In
atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
, the effective nuclear charge is the actual amount of positive (nuclear) charge experienced by an electron in a multi-electron atom. The term "effective" is used because the
shielding effect
In chemistry, 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 re ...
of negatively charged electrons prevent higher energy electrons from experiencing the full nuclear charge of the
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
* Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucl ...
due to the repelling effect of inner layer. The effective nuclear charge experienced by an 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. Most of the physical and chemical properties of the elements can be explained on the basis of electronic configuration. Consider the behavior of
ionization energies
Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule i ...
in the periodic table. It is known that the magnitude of ionization potential depends upon the following factors:
# Size of atom;
# The nuclear charge;
# The screening effect of the inner shells, and
# The extent to which the outermost electron penetrates into the charge cloud set up by the inner lying electron.
In the periodic table, effective nuclear charge decreases down a group and increases left to right across a period.
Description
The effective atomic number Z
eff, (sometimes referred to as the effective nuclear charge) of an
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
is the number of
protons
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mas ...
that an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
in the element effectively 'sees' due to screening by
inner-shell electrons Core electrons are the electrons in an atom that are not valence electrons and do not participate in chemical bonding. The nucleus and the core electrons of an atom form the atomic core. Core electrons are tightly bound to the nucleus. Therefore, un ...
. It is a measure of the electrostatic interaction between the negatively charged electrons and positively charged protons in the atom. One can view the electrons in an atom as being 'stacked' by energy outside the nucleus; the lowest energy electrons (such as the 1s and 2s electrons) occupy the space closest to the nucleus, and electrons of higher energy are located further from the nucleus.
The
binding energy
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
of an electron, or the energy needed to remove the electron from the atom, is a function of the
electrostatic
Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...
interaction between the negatively charged electrons and the positively charged nucleus. For instance, in
iron
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
(atomic number 26) the nucleus contains 26 protons. The electrons that are closest to the nucleus will 'see' nearly all of them. However, electrons further away are screened from the nucleus by other electrons in between, and feel less electrostatic interaction as a result. The
1s electron of iron (the closest one to the nucleus) sees an effective atomic number (number of protons) of 25. The reason why it is not 26 is that some of the electrons in the atom end up repelling the others, giving a net lower electrostatic interaction with the nucleus. One way of envisioning this effect is to imagine the 1s electron sitting on one side of the 26 protons in the nucleus, with another electron sitting on the other side; each electron will feel less than the attractive force of 26 protons because the other electron contributes a repelling force. The 4s electrons in iron, which are furthest from the nucleus, feel an effective atomic number of only 5.43 because of the 25 electrons in between it and the nucleus screening the charge.
Effective atomic numbers are useful not only in understanding why electrons further from the nucleus are so much more weakly bound than those closer to the nucleus, but also because they can tell us when to use simplified methods of calculating other properties and interactions. For instance,
lithium
Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense solid el ...
, atomic number 3, has two electrons in the 1s shell and one in the 2s shell. Because the two 1s electrons screen the protons to give an effective atomic number for the 2s electron close to 1, we can treat this 2s valence electron with a hydrogenic model.
Mathematically, the effective atomic number ''Z''
eff can be calculated using methods known as "
self-consistent field
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
" calculations, but in simplified situations is just taken as the atomic number minus the number of electrons between the nucleus and the electron being considered.
Calculations
In an atom with one electron, that electron experiences the full charge of the positive
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
* Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucl ...
. In this case, the effective nuclear charge can be calculated by
Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
.
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:
where
*''Z'' is the number of
protons
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mas ...
in the nucleus (
atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
), and
*''S'' is the shielding constant.
''S'' can be found by the systematic application of various rule sets.
Slater's rules
The simplest method for determining the shielding constant for a given electron is the use of "
Slater's rules" (named after
John C. Slater
John Clarke Slater (December 22, 1900 – July 25, 1976) was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. He also made major contributions to microwave electroni ...
). These algebraic rules are significantly simpler than finding shielding constants using
ab initio calculation
''Ab initio'' quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the exci ...
.
Hartree–Fock method
A more theoretically justified method is to calculate the shielding constant using the
Hartree-Fock method.
Douglas Hartree
Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the ...
defined the effective ''Z'' of a Hartree–Fock orbital to be:
where
*
is the mean
radius
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
of the orbital for
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
, and
*
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.
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.
Comparison with nuclear charge
Nuclear charge is the
electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
of a nucleus of an atom, equal to the number of protons in the nucleus times the
elementary charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
. In contrast, the effective nuclear charge is the attractive positive charge of nuclear protons acting on valence electrons, which is always less than the total number of protons present in a nucleus due to the
shielding effect
In chemistry, 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 re ...
.
See also
*
Atomic orbitals
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any sp ...
*
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 shie ...
*
d-block contraction
The d-block contraction (sometimes called scandide contraction) is a term used in chemistry to describe the effect of having full d orbitals on the period 4 elements. The elements in question are gallium, germanium, arsenic, selenium, bromine, ...
(or scandide contraction)
*
Electronegativity
Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the d ...
*
Lanthanide contraction
The lanthanide contraction is the greater-than-expected decrease in atomic radii/ionic radii of the elements in the lanthanide series from atomic number 57, lanthanum, to 71, lutetium, which results in smaller than otherwise expected atomic radii ...
*
Shielding effect
In chemistry, 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 re ...
*
Slater-type orbitals Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named after the physicist John C. Slater, who introduced them in 1930.
They possess exponential decay ...
*
Valence electrons
In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair forms ...
*
Weak charge
References
Resources
*Brown, Theodore; intekhab khan, 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.
Chemical bonding