atomiC radii oF the eLements
The simple model of an atom as a hard sphere that can approach
only to a fixed distance from another atom to which it is not bond-
ed has proved useful in interpreting crystal structures and other
molecular properties . The term van der Waals radius, r
vdw
,
was
originally introduced by Pauling as a measure of this atomic size .
Thus in a closely packed structure two non-bonded atoms A and
B will be separated by the sum of their van der Waals radii r
vdw
(A)
and r
vdw
(B) . The set of
van der Waals radii proposed by Pauling
was refined by Bondi (Reference 1) based on crystallographic data,
gas kinetic collision cross sections, and liquid state properties . The
non-bonded contact distances predicted from the recommended
r
vdw
of Bondi have been compared with actual data in the collec-
tion of the Cambridge Crystallographic Data Center by Rowland
and Taylor (Reference 2) and modified slightly . Their recommend-
ed van der Waals radii are given in the third column of this table .
The Cambridge Crystallographic Data Center also makes use
of a set of “covalent radii” to determine which atoms in a crystal
are bonded to each other . Thus two atoms A and B are judged to
be connected by a covalent bond if their separation falls within a
tolerance of ±0 .4 Å of the sum r
cov
(A) + r
cov
(B) . The covalent radii
are given in the fourth column of the table .
references
1 . Bondi, A ., J. Phys. Chem. 68, 441, 1964 .
2 . Rowland, R . S . and Taylor, R ., J. Phys. Chem. 100, 7384, 1996 .
3 . Cambridge Crystallographic Data Center, www .ccdc .cam .ac .uk/prod-
ucts/csd/radii/
Element
Symbol r
vdw
/Å r
cov
/Å
Actinium
Ac
1 .88
Aluminum
Al
1 .35
Americium
Am
1 .51
Antimony
Sb
1 .46
Argon
Ar
1 .88
1 .51
Arsenic
As
1 .85
1 .21
Astatine
At
1 .21
Barium
Ba
1 .34
Berkelium
Bk
1 .54
Beryllium
Be
0 .35
Bismuth
Bi
1 .54
Boron
B
0 .83
Bromine
Br
1 .85
1 .21
Cadmium
Cd
1 .58
1 .69
Cesium
Cs
1 .67
Calcium
Ca
0 .99
Californium
Cf
1 .83
Carbon
C
1 .70
0 .68
Cerium
Ce
1 .83
Chlorine
Cl
1 .75
0 .99
Chromium
Cr
1 .35
Cobalt
Co
1 .33
Copper
Cu
1 .40
1 .52
Curium
Cm
0 .99
Dysprosium
Dy
1 .75
Erbium
Er
1 .73
Europium
Eu
1 .99
Fluorine
F
1 .47
0 .64
Gadolinium
Gd
1 .79
Gallium
Ga
1 .87
1 .22
Germanium
Ge
1 .17
Gold
Au
1 .66
Element
Symbol r
vdw
/Å r
cov
/Å
Hafnium
Hf
1 .57
Helium
He
1 .40
Holmium
Ho
1 .74
Hydrogen
H
1 .09
0 .23
Indium
In
1 .93
1 .63
Iodine
I
1 .98
1 .40
Iridium
Ir
1 .32
Iron
Fe
1 .34
Krypton
Kr
2 .02
Lanthanum
La
1 .87
Lead
Pb
2 .02
1 .54
Lithium
Li
1 .82
0 .68
Lutetium
Lu
1 .72
Magnesium
Mg
1 .73
1 .10
Manganese
Mn
1 .35
Mercury
Hg
1 .55
1 .70
Molybdenum
Mo
1 .47
Neodymium
Nd
1 .81
Neon
Ne
1 .54
Neptunium
Np
1 .55
Nickel
Ni
1 .63
Niobium
Nb
1 .48
Nitrogen
N
1 .55
0 .68
Osmium
Os
1 .37
Oxygen
O
1 .52
0 .68
Palladium
Pd
1 .63
Phosphorus
P
1 .80
1 .05
Platinum
Pt
1 .72
Plutonium
Pu
1 .53
Polonium
Po
1 .68
Potassium
K
2 .75
1 .33
Praseodymium Pr
1 .82
Element
Symbol r
vdw
/Å r
cov
/Å
Promethium
Pm
1 .80
Protactinium
Pa
1 .61
Radium
Ra
1 .90
Rhenium
Re
1 .35
Rhodium
Rh
1 .45
Rubidium
Rb
1 .47
Ruthenium
Ru
1 .40
Samarium
Sm
1 .80
Scandium
Sc
1 .44
Selenium
Se
1 .90
1 .22
Silicon
Si
2 .10
1 .20
Silver
Ag
1 .72
1 .59
Sodium
Na
2 .27
0 .97
Strontium
Sr
1 .12
Sculpture
S
1 .80
1 .02
Tantalum
Ta
1 .43
Technetium
Tc
1 .35
Tellurium
Te
2 .06
1 .47
Terbium
Tb
1 .76
Thallium
Tl
1 .96
1 .55
Thorium
Th
1 .79
Thulium
Tm
1 .72
Tin
Sn
2 .17
1 .46
Titanium
Ti
1 .47
Tungsten
W
1 .37
Uranium
U
1 .86
1 .58
Vanadium
V
1 .33
Xenon
Xe
2 .16
Ytterbium
Yb
1 .94
Yttrium
Y
1 .78
Zinc
Zn
1 .39
1 .45
Zirconium
Zr
1 .56
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