Electron cloud, radius

The "new ionic radii (4, 5) split the interionic distance D into two ionic Structural Radii r at the point where the electron-density has its minimum value, hence by means of X-ray observations on the Electron-cloud Radius y. But electron clouds, as wave-mechanics would predict, have no sharp radius. One might therefore measure electron-cloud radii in some other way at a different electron-density, and split the inter-ionic distance in a different ratio this is, ls we shall see later, one of the two foundations of the Goldschmidt-Pauling system. 

We here consider yrms (the root-mean-square Electron-Cloud Radius of the outermost electrons) obtained by equation 1 from the outer diamagnetism. This quantity will be compared with X-ray evidence on ionic Electron-Cloud radii (cp. a pioneer paper by Bider (17)), with Structural Radii for different types of bond, and Avith theoretical calculations for the free atoms and ions. 

The hydride ion provides however a notable exception. This is not due to faults in the calculation, for a full variation-calculation (33) gives for the polarizeability a = 30 cm /naole while crystal data (34) lead to the much smaller value 3 cm /mole — a contraction of the electron-cloud radius by a factor of ]/10 1.8. An unusually large effect would of... 

If the electron-cloud radius yrms were exactly equal to the structural radius r, Wasastjerna s criterion would be obviously true. But in fact, for ions r ce. 2 yrms (Table 3). Hence the criterion needs justification. It is obviously most probable for isoelectronic ions (cp. Eauling (/)), but the electron-cloud radii should refer to the ions in the crystals, not to the free ions. For, with a gross difference between crystal and free-ion electron-cloud radii for the hydride ion, there may be significant differences for others 40). For the crystals the electron-cloud radii could be obtained either from polarizeability or from magnetic susceptibility. The theory of polarizeability is less certain and there is a considerable correction to infinite wavelength. We therefore adopt the magnetic evidence. But this must be corrected for the inner shell contribution (Table 3). 

X> Electron-cloud radius ratio (Table 3) Structural radii deduced... 

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

The three particles that make up atoms are protons, neutrons, and electrons. Protons and neutrons are heavier than electrons and reside in the "nucleus," which is the center of the atom. Protons have a positive electrical charge, and neutrons have no electrical charge. Electrons are extremely lightweight and are negatively charged. They exist in a cloud that surrounds the atom. The electron cloud has a radius 10,000 times greater than the nucleus. 

Electrical Conduction by Proton Jumps. As mentioned in Sec. 24, a hydroxyl ion may be regarded as a doubly charged oxygen ion 0 , containing a proton inside the electronic cloud of the ion, which has the same number of electrons as a fluoride ion. The radius of the hydroxyl ion cannot be very different from that of the fluoride ion. But it will be seen from Table 2 that the mobility of the hydroxyl ion is about four times as great. This arises from the fact that a large part of the mobility is undoubtedly due to proton transfers.1 Consider a water molecule in contact with a hydroxyl ion. If a proton jumps from the molecule to the ion,... 

Strictly speaking, the size of an atom is a rather nebulous concept The electron cloud surrounding the nucleus does not have a sharp boundary. However, a quantity called the atomic radius can be defined and measured, assuming a spherical atom. Ordinarily, the atomic radius is taken to be one half the distance of closest approach between atoms in an elemental substance (Figure 6.12). 

FIGURE 1.31 The three-dimensional electron cloud corresponding to an electron in a Ij-orbital of hydrogen. The density of shading represents the probability of finding the electron at any point. The superimposed graph shows how the probability varies with the distance of the point from the nucleus along any radius. 

Table 84 shows two properties of the 10-electron isoeiectronic sequence. A progressive increase in nuclear charge results in a corresponding decrease in ionic radius, a result of stronger electrical force between the nucleus and the electron cloud. For the same reason, as Z increases, it becomes progressively more difficult to remove an electron. 

The Lewis dot formalism shows any halogen in a molecule surrounded by three electron lone pairs. An unfortunate consequence of this perspective is that it is natural to assume that these electrons are equivalent and symmetrically distributed (i.e., that the iodine is sp3 hybridized). Even simple quantum mechanical calculations, however, show that this is not the case [148]. Consider the diiodine molecule in the gas phase (Fig. 3). There is a region directly opposite the I-I sigma bond where the nucleus is poorly shielded by the atoms electron cloud. Allen described this as polar flattening , where the effective atomic radius is shorter at this point than it is perpendicular to the I-I bond [149]. Politzer and coworkers simply call it a sigma hole [150,151]. This area of positive electrostatic potential also coincides with the LUMO of the molecule (Fig. 4). 

A Johannes van der Waals (1837-1923) defined the atomic radius as half the distance between two atomic nuclei. In reality, the electron clouds have no dear boundaries. 

The unique properties of the proton have been attributed by some authors to the fact that it has no electronic or geometric structure. The absence of any electron shell implies that it will have a radius that is about 105 times smaller than any other cation and that there will be no repulsive interactions between electron clouds as a proton approaches another reactant species. The lack of any geometric or electronic structure also implies that there will not be any steric limitations with regard to orientation of the proton. However, it still must attack the other reactant molecule at the appropriate site. 

The radius, R, of each electron cloud is taken to be the root mean square distance of the electron from the center of the cloud. The equation of a sphere of radius, r, is x2 + y2 + z2 = r2, so on average ... 

Thirdly, there is the purely structural argument from Relative Size if ions of one type are much the largest, they will effectively fix the structure since the others can pack between them. This argument, which makes no assumption whatever about electron-clouds, is often referred only to lithium iodide, but much more evidence is available. Such questions of crystal-form and isomorphism are in fact the most important applications of ionic-radius systems in chemistry and mineralogy (cp. the classical work of V. M. Goldschmidt (2)). 

This distinction between electron-cloud radii and structural radii is then used to refine the system of ionic radii due to Pauling and Goldschmidt. Some further examples of anion-anion contact are discussed, and a value deduced for the crystal radius of the hydride anion. These cases of anion-anion contact argue for the Pauling tradition and against the new electron-density-minimum (EDM) radii. 

These ions all have the same number of electrons as the neon atom, as is true of the negative ions of the previous period N3, O2-, F". From N3 to Cl7+ the nuclear charge rises from seven to seventeen, resulting in a steady contraction of the electron cloud, or, in other words, a contraction of the ionic radius. Now let us compare the ions in a column of the system, for example, the alkali metals... 

Atoms in crystals cannot be regarded as scattering points the diameter of the electron cloud of an atom is of the same order of size as the distance between the centres of adjacent atoms—in fact, to a first approximation, the atoms in many crystals may be regarded as spheres of definite radius in contact with each other the electron clouds... 

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. 

The size of an arsenic atom depends on its valence state and the number of surrounding atoms (its coordination number). When valence electrons are removed from an atom, the radius of the atom not only decreases because of the removal of the electrons, but also from the protons attracting the remaining electrons closer to the nucleus (Nebergall, Schmidt and Holtzclaw, 1976), 141. An increase in the number of surrounding atoms (coordination number) will deform the electron cloud of an ion and change its ionic radius (Faure, 1998), 91. Table 2.2 lists the radii in angstroms (A) for arsenic and its ions with their most common coordination numbers. 

It is, of course, impossible to measure the absolute size of an isolated atom its electron cloud extends to infinity. It is possible to calculate the radius within which (say) 95% of its total electron cloud is confined but most measures of atomic/ionic size are based upon experimental measurements of internuclear distances in molecules and crystals. This means that the measurement is dependent on the nature of the bonding in the species concerned, and is a property of the atom or ion under scrutiny in a particular substance or group of substances. This must always be borne in mind in making use of tabulated radii of atoms or ions. The most important dictum to remember is that radii are significant only insofar as they reproduce experimental internuclear distances when added together. The absolute significance of a radius is highly suspect,... 

At shorter distances the repulsive forces start to dominate. The repulsive interaction between two molecules can be described by the power-law potential l/rn (n>9) caused by overlapping of electron clouds resulting in a conflict with the Pauli exclusion principle. For a completely rigid tip and sample whose atoms interact as 1/r12, the repulsion would be described by W-l/D7. In practice, both the tip and the sample are deformable (Fig. 3d). The tip-sample attraction is balanced by mechanical stress which arises in the contact area. From the Hertz theory [77,79], the relation between the deformation force Fd and the contact radius a is given by ... 

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