Radius of the atom

FIGURE 1 6 Molecular models of methane (CH4) (a) Framework (tube) models show the bonds connecting the atoms but not the atoms themselves (b) Ball and stick (ball and spoke) models show the atoms as balls and the bonds as rods (c) Space filling models portray overall molecular size the radius of each sphere approximates the van der Waals radius of the atom (d) An electrostatic potential map of methane... 

To calculate the fraction of occupied space in a close-packed structure, we considei a ccp structure, e can use the radius of the atoms to find the volume of the cube and ow muc o t at volume is taken up by atoms. First, we look at how the cube is built rom t e atoms. In Fig. 5.29, we see that the corners of the cubes are at the centers of etg t atoms, n y 1/8 of each corner atom projects into the cube, so the corner atoms collectively contribute 8xi/S=1 atom to the cube. There is half an atom on each of t e six aces, so the atoms on each face contribute 6 X 1/2 = 3 atoms, giving four... 

A way to overcome some of these difficulties can be developed on the assumption that in metals and intermetallic compounds the nonequivalent bond orbitals in an atom may have different hybrid character, such as to correspond to suitable values of R, the single-bond radius of the atom. A set of empirical equations giving the single-bond radius as a function... 

There are two general conclusions of importance. First, the distance r(Z- X), where Z is the electron donor atom/centre in the complex B- XY, is smaller than the sum of the van der Waals radii ax and ax of these atoms. This result has been shown [179] to be consistent with the conclusion that the van der Waals radius of the atom X in the dihalogen molecule X is shorter along the XY internuclear axis than it is perpendicular to it, i.e. there is a polar flattening of the atom X in the molecule XY of the type suggested by Stone et al. [180]. This result has been shown to hold for the cases XY = CI2 [174], BrCl [175], C1F [176] and IC1 [178], but not for F2, in which the F atom in the molecule appears (admittedly on the basis of only a few examples) to be more nearly spherical [177]. 

To a first approximation, atoms in molecules may be regarded as hard spheres with a segment cut off in the bonding direction, as in the familiar space-filling models. The radius of the atom in a nonbonding direction is called the van der Waals radius. Half the distance between two atoms of the same kind in adjacent molecules at equilibrium is taken as the van der Waals radius (Figure 5.1). In assigning a fixed radius in this way, we assume that atoms... 

We can determine the amount of empty space in the simple cubic (a space-filling model is shown in Figure 7.15) structure by considering it to have an edge length l, which will be twice the radius of an atom. Therefore, the radius of the atom is 1/2, so the volume of one atom is (4/3)7r(l/2)3 = 0.52413, but the volume of the cube is P. From this we see that because the cube contains only one atom that occupies 52.4% of the volume of the cube, there is 47.6% empty space. Because of the low coordination number and the large amount of empty space, the simple cubic structure does not represent an efficient use of space and does not maximize the number of metal atoms bonded to each other. Consequently, the simple cubic structure is not a common one for metals. 

Role of the Radius of the Atom Bearing a Free Valence... 

Thus, the radius of the atom carrying the free valence has a substantial influence on the activation barrier to the addition reaction the greater the radius of this atom, the higher the activation energy. Apparently, this effect is due to the repulsion in the transition state, which is due to the interaction between the electron shells of the attacked double bond and the atom that attacks this bond. 

As one moves down the group, size (radius) of the atoms increases... 

A certain metal crystallizes in a face-centered cube measuring 4.00 x 102 picometers on each edge. What is the radius of the atom (1 picometer (pm) = 1 x 10 12 meter)... 

Electronegativity is the tendency of an atom to attract the bonding electrons within a compound to itself. It depends upon the nuclear charge (proton number) and the atomic radius of the atom. It is these factors that control the ionization energy of the atom which in turn is related to the ability of an atom to attract electrons. 

According to Gordy (1946), electronegativity is represented by the value of the potential resulting from the effect of the nuclear charge of an unshielded atom on a valence electron located at a distance corresponding to the covalent radius of the atom. 

In a manner similar to that nsed to calculate the density of a nnit cell, we can calcn-late the density of atoms on a plane, or planar density. The perpendicular intersection of a plane and sphere is a circle, so the radius of the atoms will be helpful in calcnlat-ing the area they occnpy on the plane. Refer back to Example Problem 1.4 when we calcnlated the lattice parameter for a BCC metal. The section shown along the body diagonal is actually the (110) plane. The body-centered atom is entirely enclosed by this plane, and the comer atoms are located at the confluence of four adjacent planes, so each contributes 1/4 of an atom to the (110) plane. So, there are a total of two atoms on the (110) plane. If we know the lattice parameter or atomic radius, we can calculate the area of the plane, Ap, the area occupied by the atoms, Ac, and the corresponding... 

The distance along any side of the body-centred cubic lattice as shown in Figure 7.1(a) is equal to twice the metallic radius of the atom, 2rM. The distance between the centre of the atom in the centre of the unit cell and the centre of any atom at the cube corner is 31/3/ m. The distance between the centres of two atoms at the centres of adjacent cubes is 2rM. This means that any atom in the body- centred cubic arrangement is coordinated by eight atoms at the 1 cube corners with a distance 3l/3rM, and six more atoms in the centres of the six adjacent cubes with a distance 2rM. The extra six atoms contributing to the coordination number of body-centred atoms are 100 x (2rM - 3,/3rM)/(3I/3rM) = 15.5% further away from the central atom than the eight nearest neighbours. 

The Arw and AVW are the van der Waals radius of the atom of substituents directly bound to the ring and the van der Waals molar volume of substituents, respectively, those of the chlorine substituent being taken as reference. 

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