The size of atoms

Quantum mechanics makes it clear that no atom has a fixed size. Electron orbitals extend from the nucleus to a greater or lesser extent, depending upon the chemical and physical environment in the locality of the atomic nucleus. Indeed, recent research on Bose-Einstein and Fermi condensation reveals that a collection of millions of atoms can enter an identical quantum state at temperatures just above 0 K and behave as a single atom, with a single wavefunction that spreads over the whole collection. 

The concept of atomic size becomes more difficult to pin down in compounds. The interactions of nearest neighbours seriously perturb the electron charge clouds of the atoms, and this effect, chemical bonding, has a major influence upon the interatomic distances between bonded atoms. 

It may be thought that the scattering of X-rays and electrons can give absolute values for the 

Crystals and Crystal Structures. Richard J. D. Tilley 2006 John Wiley Sons, Ltd 

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The ball and wire display is used for model building Although it is convenient for this purpose other model displays show three dimensional molecular structure more clearly and may be preferred The space filling display is unique m that it portrays a molecule as a set of atom centered spheres The individual sphere radii are taken from experi mental data and roughly correspond to the size of atomic electron clouds Thus the space filling display attempts to show how much space a molecule takes up... 

Another property that is closely related to electronegativity and position in the periodic table is polarizability. Polarizability is related to the size of atoms and ions and the... 

This argumentation was strongly attacked by Aristotle who said that water can also move and flow without observable empty spaces in it. Maybe Aristotle simply overestimated the size of atoms as thought by Leukipp and Demokrit (Home, 1975). To justify his denial of empty spaces between atoms, one student said Well, you can t see open spaces in water (Lee et al., 1993, p. 257). Such misleading ideas about the size of atoms and particles are reported for students, too (e.g. Lee et al., 1993). Hence, learning difficulties can be explained by this frame When expecting that particles should be observable but no such particles can be seen, why should a learner believe in the existence of atoms ... 

In the study of inorganic chemistry, it is important to understand how atoms vary in size. The relative sizes of atoms determine to some extent the molecular structures that are possible. Table 1.2 shows the sizes of atoms in relationship to the periodic table. 

Some of the important trends in the sizes of atoms can be summarized as follows. 

The structurally related salts [M(Cp )2] [M (tds)2] (M = Fe, Mn, Cr M = Ni, Pt) and [Fe(Cp )2][Pt(tds)2] allowed a systematic study of the effect of a diversity of variables on the magnetic behavior of these compounds, such as the variation of the spin of the cation, the role of the single ion anisotropy, the effect of the variation of the size of atoms involved in the intermolecular contacts. Furthermore, the analysis of the intermolecular contacts in these compounds provided a reasonable interpretation of the intra and interchain magnetic coupling, and its relative strength within the series [44, 45]. 

The reason why the sizes of atoms do not simply increase with atomic number is because electrons often are added successively to the same subshell. These electrons do not fully screen each other from the nuclear charge (they do not effectively get between each other and the nucleus). Consequently, as each electron is added to a subshell and the nuclear charge increases by one unit, all of the electrons in this subshell are drawn more closely into the nucleus. 

Hypothesize about the size of atoms that make up matter. 

Figure 2.30 Molecular models depicting 4,4-dimethylcyclohexanecarboxylic acid (a) framework (b) ball-and-stick (c) space-filling. Note that the size of atoms reflects the electronic charge associated with the atom. Therefore, as seen in models (b) and (c), a hydrogen atom attached to electronegative oxygen appears smaller than a hydrogen atom attached to carbon...

The convenience of using X-rays for stmcture determination stems from the nature of their interactions with matter the wavelengths of radiation in the X-ray region of the electromagnetic spectmm are comparable to the sizes of atoms and interatomic distances that are to be analyzed. Although, in principle, interatomic distances can be determined by electron microscopy, unlike electron microscopic... 

A study of the atoms in the groups and periods reveals a trend in the size of atoms moving from top to bottom and left to right of the periodic table ... 

Another interesting fact about the size of atoms is that atoms that have lost an electron are smaller than the original atom, while atoms that have gained an electron are larger than the original atom. 

Polarisability follows roughly the order of the size of atoms, which is also consistent with lower ionization potentials of larger atoms and ions (e.g., Se>S>0, Se2 >S2 >02 ). 

Interpretation of diffraction effects of non-crystalline substances. It has been pointed out in Chapter V that there is no sharp dividing line between crystalline and amorphous substances with decrease of crystal size, X-ray diffraction patterns become more and more diffuse until, finally, any attempt to calculate crystal size by the method given earlier in this chapter gives a figure of only a few Angstrom units— that is, about one unit cell in these circumstances the word crystal , with its implication of pattern repetition, is inappropriate. The alternative word amorphous is not entirely satisfactory either on account of the sizes of atoms and their preference for particular environments, the distribution of atomic centres.cannot be entirely random. The word non-crystalline is really preferable. 

We note that the term dipole implies the existence of another charge, —q, that remains fixed at the origin all the time. If the charge q is accelerating, it will emit radiation according to Eq. 2.61, where we replace the product qjr by the second derivative of p with respect to time, p. Dimensions of the displacement of charge will be of the order of the size of atoms or molecules, usually assumed to be small with regard to both... 

The size of atoms gradually decreases in moving from left to right across any period. Atomic size is a periodic (repeating) property. 

For transitions between different atomic or molecular electronic states, the wavelengths usually lie in the ultraviolet typically, A 103 A. For vibrational and rotational transitions, A is even larger. The size of atoms and molecules is about 1 A. Hence A is usually much greater than the size of the molecule as far as electrons confined to move within the molecule are concerned, the spatial variation of the radiation s electric field is negligible zjA 0. With this further approximation, we have... 

Transitions due to such matrix elements are called electric-quadrupole transitions. Since the wavelength of ultraviolet light is about 103 times the size of atoms, electric-quadrupole transitions are about 1/106 the intensity of electric-dipole transitions. 

There is one metric unit with a special name that scientists frequently use because it permits the use of simple numbers when talking about the sizes of atoms and molecules. It is called an angstrom (A) 1 A = 10 8 cm-... 

Just as there are systematic differences in the sizes of atoms (Section 5.15), there are also systematic differences in the sizes of ions. As shown in Figure 6.1 for the elements of groups 1A and 2A, atoms shrink dramatically when an electron is removed to form a cation. The radius of an Na atom, for example, is 186 pm, while that of an Na+ cation is 102 pm. Similarly, the radius of an Mg atom is 160 pm, and that of an Mg2+ cation is 72 pm. 

The sizes of atomic orbitals also increase with the energy indeed as in the Bohr theory (see eqn 4.13), the average radius of an orbital is given approximately by... 

The most obvious chemical significance of the electronic structure of atoms lies in the factors that determine ionization energies, electron affinities, and the sizes of atoms. This section looks briefly at some of the trends— vertically and horizontally in the periodic table—in such properties. 

While some scientists continue to debate how realistic Drexlerian nanotechnology is, a far greater number are moving ahead with research on techniques and devices at the nanometer level. Over the past two decades, it has become abundantly clear that whether or not the world ever sees an assembler or a replicator, it will certainly see a host of machines the size of atomic and molecular clusters. 

One problem that arises is that although Newtonian mechanics is sufficient to describe the overall translational motion of particles of the size of atoms and molecules, quantum mechanics is required to describe their rotational and internal motion. Quantum mechanics is essential in dealing with the motion of particles as small as electrons. Because knowledge of quantum mechanics is not assumed of the reader of this book, we will be content to develop the framework into which quantum mechanical results can be later be inserted. We will apply this framework to two systems that can be treated classically, namely the monatomic ideal gas and polymer chains. 

To compare the size of an atom, we need to compare radii among different atoms using some standard. As seen to the right, the sizes of atoms decrease with period number and increase with group number. This trend is similar to the trend described above for metallic character. The smallest atom is helium. 

Alkali metals are shiny, soft, metallic solids. They have low melting points and low densities compared with other metals (see squares in figures on the following page) because they have a weaker metallic bond. Measures of intermolecular attractions including their melting points decrease further down the periodic table due to weaker metallic bonds as the size of atoms increases. 

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