Periodic properties of atoms

For vanadium, the first two electrons enter the 4, — and 4, -I-1 levels, the next three are all in the 3d, — level, and vanadium has the configuration As 3d. The 3d, — line crosses the 4, + k line between V and Cr. When the six electrons of chromium are 

A valuable aspect of the arrangment of atoms on the basis of similar electronic configurations within the periodic table is that an atom s position provides information about its properties. Some of these properties, and how they vary across periods and groups, are now discussed. 

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The universal function x(x) obtained by numerical integration and valid for all neutral atoms decreases monotonically. The electron density is similar for all atoms, except for a different length scale, which is determined by the quantity b and proportional to Z. The density is poorly determined at both small and large values of r. However, since most electrons in complex atoms are at intermediate distances from the nucleus the Thomas-Fermi model is useful for calculating quantities that depend on the average electron density, such as the total energy. The Thomas-Fermi model therefore cannot account for the periodic properties of atoms, but provides a good estimate of initial fields used in more elaborate calculations like those to be discussed in the next section. 

The principle that governs the periodic properties of atomic matter is the composition of atoms, made up of integral numbers of discrete sub-atomic units - protons, neutrons and electrons. Each nuclide is an atom with a unique ratio of protonsmeutrons, which defines a rational fraction. The numerical function that arranges rational fractions in enumerable order is known as a Farey sequence. A simple unimodular Farey sequence is obtained by arranging the fractions (n/n+1) as a function of n. The set of /c-modular sequences ... 

State whether or not atomic radius is a periodic property of atoms. Give evidence to support your answer. 

The chemical and physical properties of dements are a periodic function of atomic number. 

For the purposes of fixing the stationary states we have up to this point only considered simply or multiply periodic systems. However the general solution of the equations frequently yield motions of a more complicated character. In such a case the considerations previously discussed are not consistent with the existence and stability of stationary states whose energy is fixed with the same exactness as in multiply periodic systems. But now in order to give an account of the properties of the elements, we are forced to assume that the atoms, in the absence of external forces at any rate always possess sharp stationary states, although the general solution of the equations of motion for the atoms with several electrons exhibits no simple periodic properties of the type mentioned (Bohr [1923]). 

Why Do We Need to Know This Material Atoms are the fundamental building blocks of matter. They are the currency of chemistry in the sense that almost all the explanations of chemical phenomena are expressed in terms of atoms. This chapter explores the periodic variation of atomic properties and shows how quantum mechanics is used to account for the structures and therefore the properties of atoms. 

A detailed discussion of redox reactions must wait until Chapter 19, after we explore the nature of the atom, periodic properties of the elements, and thermodynamics. For now, we focus on only a few types of redox reactions that are common and relatively simple. 

These are some of the general trends that relate the ionization potentials of atoms with regard to their positions in the periodic table. We will have opportunities to discuss additional properties of atoms later. 

Wolfgang Pauh (1900-1958), an American physicist, was awarded a Nobel Prize in 1945 for developing the exclusion principle. In essence, it states that a particular electron in an atom has only one of fom energy states and that all other electrons are excluded from this electron s energy level or orbital. In other words, no two electrons may occupy the same state of energy (or position in an orbit around the nucleus). This led to the concept that only a certain number of electrons can occupy the same shell or orbit. In addition, the wave properties of electrons are measmed in quantum amounts and are related to the physical and, thus, the chemical properties of atoms. These concepts enable scientists to precisely define important physical properties of the atoms of different elements and to more accmately place elements in the periodic table. 

A closer look at the periodic table points out some interesting trends. These trends not only help us predict how one element might perform relative to another, but also give us some insight into the important properties of atoms and ions that determine their performance. For example, examination of the melting points of the elements in Table 1.3 shows that there is a general trend to decrease melting point as we go down... 

Thus, during the years after 1913, the feeling grew that the chemical properties of atoms could be pretty well understood. The idea that there were undiscovered elements, as indicated by gaps m the periodic system, was reinforced. These elements and more have since been discovered. 

Calculations using the methods of non-relativistic quantum mechanics have now advanced to the point at which they can provide quantitative predictions of the structure and properties of atoms, their ions, molecules, and solids containing atoms from the first two rows of the Periodical Table. However, there is much evidence that relativistic effects grow in importance with the increase of atomic number, and the competition between relativistic and correlation effects dominates over the properties of materials from the first transition row onwards. This makes it obligatory to use methods based on relativistic quantum mechanics if one wishes to obtain even qualitatively realistic descriptions of the properties of systems containing heavy elements. Many of these dominate in materials being considered as new high-temperature superconductors. 

Almost all chemical properties can be explained in terms of the properties of atoms, so this material is central to developing an understanding of chemistry. The topics we cover here account for the structure of the periodic table, the great organizing principle of chemistry, and provide a basis for understanding how elements combine to form compounds. The material is also important because it introduces the theory of matter known as quantum mechanics, which is essential for understanding how electrons behave. 

What fundamental property of atoms is responsible for the periodic variations we observe in atomic radii and in so many other characteristics of the elements This question occupied the thoughts of chemists for more than 50 years after Mendeleev, and it was not until well into the 1920s that the answer was established. To understand how the answer slowly emerged, it s necessary to look first at the nature of visible light and other forms of radiant energy. Historically, studies of the interaction of radiant energy with matter have provided immense insight into atomic and molecular structure. 

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. 

In 1869, two scientists working independently and unaware of each other, Dmitri Mendeleev (a Russian chemist) and Lothar Meyer (a German scientist) made similar classifications of the elements. Both scientists classified the elements in the order of increasing atomic mass, and, as a result, they noticed some similar periodic properties among some elements. Mendeleev s work and ideas on periodic properties of elements attracted much attention. 

The four different periodic tables account for the observed elemental diversity and provide compelling evidence that the properties of atomic matter are intimately related to the local properties of space-time, conditioned by the golden parameter r = l/. The appearance of r in the geometrical description of the very small (atomic nuclei) and the very large (spiral galaxies) emphasizes its universal importance and implies the symmetry relationship of self-similarity between all states of matter. This property is vividly illustrated by the formulation of r as a continued fraction ... 

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