Atomic number effective

Most common materials consist of a mix of elements. Yet a uniform material will attenuate X-rays as if it were composed of a single effective atomic number, which may assume a non-integer value. Remarkably, Z g depends solely on the elemental composition and is essentially independent of X-ray energy. 

Assume a material is a uniform compound consisting of N elements, having an atomic number Z, and contributing mass m, (i=l.N). In chemistry, the concept of average atomic number, is defined as 

/H where H, is the atomic weight. Strictly speaking, a, is proportional to each element s bulk electron density, which to a good approximation is proportional to the element s bulk density. The choice of the exponent value (=3.5) is empirical and other authors have presented similar formulas with somewhat different choices for the exponent. 

---

For the transition metals it is often impossible to reach a noble gas structure except in covalent compounds (see effective atomic number rule) and it is found that relative stability is given by having the sub-shells (d or f) filled, half-filled or empty. 

For many species the effective atomic number (FAN) or 18- electron rule is helpful. Low spin transition-metal complexes having the FAN of the next noble gas (Table 5), which have 18 valence electrons, are usually inert, and normally react by dissociation. Fach normal donor is considered to contribute two electrons the remainder are metal valence electrons. Sixteen-electron complexes are often inert, if these are low spin and square-planar, but can undergo associative substitution and oxidative-addition reactions. 

Table 5. Complexes Having Effective Atomic Numbers (EAN) of a Noble Gas ...

Earlandite structure, 6,849 Edge-coalesced icosahedra eleven-coordinate compounds, 1, 99 repulsion energy coefficients, 1,33,34 Edta — see Acetic acid, ethylenediaminetetra-Effective atomic number concept, 1,16 Effective bond length ratios non-bonding electron pairs, 1,37 Effective d-orbital set, 1,222 Egta — see Acetic acid,... 

As well as being attracted to the nucleus, each electron in a many-electron atom is repelled by the other electrons present. As a result, it is less tightly bound to the nucleus than it would be if those other electrons were absent. We say that each electron is shielded from the full attraction of the nucleus by the other electrons in the atom. The shielding effectively reduces the pull of the nucleus on an electron. The effective nuclear charge, Z lle, experienced by the electron is always less than the actual nuclear charge, Ze, because the electron-electron repulsions work against the pull of the nucleus. A very approximate form of the energy of an electron in a many-electron atom is a version of Eq. 14b in which the true atomic number is replaced by the effective atomic number ... 

Atomic radii generally decrease from left to right across a period as the effective atomic number increases, and they increase dotvn a group as successive shells are occupied. 

The effective atomic numbers in the radial wave functions cannot be evaluated by minimizing the energy integral, because of neglect of inner shells. In all the calculations reported the effective atomic numbers were given the value 1. 

When the effective atomic number becomes a little greater than the value for iron, however, the stable atomic orbitals are occupied by one electron per orbital, and further electrons can enter this set of orbitals only by becoming paired accordingly, the magnetic moment begins to fall, as is indicated by the experimental data. The magnetic moment drops to the value 1.7 for cobalt and 0.6 for nickel, and to zero at a point 60 percent of the way between nickel and copper. 

The parameter Z is an effective atomic number whose value is determined by the minimization of in equation (9.2). Since the hydrogen-like wave functions 01 and 02 are normalized, we have... 

Many other TT-organometallic compounds have been prepared. In the most stable of these, the total number of electrons contributed by the ligands (e.g., four for allyl anions and six for cyclopentadiene anion) plus the valence electrons on the metal atom or ion is usually 18, to satisfy the effective atomic number rule.31 ... 

Atomic Number—The number of protons in the nucleus of an atom. The "effective atomic number" is calculated from the composition and atomic numbers of a compound or mixture. An element of this atomic number would interact with photons in the same way as the compound or mixture. (Symbol Z). 

This mode of calculation has been called the EAN rule (effective atomic number rule). It is valid for arbitrary metal clusters (closo and others) if the number of electrons is sufficient to assign one electron pair for every M-M connecting line between adjacent atoms, and if the octet rule or the 18-electron rule is fulfilled for main group elements or for transition group elements, respectively. The number of bonds b calculated in this way is a limiting value the number of polyhedron edges in the cluster can be greater than or equal to b, but never smaller. If it is equal, the cluster is electron precise. 

The effective atomic number rule (the 18-electron rule) was described briefly in Chapter 16, but we will consider it again here because it is so useful when discussing carbonyl and olefin complexes. The composition of stable binary metal carbonyls is largely predictable by the effective atomic number (EAN) rule, or the "18-electron rule" as it is also known. Stated in the simplest terms, the EAN rule predicts that a metal in the zero or other low oxidation state will gain electrons from a sufficient number of ligands so that the metal will achieve the electron configuration of the next noble gas. For the first-row transition metals, this means the krypton configuration with a total of 36 electrons. 

IB 58Ni has a mass number of 58 and an atomic number of 28. A positron has a mass number of 0 and an effective atomic number of +1. Emission of a positron has the seeming effect of transforming a proton into a neutron. The parent nuclide must be copper-58. 

Effective atomic number rule, 76 60-61 Effective attenuation length (EAL), 24 88-89... 

Hexaammineplatinum(IV), effective atomic number of noble gas, 7 590t Hexaaquachromium(III) ion, 6 533 Hexaaquamolybdenum(III) ion, 27 26-27 Hexaarylbiimidazolyl (HABI), piezochromic materials, 6 608 Hexabis(benzylthiomethyl)benzene, 24 180 Hexaborane(lO), physical properties of, 4 184t Hexaborane(12), 4 186 Hexabromocyclododecane, 22 467-468 formulations of, 22 460t physical properties of, 4 355t Hexabromocyclohexane, 3 602 Hexachlorobenzene, 3 602 Antoine constants, 6 215t physical and thermodynamic properties, 6 214t... 

Iron oxide yellows, 19 399—401 Iron pellets, 14 498—499 Iron pentacarbonyl, 7 591 14 550 16 71 effective atomic number of noble gas, 7 590t... 

The sensitivity of Z contrast for the detection of small clusters depends not only on the signal Z dependence, but also depends on the microscope resolution, which is governed by the probe size 6. A small cluster containing N atoms of atomic number Zi, supported on a film of effective atomic number Z2 of thickness t, will have a contrast in the annular detector signal given by... 

---