Effective principal quantum number

Z is tlie atomic number and cr is a shielding constant, determined as below, n is an effective principal quantum number, which takes the same value as the true principal quantum number for u = 1, 2 or 3, but for u = 4, 5, 6 has the values 3.7, 4.0, 4.2, respectively. The shielding constant is obtained as follows ... 

FIGURE 1.47 The periodic variation in the atomic radii of the elements. The variation across a period can be explained in terms of the effect of increasing effective nuclear charge that down a group by the occupation of shells with inc reasing principal quantum number. 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

The angular momentum quantum number is denoted /. It also affects the energy of the electron, but in general not as much as the principal quantum number does. In the absence of an electric or magnetic field around the atom, only these two quantum numbers have any effect on the energy of the electron. The value of / can be 0 or any positive integer up to, but not including, the value of n for that electron. 

Inamoto and co-workers (97,98) introduced a new inductive parameter i (iota) based on atomic properties of X, namely the effective nuclear charge in the valence shell and the effective principal quantum number, as well as E(X) (97). They thereby established a reasonable correlation between the a-SCSs in substituted methanes and ethanes and the t. parameters for a series of substituents not including X = CN and I (97). 

This simple method can easily be refined for our present purpose. All the electrons are involved but the effect is predominantly due to the outermost shell fory is (in the hydrogen-like approximation) proportional to the fourth power of the principal quantum number n and inversely as the square of the effective shielded charge Y which is least (and y therefore greatest) for the outermost electrons. The small correction for the inner electrons can therefore be made by screening-constant approximations (15). This simple method suffers from two disadvantages ... 

Almost all the parameters yielded by the various types of radiofrequency spectroscopy arise from the interaction of nuclear magnetic or electrostatic moments with the magnetic or electrostatic fields produced by the surrounding electrons. A consideration of the way these interactions arise shows that they fall into two groups one of the groups contains terms proportional to the electron density at the nucleus, N, itself, Vn(0), and consequently reflects only the s-character of the wave-function centered on N, v>n while the other is proportional to the value for all or some of the electrons surroimding the nucleus N (Table 1). This latter term vanishes for s-type orbitals and for p, d, f orbitals of the same principal quantum number has values in the order p > > d > > f. In practice this means that in a first approximation, only p-electrons contribute to and that the direct effect of the d-orbitals is only... 

The dependence on formal oxidation state can be attributed to electrostatic lowering of the metal d orbitals thereby narrowing the gap with ligand orbitals. The effect of principal quantum number may be due to better overlap of the larger Ad and 5d orbitals with ligand orbitals, compared to the more compact 3d orbitals. Thus 0 increases in the... 

Ch. Jungen The vibronic coupling is included through the R dependence of the diagonal and off-diagonal quantum defect matrix elements. The effective principal quantum number, or more precisely the quantum defect, gives a handle on the electronic wave function. The variation with R then contains the information concerning the derivative with respect to R of the electronic wave function. 

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