80 | ||||||||||
50 | Tin | Sn | 69 | ||||||||||
51 | Antimony | Sb | 76 | 60 | |||||||||
52 | Tellurium | Te | 221 | 97 | 56 | ||||||||
53 | Iodine | I | 220 | 95 | 53 | ||||||||
54 | Xenon | Xe | 48 | ||||||||||
55 | Caesium | Cs | 167 | ||||||||||
56 | Barium | Ba | 135 | ||||||||||
57 | Lanthanum | La | 103.2 | ||||||||||
58 | Cerium | Ce | 101 | 87 | |||||||||
59 | Praseodymium | Pr | 99 | 85 | |||||||||
60 | Neodymium | Nd | 129 (8) | 98.3 | |||||||||
61 | Promethium | Pm | 97 | ||||||||||
62 | Samarium | Sm | 122 (8) | 95.8 | |||||||||
63 | Europium | Eu | 117 | 94.7 | |||||||||
64 | Gadolinium | Gd | 93.5 | ||||||||||
65 | Terbium | Tb | 92.3 | 76 | |||||||||
66 | Dysprosium | Dy | 107 | 91.2 | |||||||||
67 | Holmium | Ho | 90.1 | ||||||||||
68 | Erbium | Er | 89 | ||||||||||
69 | Thulium | Tm | 103 | 88 | |||||||||
70 | Ytterbium | Yb | 102 | 86.8 | |||||||||
71 | Lutetium | Lu | 86.1 | ||||||||||
72 | Hafnium | Hf | 71 | ||||||||||
73 | Tantalum | Ta | 72 | 68 | 64 | ||||||||
74 | Tungsten | W | 66 | 62 | 60 | ||||||||
75 | Rhenium | Re | 63 | 58 | 55 | 53 | |||||||
76 | Osmium | Os | 63 | 57.5 | 54.5 | 52.5 | 39 (4) | ||||||
77 | Iridium | Ir | 68 | 62.5 | 57 | ||||||||
78 | Platinum | Pt | 80 | 62.5 | 57 | ||||||||
79 | Gold | Au | 137 | 85 | 57 | ||||||||
80 | Mercury | Hg | 119 | 102 | |||||||||
81 | Thallium | Tl | 150 | 88.5 | |||||||||
82 | Lead | Pb | 119 | 77.5 | |||||||||
83 | Bismuth | Bi | 103 | 76 | |||||||||
84 | Polonium | Po | 94 | 67 | |||||||||
85 | Astatine | At | 62 | ||||||||||
87 | Francium | Fr | 180 | ||||||||||
88 | Radium | Ra | 148 (8) | ||||||||||
89 | Actinium | Ac | 112 | ||||||||||
90 | Thorium | Th | 94 | ||||||||||
91 | Protactinium | Pa | 104 | 90 | 78 | ||||||||
92 | Uranium | U | 102.5 | 89 | 76 | 73 | |||||||
93 | Neptunium | Np | 110 | 101 | 87 | 75 | 72 | 71 | |||||
94 | Plutonium | Pu | 100 | 86 | 74 | 71 | |||||||
95 | Americium | Am | 126 (8) | 97.5 | 85 | ||||||||
96 | Curium | Cm | 97 | 85 | |||||||||
97 | Berkelium | Bk | 96 | 83 | |||||||||
98 | Californium | Cf | 95 | 82.1 | |||||||||
99 | Einsteinium | Es | 83.5 |
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