Atomic radius definition

Several physical properties, including density, melting point, and boiling point, are related to the sizes of atoms, but atomic size is difficult to define. As we saw in Section 2.2, the electron density in an atom extends far beyond the nucleus, but we normally think of atonfic size as the volume containing about 90 percent of the total electron density around the nucleus. When we must be more specific, we define the size of an atom in terms of its atomic radius. Definitions for atonfic radius depend upon the identity and environment of the element in question ... 

The size of an atom is not a simple concept. An inspection of the wave function for any atom shows that it is asymptotic to infinity, so some practical definition of size is required. There are two ways of assigning sizes to atoms atomic radius and covalent radius. 

The unique ligating behavior of the bridging 2,6-dimethoxyphcnyl ligand with respect to promoting a substantial decrease in the metal atom separation for molybdenum(II) dimers is even more prominent in the case of chromium. The chromium-chromium distance of 1.847(1) A in Cr2(DMP)4 (90) is more than 0.1 A less than the corresponding value in any other chromous dimer yet reported. To compare homonuclear multiple bonds among elements with inherently different atomic radii, Cotton, Koch, and Millar proposed a normalized value for intemuclear distances based on Pauling s atomic radius of the element in question (209). A simple definition of formal shortness as t/(M—M)/2r(M) then follows as a measure of the relative compactness of the attractive interaction (90). The formal shortness ratio of 0.778 for the quadruple bond in... 

Electron clouds do not have sharp boundaries, so we cannot really speak of the radius of an atom. However, when atoms pack together in solids and molecules, their centers are found at definite distances from one another. The atomic radius of an element is defined as half the distance between the nuclei of neighboring atoms (11). If the element is a metal or a noble gas, we use the distance between the centers of neighboring atoms in a solid sample. For instance, because the distance between... 

One of the many periodic properties of the elements that can be explained by electron configurations is size, or atomic radius. You might wonder, though, how we can talk about a definite "size" for an atom, having said in Section 5.8 that the electron clouds around atoms have no specific boundaries. What s usually done is to define an atom s radius as being half the distance between the nuclei of two identical atoms when they are bonded together. In the Cl2 molecule, for example, the distance between the two chlorine nuclei is 198 pm in diamond (elemental carbon), the distance between two carbon nuclei is 154 pm. Thus, we say that the atomic radius of chlorine is half the Cl-Cl distance, or 99 pm, and the atomic radius of carbon is half the C-C distance, or 77 pm. 

C is correct. A family or group is the name for any vertical column on the periodic table. Of the choices given, only atomic radius increases going down a column. Although electron affinity is a possible choice depending upon the definition used, atomic radius is an unambiguous choice. 

The mean radius of a Rydberg state is approximately aon 2, where ao is the Bohr radius. Although the atom in its ground state is a quantum object, it eventually ceases to be so as n increases for n 100, the diameter of the atom is 104 x 2ao which is roughly 1 /xm, at which point the atom is definitely reaching macroscopic size. For n 1000, the diameter of the atom is l/10th of a millimetre. 

If the expression the size of an atom is to have any meaning, it must have something to do with the distance between the electron and the nucleus. Several definitions are possible at this stage we choose to identify the atomic radius with the maximum distance allowed by classical physics, equation (1.7) ... 

A monatomic ion, like an atom, is a nucleus surrounded by a distribution of electrons. The ionic radius is a measure of the size of the spherical region around the nucleus of an ion within which the electrons are most likely to be found. As for an atomic radius, defining an ionic radius is somewhat arbitrary, because an electron distribution never abruptly ends. However, if we imagine ions to be spheres of definite size, we can obtain their radii from known distances between nnclei in crystals. (These distances can be determined accurately by observing how crystals diffract X rays.) ... 

Inmitively, we think of the atomic radius as the distance between the nucleus of an atom and its valence shell (i.e., the outermost shell that is occupied by one or more electrons), because we usually envision atoms as spheres with discrete boundaries. According to the quantum mechanical model of the atom, though, there is no specific distance from the nucleus beyond which an electron may not be found [W Section 6.7]. Therefore, the atomic radius requires a specific definition. 

On equating the atomic radius to a characteristic atomic radius, r, a single curve of d vs D describes homonuclear covalent interaction, irrespective of bond order. Practical use of the formulae requires definition of a complex set of characteristic radii, which could be derived empirically [1] and was used subsequently to calculate molecular shape descriptors [2] and as the basis of a generalized Heitler-London procedure, valid for all pairwise covalent interactions [3,4], In all of these applications, interaction is correctly described by the dimensionless curves of Fig. 1. 

Note The atomic radius of noble-gas atoms can be obtained from low-temperature solids (high pressure for helium). These atoms are held together by weak, van der Waals forces (Chapter 6), so their size defined in this way is actually larger than the covalent radius of the neighboring halogen atom. There are other definitions of size. If all atomic sizes are defined from atomic wavefunctions, then each noble-gas atom is smaller than its neighboring halogen atom. 

In previous chapters, we saw that the volume of an atom is taken up primarily by its electrons (Chapter 2) occupying quantum-mechanical orbitals (Chapter 7). We also saw that these orbitals do not have a definite boundary but represent only a statistical probability distribution for where the electron is found. So how do we define the size of an atom One way to define atomic radii is to consider the distance between nonbonding atoms that are in direct contact. For example, krypton can be frozen into a solid in which the krypton atoms are touching each other but are not bonded together. The distance between the centers of adjacent krypton atoms—which can be determined from the solid s density—is then twice the radius of a krypton atom. An atomic radius determined in this way is called the nonbonding atomic radius or the van der Waals radius. The van der Waals radius represents the radius of an atom when it is not bonded to another atom. 

All this being said, perhaps the most definitive study of the relative roles of electrostatic and van der Waals forces was performed by Gady et al. [86,101,102]. In their studies, they attached a spherical polystyrene particle, having a radius between 3 and 6 p.m, to the cantilever of an atomic force microscope. They then conducted three distinct measurements that allowed them to distinguish between electrostatic and van der Waals forces that attracted the particle to various conducting, smooth substrates. 

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