# Effective nuclear charge

The effective nuclear charge (often symbolized as ${\displaystyle Z_{\mathrm {eff} }}$ or ${\displaystyle Z^{\ast }}$) is the net positive charge experienced by an electron in a polyelectronic atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons. The effective nuclear charge experienced by the electron is also called the core charge. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom.

Effective nuclear charge diagram

## Calculations

In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law.

However, in an atom with many electrons, the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:

${\displaystyle Z_{\mathrm {eff} }=Z-S}$

where

Z is the number of protons in the nucleus (atomic number), and
S is the number of non-valence electrons.

S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater). Douglas Hartree defined the effective Z of a Hartree–Fock orbital to be:

${\displaystyle Z_{\mathrm {eff} }={\frac {\langle r\rangle _{\rm {H}}}{\langle r\rangle _{Z}}}}$

where

${\displaystyle \langle r\rangle _{\rm {H}}}$ is the mean radius of the orbital for hydrogen, and
${\displaystyle \langle r\rangle _{Z}}$ is the mean radius of the orbital for a proton configuration with nuclear charge Z.

## Values

Updated effective nuclear charge values were provided by Clementi et al. in 1963 and 1967.[1][2] In their work, screening constants were optimized to produce effective nuclear charge values that agree with SCF calculations. Though useful as a predictive model, the resulting screening constants contain little chemical insight as a qualitative model of atomic structure.

 H He Z 1 2 1s 1.000 1.688 Li Be B C N O F Ne Z 3 4 5 6 7 8 9 10 1s 2.691 3.685 4.680 5.673 6.665 7.658 8.650 9.642 2s 1.279 1.912 2.576 3.217 3.847 4.492 5.128 5.758 2p 2.421 3.136 3.834 4.453 5.100 5.758 Na Mg Al Si P S Cl Ar Z 11 12 13 14 15 16 17 18 1s 10.626 11.609 12.591 13.575 14.558 15.541 16.524 17.508 2s 6.571 7.392 8.214 9.020 9.825 10.629 11.430 12.230 2p 6.802 7.826 8.963 9.945 10.961 11.977 12.993 14.008 3s 2.507 3.308 4.117 4.903 5.642 6.367 7.068 7.757 3p 4.066 4.285 4.886 5.482 6.116 6.764 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Z 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1s 18.490 19.473 20.457 21.441 22.426 23.414 24.396 25.381 26.367 27.353 28.339 29.325 30.309 31.294 32.278 33.262 34.247 35.232 2s 13.006 13.776 14.574 15.377 16.181 16.984 17.794 18.599 19.405 20.213 21.020 21.828 22.599 23.365 24.127 24.888 25.643 26.398 2p 15.027 16.041 17.055 18.065 19.073 20.075 21.084 22.089 23.092 24.095 25.097 26.098 27.091 28.082 29.074 30.065 31.056 32.047 3s 8.680 9.602 10.340 11.033 11.709 12.368 13.018 13.676 14.322 14.961 15.594 16.219 16.996 17.790 18.596 19.403 20.219 21.033 3p 7.726 8.658 9.406 10.104 10.785 11.466 12.109 12.778 13.435 14.085 14.731 15.369 16.204 17.014 17.850 18.705 19.571 20.434 4s 3.495 4.398 4.632 4.817 4.981 5.133 5.283 5.434 5.576 5.711 5.842 5.965 7.067 8.044 8.944 9.758 10.553 11.316 3d 7.120 8.141 8.983 9.757 10.528 11.180 11.855 12.530 13.201 13.878 15.093 16.251 17.378 18.477 19.559 20.626 4p 6.222 6.780 7.449 8.287 9.028 9.338 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Z 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 1s 36.208 37.191 38.176 39.159 40.142 41.126 42.109 43.092 44.076 45.059 46.042 47.026 48.010 48.992 49.974 50.957 51.939 52.922 2s 27.157 27.902 28.622 29.374 30.125 30.877 31.628 32.380 33.155 33.883 34.634 35.386 36.124 36.859 37.595 38.331 39.067 39.803 2p 33.039 34.030 35.003 35.993 36.982 37.972 38.941 39.951 40.940 41.930 42.919 43.909 44.898 45.885 46.873 47.860 48.847 49.835 3s 21.843 22.664 23.552 24.362 25.172 25.982 26.792 27.601 28.439 29.221 30.031 30.841 31.631 32.420 33.209 33.998 34.787 35.576 3p 21.303 22.168 23.093 23.846 24.616 25.474 26.384 27.221 28.154 29.020 29.809 30.692 31.521 32.353 33.184 34.009 34.841 35.668 4s 12.388 13.444 14.264 14.902 15.283 16.096 17.198 17.656 18.582 18.986 19.865 20.869 21.761 22.658 23.544 24.408 25.297 26.173 3d 21.679 22.726 25.397 25.567 26.247 27.228 28.353 29.359 30.405 31.451 32.540 33.607 34.678 35.742 36.800 37.839 38.901 39.947 4p 10.881 11.932 12.746 13.460 14.084 14.977 15.811 16.435 17.140 17.723 18.562 19.411 20.369 21.265 22.181 23.122 24.030 24.957 5s 4.985 6.071 6.256 6.446 5.921 6.106 7.227 6.485 6.640 (empty) 6.756 8.192 9.512 10.629 11.617 12.538 13.404 14.218 4d 15.958 13.072 11.238 11.392 12.882 12.813 13.442 13.618 14.763 15.877 16.942 17.970 18.974 19.960 20.934 21.893 5p 8.470 9.102 9.995 10.809 11.612 12.425

## References

1. ^ Clementi, E.; Raimondi, D. L. (1963). "Atomic Screening Constants from SCF Functions". J. Chem. Phys. 38 (11): 2686–2689. Bibcode:1963JChPh..38.2686C. doi:10.1063/1.1733573.
2. ^ Clementi, E.; Raimondi, D. L.; Reinhardt, W. P. (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". Journal of Chemical Physics. 47: 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.

## Resources

• Brown, Theodore; LeMay, H.E.; & Bursten, Bruce (2002). Chemistry: The Central Science (8th revised edition). Upper Saddle River, New Jersey 07458: Prentice-Hall. ISBN 0-13-061142-5.
Alkali metal

The alkali metals are a group (column) in the periodic table consisting of the chemical elements lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr). This group lies in the s-block of the periodic table of elements as all alkali metals have their outermost electron in an s-orbital: this shared electron configuration results in their having very similar characteristic properties. Indeed, the alkali metals provide the best example of group trends in properties in the periodic table, with elements exhibiting well-characterised homologous behaviour.

The alkali metals are all shiny, soft, highly reactive metals at standard temperature and pressure and readily lose their outermost electron to form cations with charge +1. They can all be cut easily with a knife due to their softness, exposing a shiny surface that tarnishes rapidly in air due to oxidation by atmospheric moisture and oxygen (and in the case of lithium, nitrogen). Because of their high reactivity, they must be stored under oil to prevent reaction with air, and are found naturally only in salts and never as the free elements. Caesium, the fifth alkali metal, is the most reactive of all the metals. In the modern IUPAC nomenclature, the alkali metals comprise the group 1 elements, excluding hydrogen (H), which is nominally a group 1 element but not normally considered to be an alkali metal as it rarely exhibits behaviour comparable to that of the alkali metals. All the alkali metals react with water, with the heavier alkali metals reacting more vigorously than the lighter ones.

All of the discovered alkali metals occur in nature as their compounds: in order of abundance, sodium is the most abundant, followed by potassium, lithium, rubidium, caesium, and finally francium, which is very rare due to its extremely high radioactivity; francium occurs only in the minutest traces in nature as an intermediate step in some obscure side branches of the natural decay chains. Experiments have been conducted to attempt the synthesis of ununennium (Uue), which is likely to be the next member of the group, but they have all met with failure. However, ununennium may not be an alkali metal due to relativistic effects, which are predicted to have a large influence on the chemical properties of superheavy elements; even if it does turn out to be an alkali metal, it is predicted to have some differences in physical and chemical properties from its lighter homologues.

Most alkali metals have many different applications. One of the best-known applications of the pure elements is the use of rubidium and caesium in atomic clocks, of which caesium atomic clocks are the most accurate and precise representation of time. A common application of the compounds of sodium is the sodium-vapour lamp, which emits light very efficiently. Table salt, or sodium chloride, has been used since antiquity. Lithium finds use as a psychiatric medication. Sodium and potassium are also essential elements, having major biological roles as electrolytes, and although the other alkali metals are not essential, they also have various effects on the body, both beneficial and harmful.

The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding cloud of electrons. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Three widely used definitions of atomic radius are: Van der Waals radius, ionic radius, and covalent radius.

Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bound in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. The value of the radius may depend on the atom's state and context.Electrons do not have definite orbits, or sharply defined ranges. Rather, their positions must be described as probability distributions that taper off gradually as one moves away from the nucleus, without a sharp cutoff. Moreover, in condensed matter and molecules, the electron clouds of the atoms usually overlap to some extent, and some of the electrons may roam over a large region encompassing two or more atoms.

Under most definitions the radii of isolated neutral atoms range between 30 and 300 pm (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm), and less than 1/1000 of the wavelength of visible light (400–700 nm).

For many purposes, atoms can be modeled as spheres. This is only a crude approximation, but it can provide quantitative explanations and predictions for many phenomena, such as the density of liquids and solids, the diffusion of fluids through molecular sieves, the arrangement of atoms and ions in crystals, and the size and shape of molecules.Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group (column). The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii (and of various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory. The atomic radii decrease across the Periodic Table because as the atomic number increases, the number of protons increases across the period, but the extra electrons are only added to the same quantum shell. Therefore, the effective nuclear charge towards the outermost electrons increases, drawing the outermost electrons closer. As a result, the electron cloud contracts and the atomic radius decreases.

Core charge

Core charge is the effective nuclear charge experienced by an outer shell electron. In other words, core charge is an expression of the attractive force experienced by the valence electrons to the core of an atom which takes into account the shielding effect of core electrons. Core charge can be calculated by taking the number of protons in the nucleus minus the number of core electrons, also called inner shell electrons, and is always a positive value.

Core charge is a convenient way of explaining trends in the periodic table. Since the core charge increases as you move across a row of the periodic table, the outer-shell electrons are pulled more and more strongly towards the nucleus and the atomic radius decreases. This can be used to explain a number of periodic trends such as atomic radius, first ionization energy (IE), electronegativity, and oxidizing.

Core charge can also be calculated as 'atomic number' minus 'all electrons except those in the outer shell'. For example, chlorine (element 17), with electron configuration 1s2 2s2 2p6 3s2 3p5, has 17 protons and 10 inner shell electrons (2 in the first shell, and 8 in the second) so:

Core charge = 17 − 10 = +7A core charge is the net charge of a nucleus, considering the completed shells of electrons to act as a 'shield.' As a core charge increases, the valence electrons are more strongly attracted to the nucleus, and the atomic radius decreases across the period.

Effective atomic number

Effective atomic number has two different meanings: one that is the effective nuclear charge of an atom, and one that calculates the average atomic number for a compound or mixture of materials. Both are abbreviated Zeff.

Fermium

Fermium is a synthetic element with symbol Fm and atomic number 100. It is an actinide and the heaviest element that can be formed by neutron bombardment of lighter elements, and hence the last element that can be prepared in macroscopic quantities, although pure fermium metal has not yet been prepared. A total of 19 isotopes are known, with 257Fm being the longest-lived with a half-life of 100.5 days.

It was discovered in the debris of the first hydrogen bomb explosion in 1952, and named after Enrico Fermi, one of the pioneers of nuclear physics. Its chemistry is typical for the late actinides, with a preponderance of the +3 oxidation state but also an accessible +2 oxidation state. Owing to the small amounts of produced fermium and all of its isotopes having relatively short half-lives, there are currently no uses for it outside basic scientific research.

Frenkel defect

A Frenkel defect or Dislocation defect is a type of defect in crystalline solids named after its discoverer Yakov Frenkel.

In an ionic crystal, this defect forms when an ion is displaced from its lattice position to an interstitial site, creating a vacancy at the original site and an interstitial defect at the new location without any changes in chemical properties. This defect appears in an ionic solid which usually possess low coordination number and/or a considerable disparity in the sizes of the ions. The smaller ion (usually the cation) is dislocated; e.g. in ZnS, AgCl, AgBr, and AgI due to the small size of the zinc ion with charge +2 and the silver ion with charge +1, the cations in the respective cases get dislocated. It must be noted here, however, that AgBr exhibits both Frenkel defect and Schottky defect, in apparent contravention to the aforementioned conditions, as, the usual condition for the exhibition of Schottky defect is that, inter alia, there is no considerable disparity in the sizes of the constituent ions of an ionic solid that exhibits the Schottky defect.

Gallium(III) bromide

Gallium(III) bromide (GaBr3) is a chemical compound, and one of four Gallium trihalides.

Group 4 element

Group 4 is a group of elements in the periodic table.

It contains the elements titanium (Ti), zirconium (Zr), hafnium (Hf) and rutherfordium (Rf). This group lies in the d-block of the periodic table. The group itself has not acquired a trivial name; it belongs to the broader grouping of the transition metals.

The three Group 4 elements that occur naturally are titanium, zirconium and hafnium. The first three members of the group share similar properties; all three are hard refractory metals under standard conditions. However, the fourth element rutherfordium (Rf), has been synthesized in the laboratory; none of its isotopes have been found occurring in nature. All isotopes of rutherfordium are radioactive. So far, no experiments in a supercollider have been conducted to synthesize the next member of the group, unpentoctium (Upo, element 158), and it is unlikely that they will be synthesized in the near future.

Halogen

The halogens () are a group in the periodic table consisting of five chemically related elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). The artificially created element 117 (tennessine, Ts) may also be a halogen. In the modern IUPAC nomenclature, this group is known as group 17. The symbol X is often used generically to refer to any halogen.

The name "halogen" means "salt-producing". When halogens react with metals they produce a wide range of salts, including calcium fluoride, sodium chloride (common table salt), silver bromide and potassium iodide.

The group of halogens is the only periodic table group that contains elements in three of the main states of matter at standard temperature and pressure. All of the halogens form acids when bonded to hydrogen. Most halogens are typically produced from minerals or salts. The middle halogens, that is chlorine, bromine and iodine, are often used as disinfectants. Organobromides are the most important class of flame retardants. Elemental halogens are dangerous and can be lethally toxic.

Ionization energy

In physics and chemistry, ionization energy (American English spelling) or ionisation energy (British English spelling), denoted Ei, is the minimum amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated neutral gaseous atom or molecule. It is quantitatively expressed as

X + energy → X+ + e−where X is any atom or molecule capable of ionization, X+ is that atom or molecule with an electron removed, and e− is the removed electron. This is generally an endothermic process. Generally, the closer the outermost electrons are to the nucleus of the atom , the higher the atom's or element's ionization energy.

The sciences of physics and chemistry use different measures of ionization energy. In physics, the unit is the amount of energy required to remove a single electron from a single atom or molecule, expressed as electronvolts. In chemistry, the unit is the amount of energy required for all of the atoms in a mole of substance to lose one electron each: molar ionization energy or enthalpy, expressed as kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).Comparison of Ei of elements in the periodic table reveals two periodic trends:

Ei generally increases as one moves from left to right within a given period (that is, row).

Ei generally decreases as one moves from top to bottom in a given group (that is, column).The latter trend results from the outer electron shell being progressively farther from the nucleus, with the addition of one inner shell per row as one moves down the column.

The nth ionization energy refers to the amount of energy required to remove an electron from the species with a charge of (n-1). For example, the first three ionization energies are defined as follows:

1st ionization energy

X → X+ + e−2nd ionization energy

X+ → X2+ + e−3rd ionization energy

X2+ → X3+ + e−The term ionization potential is an older name for ionization energy, because the oldest method of measuring ionization energy was based on ionizing a sample and accelerating the electron removed using an electrostatic potential. However this term is now considered obsolete.

Some factors affecting the ionization energy include:

Nuclear charge: the greater the magnitude of nuclear charge the more tightly the electrons are held by the nucleus and hence more will be ionization energy.

Number of electron shells: the greater the size of the atom less tightly the electrons are held by the nucleus and ionization energy will be less.

Effective nuclear charge (Zeff): the greater the magnitude of electron shielding and penetration the less tightly the electrons are held by the nucleus, the lower the Zeff of the electron, and hence less will be the ionization energy.

Type of orbital ionized: the atom having a more stable electronic configuration has less tendency to lose electrons and consequently has high ionization energy.

Occupancy of the orbital matters: if the orbital is half or completely filled then it is harder to remove electrons

Metal K-edge

Metal K-edge spectroscopy is a spectroscopic technique used to study the electronic structures of transition metal atoms and complexes. This method measures X-ray absorption caused by the excitation of a 1s electron to valence bound states localized on the metal, which creates a characteristic absorption peak called the K-edge. The K-edge can be divided into the pre-edge region (comprising the pre-edge and rising edge transitions) and the near-edge region (comprising the intense edge transition and ~150 eV above it).

Metallic bonding

Metallic bonding is a type of chemical bonding that rises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. It may be described as the sharing of free electrons among a structure of positively charged ions (cations). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and luster.Metallic bonding is not the only type of chemical bonding a metal can exhibit, even as a pure substance. For example, elemental gallium consists of covalently-bound pairs of atoms in both liquid and solid state—these pairs form a crystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is mercurous ion (Hg2+2).

Mössbauer spectroscopy

Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer (also Moessbauer, German: "Mößbauer") in 1958, consists in the nearly recoil-free, resonant absorption and emission of gamma rays in solids.

Like nuclear magnetic resonance spectroscopy, Mössbauer spectroscopy probes tiny changes in the energy levels of an atomic nucleus in response to its environment. Typically, three types of nuclear interactions may be observed: isomer shift, also called chemical shift in the older literature; quadrupole splitting; and magnetic hyperfine splitting (see also the Zeeman effect). Due to the high energy and extremely narrow line widths of gamma rays, Mössbauer spectroscopy is a very sensitive technique in terms of energy (and hence frequency) resolution, capable of detecting changes in just a few parts per 1011.

Plum pudding model

The plum pudding model is one of several scientific models of the atom. First proposed by J. J. Thomson in 1904 soon after the discovery of the electron, but before the discovery of the atomic nucleus, the model represented an attempt to consolidate the known properties of atoms at the time: 1) electrons are negatively-charged particles and 2) atoms are neutrally-charged.

Rydberg formula

The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on 5 November 1888.

In 1880, Rydberg worked on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations by using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement. He plotted the wavenumbers (n) of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted.

First he tried the formula: ${\displaystyle \scriptstyle n=n_{0}-{\frac {C_{0}}{m+m'}}}$, where n is the line's wavenumber, n0 is the series limit, m is the line's ordinal number in the series, m' is a constant different for different series and C0 is a universal constant. This did not work very well.

Rydberg was trying: ${\displaystyle \scriptstyle n=n_{0}-{\frac {C_{0}}{\left(m+m'\right)^{2}}}}$ when he became aware of Balmer's formula for the hydrogen spectrum ${\displaystyle \scriptstyle \lambda ={hm^{2} \over m^{2}-4}}$ In this equation, m is an integer and h is a constant (not to be confused with the later Planck's constant).

Rydberg therefore rewrote Balmer's formula in terms of wavenumbers, as ${\displaystyle \scriptstyle n=n_{0}-{4n_{0} \over m^{2}}}$.

This suggested that the Balmer formula for hydrogen might be a special case with ${\displaystyle \scriptstyle m'=0\!}$ and ${\displaystyle \scriptstyle C_{0}=4n_{0}\!}$, where ${\displaystyle \scriptstyle n_{0}={\frac {1}{h}}}$, the reciprocal of Balmer's constant (this constant h is written B in the Balmer equation article, again to avoid confusion with Planck's constant).

The term Co was found to be a universal constant common to all elements, equal to 4/h. This constant is now known as the Rydberg constant, and m' is known as the quantum defect.

As stressed by Niels Bohr, expressing results in terms of wavenumber, not wavelength, was the key to Rydberg's discovery. The fundamental role of wavenumbers was also emphasized by the Rydberg-Ritz combination principle of 1908. The fundamental reason for this lies in quantum mechanics. Light's wavenumber is proportional to frequency ${\displaystyle \scriptstyle {\frac {1}{\lambda }}={\frac {f}{c}}}$, and therefore also proportional to light's quantum energy E. Thus, ${\displaystyle \scriptstyle {\frac {1}{\lambda }}={\frac {E}{hc}}}$. Modern understanding is that Rydberg's findings were a reflection of the underlying simplicity of the behavior of spectral lines, in terms of fixed (quantized) energy differences between electron orbitals in atoms. Rydberg's 1888 classical expression for the form of the spectral series was not accompanied by a physical explanation. Ritz's pre-quantum 1908 explanation for the mechanism underlying the spectral series was that atomic electrons behaved like magnets and that the magnets could vibrate with respect to the atomic nucleus (at least temporarily) to produce electromagnetic radiation, but this theory was superseded in 1913 by Niels Bohr's model of the atom.

In Bohr's conception of the atom, the integer Rydberg (and Balmer) n numbers represent electron orbitals at different integral distances from the atom. A frequency (or spectral energy) emitted in a transition from n1 to n2 therefore represents the photon energy emitted or absorbed when an electron makes a jump from orbital 1 to orbital 2.

Later models found that the values for n1 and n2 corresponded to the principal quantum numbers of the two orbitals.

Shielding effect

The shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than one electron. The shielding effect can be defined as a reduction in the effective nuclear charge on the electron cloud, due

to a difference in the attraction forces on the electrons in the atom. It is a special case of electric-field screening.

Slater's rules

In quantum chemistry, Slater's rules provide numerical values for the effective nuclear charge concept. In a many-electron atom, each electron is said to experience less than the actual nuclear charge owing to shielding or screening by the other electrons. For each electron in an atom, Slater's rules provide a value for the screening constant, denoted by s, S, or σ, which relates the effective and actual nuclear charges as -

${\displaystyle Z_{\mathrm {eff} }=Z-s.\,}$

The rules were devised semi-empirically by John C. Slater and published in 1930.

Revised values of screening constants based on computations of atomic structure by the Hartree–Fock method were obtained by Enrico Clementi et al in the 1960s.

Ytterbium(III) chloride (data page)