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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 Atomic 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, covalent bonding in , or in ionization and ; 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.
(1988). 9780471849971, Wiley. ISBN 9780471849971
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 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 picometre (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the nuclear radius (1–10 femtometre), and less than 1/1000 of the wavelength of visible light (400–700 nanometre).
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 , and the size and shape of molecules.
The concept of atomic radius was preceded in the 19th century by the concept of atomic volume, a relative measure of how much space would on average an atom occupy in a given solid or liquid material. By the end of the century this term was also used in an absolute sense, as a molar volume divided by Avogadro constant. Such a volume is different for different crystalline forms even of the same compound, but physicists used it for rough, order-of-magnitude estimates of the atomic size, getting 10−8–10−7 cm for copper.
The earliest estimates of the atomic size was made by opticians in the 1830s, particularly Cauchy, who developed models of light dispersion assuming a lattice of connected "molecules". In 1857 Rudolf Clausius developed a gas-kinetic model which included the equation for mean free path. In the 1870s it was used to estimate gas molecule sizes, as well as an aforementioned comparison with visible light wavelength and an estimate from the thickness of soap bubble film at which its contractile force rapidly diminishes. By 1900, various estimates of mercury atom diameter averaged around 275±20 pm (modern estimates give 300±10 pm, see below).
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. 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.
The atomic radius of each element generally decreases across each period due to an increasing number of protons, since an increase in the number of protons increases the attractive force acting on the atom's electrons. The greater attraction draws the electrons closer to the protons, decreasing the size of the atom. Down each group, the atomic radius of each element typically increases because there are more occupied electron electron shell and therefore a greater distance between protons and electrons.
The increasing nuclear charge is partly counterbalanced by the increasing number of electrons—a phenomenon that is known as shielding effect—which explains why the size of atoms usually increases down each column despite an increase in attractive force from the nucleus. Electron shielding causes the attraction of an atom's nucleus on its electrons to decrease, so electrons occupying higher energy states farther from the nucleus experience reduced attractive force, increasing the size of the atom. However, elements in the 5d-block (lutetium to mercury) are much smaller than this trend predicts due to the weak shielding of the 4f-subshell. This phenomenon is known as the lanthanide contraction. A similar phenomenon exists for actinides; however, the general instability of transuranic elements makes measurements for the remainder of the 5f-block difficult and for transactinides nearly impossible. Finally, for sufficiently heavy elements, the atomic radius may be decreased by relativistic effects. This is a consequence of electrons near the strongly charged nucleus traveling at a sufficient fraction of the speed of light to gain a nontrivial amount of mass.
The following table summarizes the main phenomena that influence the atomic radius of an element:
| increases the atomic radius |
| decreases the atomic radius |
| increases the atomic radius |
Due to lanthanide contraction, the 5 following observations can be drawn:
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