Nucleus charge

For the hydrogen atom, which has one nucleus (charge +e) and one electron (—e), Eq. (2) can be reduced into the following familiar form ... 

Atomic nuclei consist of nucleons (protons and neutrons). The total number of nucleons is denoted as A and is called the mass number. The nucleus charge, z, is equal to the number of protons. The nucleus bond energy comprises a combination of the nuclear interaction (attraction) energy of the nucleons and the Coulomb interaction (repulsion) energy of the protons. The characteristic feature of the nuclear forces appears to be short-range action nucleons interact only when they are in a very close contact at a distance of about 10 13 cm. Another important feature is the incompressibility of the nucleons and, due to this, the volume of the nucleus grows in proportion to the mass number and its radius, in proportion to Al,i. 

For an atom with a nucleus charge Z and one valence electron, the energy of this electron is given by ... 

It is well known that for heavy atoms the effect of the finite nucleus charge distribution has to be taken into account (among other effects) in order to describe the electronic structure of the system correctly (see e.g. (36,37)). As a preliminary step in the search for the effect of the finite nuclei on the properties of molecules the potential energy curve of the Th 73+ has been calculated for point-like and finite nuclei models (Table 5). For finite nuclei the Fermi charge distribution with the standard value of the skin thickness parameter was adopted (t = 2.30 fm) (38,39). 

ZT is the r -atom nucleus charge, being the electronegativity of the p,-atom larger than or equal to r ... 

Thus, the electronegativity values are linearly dependent on a parameter similar to the polarizing action of the cation. The dependence of the solubility on the Allred-Rochow electronegativity is divided into two sharply bounded and practically linear plots with close slopes for 3d-elements and for alkaline-earth metal-oxides (see Fig. 3.7.13). Since the slopes of these dependences are close, different positions of these plots may be explained by different relationships between the nuclear charge and Z for metals characterized by different electronic configurations. From the above-said it may be concluded that in high-temperature alkali-metal halide melts a correlation of metal-oxide solubilities with the crystal-lochemical radii of the cations is considerably simpler, i.e. it does not require the introduction of any corrections of the nucleus charge, such as Z. ... 

Fig. 11 shows that the IR of the 4d and 5d elements are, as expected, almost equal due to the well-known lanthanide contraction (of 0.020 A) which is roughly 86% a nonrelativistic effect The diminished shielding of the nucleus charge by the 4f electrons causes the contraction of the valence shells. The IR of the transactinides are about 0.05 A larger than the IR of the 5d elements. This is due to an orbital expansion of the outer 6p3/2 orbitals responsible for the size of the ions. The IR of the transactinides are, however, still smaller than the IR of the actinides due to the actinide contraction (0.030 A, being larger than the lanthanide contraction) which is mostly a relativistic effect The 5f shells are more diffuse than the 4f shells, so that the contraction of the outermore valence shells is increased by relativity to a larger extent in the case of the 6d elements as compared to the 5d elements. This has first been shown for elements 104-118 by DF and DS calculations of atomic and ionic radii by Fricke and Waber [20]. 

Here, the superscripts are the atomic mass, the subscripts are the number of protons (nucleus charge, and the star- is the excited state of the nucleus. 

Such p-based theories date back, in fact, to the early days of quantum mechanics, and the pioneering work of Thomas [137] and Fermi [138] provides a method of "statistically" describing the distribution of the electrons in an atom. Without going into detail, the Thomas-Fermi (TF) total energy of an atom with a nucleus charged Z may be directly given as... 

We focus on the electron occupying the orbital in question (that for which we are going to find f), and we try to estimate what the electron sees. The electron sees that the nucleus charge is screened by its fellow electrons. The Slater rules are as follows ... 

Since there are more than one electron in the configuration, the Hamiltonian in (2) has to be adjusted to take into account the number of electrons, the apparent (screened) nucleus charge Z, and the repulsion between electrons located at a... 

Center of positive Center of electronic charge (the nucleus) charge... 

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