Z* effective nuclear charge

The relativistic many-electron theory can then be formulated in just the same way as in the non-relativistic case above the relativistic x can be obtained and various shells and electron groups separated in it. Because of their strong Z (effective nuclear charge) dependence, relativistic effects will then be confined mainly to the inner shells and will cancel out in the calculations of molecular binding energies and other vedence electron properties. Further approximations may then be made in the formal relativistic theory for the outer shell parts of Xrei and rei to get the non-relativistic equations of this article. 

Fig. 1-16. Moseley plot for Ka2 lines. The curvature at high Z is due to a change in the effective nuclear charge (Z — 1). The insert shows the atomic number Z to be more fundamental than the atomic weight M. X-rays made possible the first experimental determinations of Z. Crosses = atomic weight dots = atomic number.

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 ... 

A similar model for many-electron atoms has been developed,6 by considering each electron to be hydrogen-like, but under the influence of an effective nuclear charge (Z — Ss)e, in which Ss is called the size-screening constant. It is found that atoms and ions containing only 5 electrons (with the quantum number l equal to zero) and completed sub-groups of... 

As a first approximation, each electron in a many-electron atom can be considered to have the distribution in space of a hydrogen-like electron under the action of the effective nuclear charge (Z—Ss)e, in which 5s represents the screening effect of inner electrons. In the course of a previous investigation,6 values of S5 for a large number of ions were derived. 

In this equation, Z is the effective nuclear charge, which takes into account the fact that an outer electron is screened from experiencing the effect of the actual nuclear charge by the electrons that are closer to the nucleus (see Section 2.4). In principle, the Allred-Rochow electronegativity scale is based on the electrostatic interaction between valence shell electrons and the nucleus. 

As effective nuclear charge (Z on the central atom increases, acid strength is likewise increased. Thus, a larger nuclear charge draws the electrons closer to the nucleus and binds them more tightly. 1 point given for correlation between and add strength. 

Their energies vary as -Z2/n2, so atoms with higher Z values will have more tightly bound electrons (for the same n). In a many-electron atom, one often introduces the concept of an effective nuclear charge Zeff, and takes this to be the full nuclear charge Z minus the number of electrons that occupy orbitals that reside radially "inside" the orbital in question. For example, Zeff = 6-2=4 for the n=2 orbitals of Carbon in the ls22s22p4... 

There are two parameters in the atomic coulomb functions, the effective nuclear charge and the quantum defect. The values of these were taken by Johnson and Rice from available spectral data. The effective atomic charge was adjusted to give the correct ionization potential of the molecule, 9.25 eV, requiring thereby z = 0.8243. The quantum defects of carbon were taken from the appropriate atomic series and were 1.04 for the 5-state and 0.73 for the p-states. It is interesting to compare the calculated molecular quantum defects (i.e., those corresponding to the Johnson-Rice LCAO function) with those which can be obtained from the various benzene Rydberg series.218 The asymptotic form of the elu orbital constructed from s atomic functions is... 

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