The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Four widely used definitions of atomic radius are: Van der Waals radius, ionic radius, metallic radius and covalent radius. Typically, because of the difficulty to isolate atoms in order to measure their radii separately, atomic radius is measured in a chemically bonded state; however theoretical calculations are simpler when considering atoms in isolation. The dependencies on environment, probe, and state lead to a multiplicity of definitions.
Depending on the definition, the term may apply 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.[1]
Electrons do not have definite orbits nor 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; these are referred to as atomic orbitals or electron clouds. 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),[2] 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.
In 1920, shortly after it had become possible to determine the sizes of atoms using X-ray crystallography, it was suggested that all atoms of the same element have the same radii.[3] However, in 1923, when more crystal data had become available, it was found that the approximation of an atom as a sphere does not necessarily hold when comparing the same atom in different crystal structures.[4]
Widely used definitions of atomic radius include:
The following table shows empirically measured covalent radii for the elements, as published by J. C. Slater in 1964.[9] The values are in picometers (pm or 1×10-12 m), with an accuracy of about 5 pm. The shade of the box ranges from red to yellow as the radius increases; gray indicates lack of data.
| Group (column) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |||
| Period (row) | |||||||||||||||||||||
| 1 | H 25 | He < | --was 31--> | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | Li 145 | Be 105 | B 85 | C 70 | N 65 | O 60 | F 50 | Ne < | --was 38--> | ||||||||||||
| 3 | Na 180 | Mg 150 | Al 125 | Si 110 | P 100 | S 100 | Cl 100 | Ar < | --was 71--> | ||||||||||||
| 4 | K 220 | Ca 180 | Sc 160 | Ti 140 | V 135 | Cr 140 | Mn 140 | Fe 140 | Co 135 | Ni 135 | Cu 135 | Zn 135 | Ga 130 | Ge 125 | As 115 | Se 115 | Br 115 | Kr | |||
| 5 | Rb 235 | Sr 200 | Y 180 | Zr 155 | Nb 145 | Mo 145 | Tc 135 | Ru 130 | Rh 135 | Pd 140 | Ag 160 | Cd 155 | In 155 | Sn 145 | Sb 145 | Te 140 | I 140 | Xe | |||
| 6 | Cs 260 | Ba 215 | Lu 175 | Hf 155 | Ta 145 | W 135 | Re 135 | Os 130 | Ir 135 | Pt 135 | Au 135 | Hg 150 | Tl 190 | Pb 180 | Bi 160 | Po 190 | At | Rn | |||
| 7 | Fr | Ra 215 | Lr | Rf | Db | Sg | Bh | Hs | Mt | Ds | Rg | Cn | Nh | Fl | Mc | Lv | Ts | Og | |||
| La 195 | Ce 185 | Pr 185 | Nd 185 | Pm 185 | Sm 185 | Eu 185 | Gd 180 | Tb 175 | Dy 175 | Ho 175 | Er 175 | Tm 175 | Yb 175 | ||||||||
| Ac 195 | Th 180 | Pa 180 | U 175 | Np 175 | Pu 175 | Am 175 | Cm | Bk | Cf | Es | Fm | Md | No | ||||||||
The way the atomic radius varies with increasing atomic number can be explained by the arrangement of electrons in shells of fixed capacity. The shells are generally filled in order of increasing radius, since the negatively charged electrons are attracted by the positively charged protons in the nucleus. As the atomic number increases along each row of the periodic table, the additional electrons go into the same outermost shell; whose radius gradually contracts, due to the increasing nuclear charge. In a noble gas, the outermost shell is completely filled; therefore, the additional electron of next alkali metal will go into the next outer shell, accounting for the sudden increase in the atomic radius.
The increasing nuclear charge is partly counterbalanced by the increasing number of electrons, a phenomenon that is known as shielding; which explains why the size of atoms usually increases down each column. However, there is one notable exception, known as the lanthanide contraction: the 5d block of elements are much smaller than one would expect, due to the weak shielding of the 4f electrons.
Essentially, the atomic radius decreases across the periods due to an increasing number of protons. Therefore, there is a greater attraction between the protons and electrons because opposite charges attract, and more protons create a stronger charge. The greater attraction draws the electrons closer to the protons, decreasing the size of the particle. Therefore, the atomic radius decreases. Down the groups, atomic radius increases. This is because there are more energy levels and therefore a greater distance between protons and electrons. In addition, electron shielding causes attraction to decrease, so remaining electrons can go farther away from the positively charged nucleus. Therefore, the size, or atomic radius, increases.
The following table summarizes the main phenomena that influence the atomic radius of an element:
| factor | principle | increase with... | tend to | effect on radius | |
|---|---|---|---|---|---|
| electron shells | quantum mechanics | principal and azimuthal quantum numbers | increase down each column | increases the atomic radius | |
| nuclear charge | attractive force acting on electrons by protons in nucleus | atomic number | increase along each period (left to right) | decreases the atomic radius | |
| shielding | repulsive force acting on outermost shell electrons by inner electrons | number of electrons in inner shells | reduce the effect of nuclear charge | increases the atomic radius |
See main article: Lanthanide contraction. The electrons in the 4f-subshell, which is progressively filled from lanthanum (Z = 57) to ytterbium (Z = 70), are not particularly effective at shielding the increasing nuclear charge from the sub-shells further out. The elements immediately following the lanthanides have atomic radii which are smaller than would be expected and which are almost identical to the atomic radii of the elements immediately above them.[10] Hence lutetium is in fact slightly smaller than yttrium, hafnium has virtually the same atomic radius (and chemistry) as zirconium, and tantalum has an atomic radius similar to niobium, and so forth. The effect of the lanthanide contraction is noticeable up to platinum (Z = 78), after which it is masked by a relativistic effect known as the inert-pair effect.
Due to lanthanide contraction, the 5 following observations can be drawn:
See main article: d-block contraction. The d-block contraction is less pronounced than the lanthanide contraction but arises from a similar cause. In this case, it is the poor shielding capacity of the 3d-electrons which affects the atomic radii and chemistries of the elements immediately following the first row of the transition metals, from gallium (Z = 31) to bromine (Z = 35).[10]
The following table shows atomic radii computed from theoretical models, as published by Enrico Clementi and others in 1967.[11] The values are in picometres (pm).
| Group (column) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | ||
| Period (row) | ||||||||||||||||||||
| 1 | H 53 | He 31 | ||||||||||||||||||
| 2 | Li 167 | Be 112 | B 87 | C 67 | N 56 | O 48 | F 42 | Ne 38 | ||||||||||||
| 3 | Na 190 | Mg 145 | Al 118 | Si 111 | P 98 | S 88 | Cl 79 | Ar 71 | ||||||||||||
| 4 | K 243 | Ca 194 | Sc 184 | Ti 176 | V 171 | Cr 166 | Mn 161 | Fe 156 | Co 152 | Ni 149 | Cu 145 | Zn 142 | Ga 136 | Ge 125 | As 114 | Se 103 | Br 94 | Kr 88 | ||
| 5 | Rb 265 | Sr 219 | Y 212 | Zr 206 | Nb 198 | Mo 190 | Tc 183 | Ru 178 | Rh 173 | Pd 169 | Ag 165 | Cd 161 | In 156 | Sn 145 | Sb 133 | Te 123 | I 115 | Xe 108 | ||
| 6 | Cs 298 | Ba 253 | Lu 217 | Hf 208 | Ta 200 | W 193 | Re 188 | Os 185 | Ir 180 | Pt 177 | Au 174 | Hg 171 | Tl 156 | Pb 154 | Bi 143 | Po 135 | At 127 | Rn 120 | ||
| 7 | Fr | Ra | Lr | Rf | Db | Sg | Bh | Hs | Mt | Ds | Rg | Cn | Nh | Fl | Mc | Lv | Ts | Og | ||
| La 226 | Ce 210 | Pr 247 | Nd 206 | Pm 205 | Sm 238 | Eu 231 | Gd 233 | Tb 225 | Dy 228 | Ho 226 | Er 226 | Tm 222 | Yb 222 | |||||||
| Ac | Th | Pa | U | Np | Pu | Am | Cm | Bk | Cf | Es | Fm | Md | No | |||||||