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 nucleus to the boundary of the surrounding cloud of electrons. 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]
The concept is difficult to define because the 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.
Despite these conceptual difficulties, 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 angstroms. 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.
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.
* Van der Waals radius: in principle, half the minimum distance between the nuclei of two atoms of the element that are not bound to the same molecule.[3]
* Ionic radius: the nominal radius of the ions of an element in a specific ionization state, deduced from the spacing of atomic nuclei in cyrstalline salts that include that ion. In principle, the spacing between two adjacent oppositely charged ions (the length of the ionic bond between them) should equal the sum of their ionic radii.[3]
* Covalent radius: the nominal radius of the atoms of an element when covalently bound to other atoms, as deduced the separation between the atomic nuclei in molecules. In principle, the distance between two atoms that are bound to each other in a molecule (the length of that covalent bond) should equal the sum of their covalent radii.[3]
* Metallic radius: the nominal radius of atoms of an element when joined to other atoms by metallic bonds.
* Bohr radius: the radius of the lowest-energy electron orbit predicted by Bohr model of the atom (1913).[4][5] It is only applicable to atoms and ions with a single electron, such as hydrogen, singly-ionized helium, and positronium. Although the model itself is now obsolete, the Bohr radius for the hydrogen atom is still regarded as an important physical constant.
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]
The concept is difficult to define because the 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.
Despite these conceptual difficulties, 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 angstroms. 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.
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.
Definitions
Widely used definitions of atomic radius include:* Van der Waals radius: in principle, half the minimum distance between the nuclei of two atoms of the element that are not bound to the same molecule.[3]
* Ionic radius: the nominal radius of the ions of an element in a specific ionization state, deduced from the spacing of atomic nuclei in cyrstalline salts that include that ion. In principle, the spacing between two adjacent oppositely charged ions (the length of the ionic bond between them) should equal the sum of their ionic radii.[3]
* Covalent radius: the nominal radius of the atoms of an element when covalently bound to other atoms, as deduced the separation between the atomic nuclei in molecules. In principle, the distance between two atoms that are bound to each other in a molecule (the length of that covalent bond) should equal the sum of their covalent radii.[3]
* Metallic radius: the nominal radius of atoms of an element when joined to other atoms by metallic bonds.
* Bohr radius: the radius of the lowest-energy electron orbit predicted by Bohr model of the atom (1913).[4][5] It is only applicable to atoms and ions with a single electron, such as hydrogen, singly-ionized helium, and positronium. Although the model itself is now obsolete, the Bohr radius for the hydrogen atom is still regarded as an important physical constant.
- ^ Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th Edn). New York: Wiley. ISBN 0-471-84997-9. p. 1385.
- ^ Jean-Louis Basdevant, James Rich & Michel Spiro (2005). Fundamentals in Nuclear Physics. Springer. p. Fig. 1.1, p. 13. ISBN 0387016724. http://books.google.com/books?id=OFx7P9mgC9oC&pg=PA375&dq=helium+%22nuclear+structure%22&lr=&as_brr=0#PPA13,M1.
- ^ a b c Pauling, Linus (1945). The Nature of the Chemical Bond. Ithaca, NY: Cornell University Press.
- ^ Niels Bohr (1913), On the Constitution of Atoms and Molecules, Part I. Philosophical Magazine, volume 26, pages 1–24. Online version.
- ^ Niels Bohr (1913), On the Constitution of Atoms and Molecules, Part II. Philosophical Magazine, volume 26, pages 476–502. Online version.
- ^ J. C. Slater (1964), Journal of Chemical Physics, volume 41, page 3199.
- ^ a b Jolly, William L. (1991). Modern Inorganic Chemistry (2nd Edn.). New York: McGraw-Hill. ISBN 0-07-112651-1. p. 22.
- ^ E. Clementi, D. L. Raimondi, and W. P. Reinhardt (1967), Journal of Chemical Physics, volume 47, page 1300.
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