Search This Blog

Friday, August 19, 2022

Electron configuration

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Electron_configuration

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s2 2s2 2p6, meaning that the 1s, 2s and 2p subshells are occupied by 2, 2 and 6 electrons respectively.

Electronic configurations describe each electron as moving independently in an orbital, in an average field created by all other orbitals. Mathematically, configurations are described by Slater determinants or configuration state functions.

According to the laws of quantum mechanics, for systems with only one electron, a level of energy is associated with each electron configuration and in certain conditions, electrons are able to move from one configuration to another by the emission or absorption of a quantum of energy, in the form of a photon.

Knowledge of the electron configuration of different atoms is useful in understanding the structure of the periodic table of elements. This is also useful for describing the chemical bonds that hold atoms together. In bulk materials, this same idea helps explain the peculiar properties of lasers and semiconductors.

Shells and subshells


s (l = 0) p (l = 1)

m = 0 m = 0 m = ±1

s pz px py
n = 1 Atomic-orbital-cloud n1 l0 m0.png


n = 2 Atomic-orbital-cloud n2 l0 m0.png Atomic-orbital-cloud n2 l1 m0.png Atomic-orbital-cloud n2 px.png Atomic-orbital-cloud n2 py.png

Electron configuration was first conceived under the Bohr model of the atom, and it is still common to speak of shells and subshells despite the advances in understanding of the quantum-mechanical nature of electrons.

An electron shell is the set of allowed states that share the same principal quantum number, n (the number before the letter in the orbital label), that electrons may occupy. An atom's nth electron shell can accommodate 2n2 electrons, for example, the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons and so on. The factor of two arises because the allowed states are doubled due to electron spin—each atomic orbital admits up to two otherwise identical electrons with opposite spin, one with a spin +12 (usually denoted by an up-arrow) and one with a spin of −12 (with a down-arrow).

A subshell is the set of states defined by a common azimuthal quantum number, l, within a shell. The value of l is in the range from 0 to n − 1. The values l = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. For example, the 3d subshell has n = 3 and l = 2. The maximum number of electrons that can be placed in a subshell is given by 2(2l + 1). This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell.

The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics, in particular the Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four quantum numbers.

Notation

Physicists and chemists use a standard notation to indicate the electron configurations of atoms and molecules. For atoms, the notation consists of a sequence of atomic subshell labels (e.g. for phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned to each subshell placed as a superscript. For example, hydrogen has one electron in the s-orbital of the first shell, so its configuration is written 1s1. Lithium has two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so its configuration is written 1s2 2s1 (pronounced "one-s-two, two-s-one"). Phosphorus (atomic number 15) is as follows: 1s2 2s2 2p6 3s2 3p3.

For atoms with many electrons, this notation can become lengthy and so an abbreviated notation is used. The electron configuration can be visualized as the core electrons, equivalent to the noble gas of the preceding period, and the valence electrons: each element in a period differs only by the last few subshells. Phosphorus, for instance, is in the third period. It differs from the second-period neon, whose configuration is 1s2 2s2 2p6, only by the presence of a third shell. The portion of its configuration that is equivalent to neon is abbreviated as [Ne], allowing the configuration of phosphorus to be written as [Ne] 3s2 3p3 rather than writing out the details of the configuration of neon explicitly. This convention is useful as it is the electrons in the outermost shell that most determine the chemistry of the element.

For a given configuration, the order of writing the orbitals is not completely fixed since only the orbital occupancies have physical significance. For example, the electron configuration of the titanium ground state can be written as either [Ar] 4s2 3d2 or [Ar] 3d2 4s2. The first notation follows the order based on the Madelung rule for the configurations of neutral atoms; 4s is filled before 3d in the sequence Ar, K, Ca, Sc, Ti. The second notation groups all orbitals with the same value of n together, corresponding to the "spectroscopic" order of orbital energies that is the reverse of the order in which electrons are removed from a given atom to form positive ions; 3d is filled before 4s in the sequence Ti4+, Ti3+, Ti2+, Ti+, Ti.

The superscript 1 for a singly occupied subshell is not compulsory; for example aluminium may be written as either [Ne] 3s2 3p1 or [Ne] 3s2 3p. In atoms where a subshell is unoccupied despite higher subshells being occupied (as is the case in some ions, as well as certain neutral atoms shown to deviate from the Madelung rule), the empty subshell is either denoted with a superscript 0 or left out altogether. For example, neutral palladium may be written as either [Kr] 4d10 5s0 or simply [Kr] 4d10, and the lanthanum(III) ion may be written as either [Xe] 4f0 or simply [Xe].

It is quite common to see the letters of the orbital labels (s, p, d, f) written in an italic or slanting typeface, although the International Union of Pure and Applied Chemistry (IUPAC) recommends a normal typeface (as used here). The choice of letters originates from a now-obsolete system of categorizing spectral lines as "sharp", "principal", "diffuse" and "fundamental" (or "fine"), based on their observed fine structure: their modern usage indicates orbitals with an azimuthal quantum number, l, of 0, 1, 2 or 3 respectively. After f, the sequence continues alphabetically g, h, i... (l = 4, 5, 6...), skipping j, although orbitals of these types are rarely required.

The electron configurations of molecules are written in a similar way, except that molecular orbital labels are used instead of atomic orbital labels (see below).

Energy of ground state and excited states

The energy associated to an electron is that of its orbital. The energy of a configuration is often approximated as the sum of the energy of each electron, neglecting the electron-electron interactions. The configuration that corresponds to the lowest electronic energy is called the ground state. Any other configuration is an excited state.

As an example, the ground state configuration of the sodium atom is 1s2 2s2 2p6 3s1, as deduced from the Aufbau principle (see below). The first excited state is obtained by promoting a 3s electron to the 3p orbital, to obtain the 1s2 2s2 2p6 3p1 configuration, abbreviated as the 3p level. Atoms can move from one configuration to another by absorbing or emitting energy. In a sodium-vapor lamp for example, sodium atoms are excited to the 3p level by an electrical discharge, and return to the ground state by emitting yellow light of wavelength 589 nm.

Usually, the excitation of valence electrons (such as 3s for sodium) involves energies corresponding to photons of visible or ultraviolet light. The excitation of core electrons is possible, but requires much higher energies, generally corresponding to X-ray photons. This would be the case for example to excite a 2p electron of sodium to the 3s level and form the excited 1s2 2s2 2p5 3s2 configuration.

The remainder of this article deals only with the ground-state configuration, often referred to as "the" configuration of an atom or molecule.

History

Irving Langmuir was the first to propose in his 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on Gilbert N. Lewis's cubical atom theory and Walther Kossel's chemical bonding theory, he outlined his "concentric theory of atomic structure". Langmuir had developed his work on electron atomic structure from other chemists as is shown in the development of the History of the periodic table and the Octet rule.

Niels Bohr (1923) incorporated Langmuir’s model that the periodicity in the properties of the elements might be explained by the electronic structure of the atom. His proposals were based on the then current Bohr model of the atom, in which the electron shells were orbits at a fixed distance from the nucleus. Bohr's original configurations would seem strange to a present-day chemist: sulfur was given as 2.4.4.6 instead of 1s2 2s2 2p6 3s2 3p4 (2.8.6). Bohr used 4 and 6 following Alfred Werner's 1893 paper. In fact, the chemists believed in atoms long before the physicists. Langmuir began his paper referenced above by saying,

«…The problem of the structure of atoms has been attacked mainly by physicists who have given little consideration to the chemical properties which must ultimately be explained by a theory of atomic structure. The vast store of knowledge of chemical properties and relationships, such as is summarized by the Periodic Table, should serve as a better foundation for a theory of atomic structure than the relatively meager experimental data along purely physical lines... These electrons arrange themselves in a series of concentric shells, the first shell containing two electrons, while all other shells tend to hold eight.…»

The valence electrons in the atom were described by Richard Abegg in 1904.

In 1924, E. C. Stoner incorporated Sommerfeld's third quantum number into the description of electron shells, and correctly predicted the shell structure of sulfur to be 2.8.6. However neither Bohr's system nor Stoner's could correctly describe the changes in atomic spectra in a magnetic field (the Zeeman effect).

Bohr was well aware of this shortcoming (and others), and had written to his friend Wolfgang Pauli in 1923 to ask for his help in saving quantum theory (the system now known as "old quantum theory"). Pauli hypothesized successfully that the Zeeman effect can be explained as depending only on the response of the outermost (i.e., valence) electrons of the atom. Pauli was able to reproduce Stoner's shell structure, but with the correct structure of subshells, by his inclusion of a fourth quantum number and his exclusion principle (1925):

It should be forbidden for more than one electron with the same value of the main quantum number n to have the same value for the other three quantum numbers k [l], j [ml] and m [ms].

The Schrödinger equation, published in 1926, gave three of the four quantum numbers as a direct consequence of its solution for the hydrogen atom: this solution yields the atomic orbitals that are shown today in textbooks of chemistry (and above). The examination of atomic spectra allowed the electron configurations of atoms to be determined experimentally, and led to an empirical rule (known as Madelung's rule (1936), see below) for the order in which atomic orbitals are filled with electrons.

Atoms: Aufbau principle and Madelung rule

The aufbau principle (from the German Aufbau, "building up, construction") was an important part of Bohr's original concept of electron configuration. It may be stated as:

a maximum of two electrons are put into orbitals in the order of increasing orbital energy: the lowest-energy subshells are filled before electrons are placed in higher-energy orbitals.
The approximate order of filling of atomic orbitals, following the arrows from 1s to 7p. (After 7p the order includes subshells outside the range of the diagram, starting with 8s.)

The principle works very well (for the ground states of the atoms) for the known 118 elements, although it is sometimes slightly wrong. The modern form of the aufbau principle describes an order of orbital energies given by Madelung's rule (or Klechkowski's rule). This rule was first stated by Charles Janet in 1929, rediscovered by Erwin Madelung in 1936, and later given a theoretical justification by V. M. Klechkowski:

  1. Subshells are filled in the order of increasing n + l.
  2. Where two subshells have the same value of n + l, they are filled in order of increasing n.

This gives the following order for filling the orbitals:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, (8s, 5 g, 6f, 7d, 8p, and 9s)

In this list the subshells in parentheses are not occupied in the ground state of the heaviest atom now known (Og, Z = 118).

The aufbau principle can be applied, in a modified form, to the protons and neutrons in the atomic nucleus, as in the shell model of nuclear physics and nuclear chemistry.

Periodic table

Electron configuration table showing blocks.

The form of the periodic table is closely related to the electron configuration of the atoms of the elements. For example, all the elements of group 2 have an electron configuration of [E] ns2 (where [E] is an inert gas configuration), and have notable similarities in their chemical properties. In general, the periodicity of the periodic table in terms of periodic table blocks is clearly due to the number of electrons (2, 6, 10, 14...) needed to fill s, p, d, and f subshells. These blocks appear as the rectangular sections of the periodic table. The exception is helium, which despite being an s-block atom is conventionally placed with the other noble gases in the p-block due to its chemical inertness, a consequence of its full outer shell.

The outermost electron shell is often referred to as the "valence shell" and (to a first approximation) determines the chemical properties. It should be remembered that the similarities in the chemical properties were remarked on more than a century before the idea of electron configuration. It is not clear how far Madelung's rule explains (rather than simply describes) the periodic table, although some properties (such as the common +2 oxidation state in the first row of the transition metals) would obviously be different with a different order of orbital filling.

Shortcomings of the aufbau principle

The aufbau principle rests on a fundamental postulate that the order of orbital energies is fixed, both for a given element and between different elements; in both cases this is only approximately true. It considers atomic orbitals as "boxes" of fixed energy into which can be placed two electrons and no more. However, the energy of an electron "in" an atomic orbital depends on the energies of all the other electrons of the atom (or ion, or molecule, etc.). There are no "one-electron solutions" for systems of more than one electron, only a set of many-electron solutions that cannot be calculated exactly (although there are mathematical approximations available, such as the Hartree–Fock method).

The fact that the aufbau principle is based on an approximation can be seen from the fact that there is an almost-fixed filling order at all, that, within a given shell, the s-orbital is always filled before the p-orbitals. In a hydrogen-like atom, which only has one electron, the s-orbital and the p-orbitals of the same shell have exactly the same energy, to a very good approximation in the absence of external electromagnetic fields. (However, in a real hydrogen atom, the energy levels are slightly split by the magnetic field of the nucleus, and by the quantum electrodynamic effects of the Lamb shift.)

Ionization of the transition metals

The naïve application of the aufbau principle leads to a well-known paradox (or apparent paradox) in the basic chemistry of the transition metals. Potassium and calcium appear in the periodic table before the transition metals, and have electron configurations [Ar] 4s1 and [Ar] 4s2 respectively, i.e. the 4s-orbital is filled before the 3d-orbital. This is in line with Madelung's rule, as the 4s-orbital has n + l = 4 (n = 4, l = 0) while the 3d-orbital has n + l = 5 (n = 3, l = 2). After calcium, most neutral atoms in the first series of transition metals (scandium through zinc) have configurations with two 4s electrons, but there are two exceptions. Chromium and copper have electron configurations [Ar] 3d5 4s1 and [Ar] 3d10 4s1 respectively, i.e. one electron has passed from the 4s-orbital to a 3d-orbital to generate a half-filled or filled subshell. In this case, the usual explanation is that "half-filled or completely filled subshells are particularly stable arrangements of electrons". However this is not supported by the facts, as tungsten (W) has a Madelung-following d4 s2 configuration and not d5 s1, and niobium (Nb) has an anomalous d4 s1 configuration that does not give it a half-filled or completely filled subshell.

The apparent paradox arises when electrons are removed from the transition metal atoms to form ions. The first electrons to be ionized come not from the 3d-orbital, as one would expect if it were "higher in energy", but from the 4s-orbital. This interchange of electrons between 4s and 3d is found for all atoms of the first series of transition metals. The configurations of the neutral atoms (K, Ca, Sc, Ti, V, Cr, ...) usually follow the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, ...; however the successive stages of ionization of a given atom (such as Fe4+, Fe3+, Fe2+, Fe+, Fe) usually follow the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, ...

This phenomenon is only paradoxical if it is assumed that the energy order of atomic orbitals is fixed and unaffected by the nuclear charge or by the presence of electrons in other orbitals. If that were the case, the 3d-orbital would have the same energy as the 3p-orbital, as it does in hydrogen, yet it clearly does not. There is no special reason why the Fe2+ ion should have the same electron configuration as the chromium atom, given that iron has two more protons in its nucleus than chromium, and that the chemistry of the two species is very different. Melrose and Eric Scerri have analyzed the changes of orbital energy with orbital occupations in terms of the two-electron repulsion integrals of the Hartree–Fock method of atomic structure calculation. More recently Scerri has argued that contrary to what is stated in the vast majority of sources including the title of his previous article on the subject, 3d orbitals rather than 4s are in fact preferentially occupied.

In chemical environments, configurations can change even more: Th3+ as a bare ion has a configuration of [Rn] 5f1, yet in most ThIII compounds the thorium atom has a 6d1 configuration instead. Mostly, what is present is rather a superposition of various configurations. For instance, copper metal is poorly described by either an [Ar] 3d10 4s1 or an [Ar] 3d9 4s2 configuration, but is rather well described as a 90% contribution of the first and a 10% contribution of the second. Indeed, visible light is already enough to excite electrons in most transition metals, and they often continuously "flow" through different configurations when that happens (copper and its group are an exception).

Similar ion-like 3dx 4s0 configurations occur in transition metal complexes as described by the simple crystal field theory, even if the metal has oxidation state 0. For example, chromium hexacarbonyl can be described as a chromium atom (not ion) surrounded by six carbon monoxide ligands. The electron configuration of the central chromium atom is described as 3d6 with the six electrons filling the three lower-energy d orbitals between the ligands. The other two d orbitals are at higher energy due to the crystal field of the ligands. This picture is consistent with the experimental fact that the complex is diamagnetic, meaning that it has no unpaired electrons. However, in a more accurate description using molecular orbital theory, the d-like orbitals occupied by the six electrons are no longer identical with the d orbitals of the free atom.

Other exceptions to Madelung's rule

There are several more exceptions to Madelung's rule among the heavier elements, and as atomic number increases it becomes more and more difficult to find simple explanations such as the stability of half-filled subshells. It is possible to predict most of the exceptions by Hartree–Fock calculations, which are an approximate method for taking account of the effect of the other electrons on orbital energies. Qualitatively, for example, we can see that the 4d elements have the greatest concentration of Madelung anomalies, because the 4d–5s gap is smaller than the 3d–4s and 5d–6s gaps.

For the heavier elements, it is also necessary to take account of the effects of special relativity on the energies of the atomic orbitals, as the inner-shell electrons are moving at speeds approaching the speed of light. In general, these relativistic effects tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals. This is the reason why the 6d elements are predicted to have no Madelung anomalies apart from lawrencium (for which relativistic effects stabilise the p1/2 orbital as well and cause its occupancy in the ground state), as relativity intervenes to make the 7s orbitals lower in energy than the 6d ones.

The table below shows the configurations of the f-block (green) and d-block (blue) atoms. It shows the ground state configuration in terms of orbital occupancy, but it does not show the ground state in terms of the sequence of orbital energies as determined spectroscopically. For example, in the transition metals, the 4s orbital is of a higher energy than the 3d orbitals; and in the lanthanides, the 6s is higher than the 4f and 5d. The ground states can be seen in the Electron configurations of the elements (data page). However this also depends on the charge: a calcium atom has 4s lower in energy than 3d, but a Ca2+ cation has 3d lower in energy than 4s. In practice the configurations predicted by the Madelung rule are at least close to the ground state even in these anomalous cases. The empty f orbitals in lanthanum, actinium, and thorium contribute to chemical bonding, as do the empty p orbitals in transition metals.

Vacant s, d, and f orbitals have been shown explicitly, as is occasionally done, to emphasize the filling order and to clarify that even orbitals unoccupied in the ground state (e.g. lanthanum 4f or palladium 5s) may be occupied and bonding in chemical compounds. (The same is also true for the p-orbitals, which are not explicitly shown because they are only actually occupied for lawrencium in gas-phase ground states.)

Electron shells filled in violation of Madelung's rule (red)
Predictions for elements 109–112
Period 4   Period 5   Period 6   Period 7
Element Z Electron Configuration   Element Z Electron Configuration   Element Z Electron Configuration   Element Z Electron Configuration
        Lanthanum 57 [Xe] 6s2 4f0 5d1   Actinium 89 [Rn] 7s2 5f0 6d1
        Cerium 58 [Xe] 6s2 4f1 5d1   Thorium 90 [Rn] 7s2 5f0 6d2
        Praseodymium 59 [Xe] 6s2 4f3 5d0   Protactinium 91 [Rn] 7s2 5f2 6d1
        Neodymium 60 [Xe] 6s2 4f4 5d0   Uranium 92 [Rn] 7s2 5f3 6d1
        Promethium 61 [Xe] 6s2 4f5 5d0   Neptunium 93 [Rn] 7s2 5f4 6d1
        Samarium 62 [Xe] 6s2 4f6 5d0   Plutonium 94 [Rn] 7s2 5f6 6d0
        Europium 63 [Xe] 6s2 4f7 5d0   Americium 95 [Rn] 7s2 5f7 6d0
        Gadolinium 64 [Xe] 6s2 4f7 5d1   Curium 96 [Rn] 7s2 5f7 6d1
        Terbium 65 [Xe] 6s2 4f9 5d0   Berkelium 97 [Rn] 7s2 5f9 6d0
        Dysprosium 66 [Xe] 6s2 4f10 5d0   Californium 98 [Rn] 7s2 5f10 6d0
        Holmium 67 [Xe] 6s2 4f11 5d0   Einsteinium 99 [Rn] 7s2 5f11 6d0
        Erbium 68 [Xe] 6s2 4f12 5d0   Fermium 100 [Rn] 7s2 5f12 6d0
        Thulium 69 [Xe] 6s2 4f13 5d0   Mendelevium 101 [Rn] 7s2 5f13 6d0
        Ytterbium 70 [Xe] 6s2 4f14 5d0   Nobelium 102 [Rn] 7s2 5f14 6d0
Scandium 21 [Ar] 4s2 3d1   Yttrium 39 [Kr] 5s2 4d1   Lutetium 71 [Xe] 6s2 4f14 5d1   Lawrencium 103 [Rn] 7s2 5f14 6d0 7p1
Titanium 22 [Ar] 4s2 3d2   Zirconium 40 [Kr] 5s2 4d2   Hafnium 72 [Xe] 6s2 4f14 5d2   Rutherfordium 104 [Rn] 7s2 5f14 6d2
Vanadium 23 [Ar] 4s2 3d3   Niobium 41 [Kr] 5s1 4d4   Tantalum 73 [Xe] 6s2 4f14 5d3   Dubnium 105 [Rn] 7s2 5f14 6d3
Chromium 24 [Ar] 4s1 3d5   Molybdenum 42 [Kr] 5s1 4d5   Tungsten 74 [Xe] 6s2 4f14 5d4   Seaborgium 106 [Rn] 7s2 5f14 6d4
Manganese 25 [Ar] 4s2 3d5   Technetium 43 [Kr] 5s2 4d5   Rhenium 75 [Xe] 6s2 4f14 5d5   Bohrium 107 [Rn] 7s2 5f14 6d5
Iron 26 [Ar] 4s2 3d6   Ruthenium 44 [Kr] 5s1 4d7   Osmium 76 [Xe] 6s2 4f14 5d6   Hassium 108 [Rn] 7s2 5f14 6d6
Cobalt 27 [Ar] 4s2 3d7   Rhodium 45 [Kr] 5s1 4d8   Iridium 77 [Xe] 6s2 4f14 5d7   Meitnerium 109 [Rn] 7s2 5f14 6d7
Nickel 28 [Ar] 4s2 3d8 or
[Ar] 4s1 3d9 (disputed)[36]
  Palladium 46 [Kr] 5s0 4d10   Platinum 78 [Xe] 6s1 4f14 5d9   Darmstadtium 110 [Rn] 7s2 5f14 6d8
Copper 29 [Ar] 4s1 3d10   Silver 47 [Kr] 5s1 4d10   Gold 79 [Xe] 6s1 4f14 5d10   Roentgenium 111 [Rn] 7s2 5f14 6d9
Zinc 30 [Ar] 4s2 3d10   Cadmium 48 [Kr] 5s2 4d10   Mercury 80 [Xe] 6s2 4f14 5d10   Copernicium 112 [Rn] 7s2 5f14 6d10

The various anomalies describe the free atoms and do not necessarily predict chemical behavior. Thus for example neodymium typically forms the +3 oxidation state, despite its configuration [Xe] 4f4 5d0 6s2 that if interpreted naïvely would suggest a more stable +2 oxidation state corresponding to losing only the 6s electrons. Contrariwise, uranium as [Rn] 5f3 6d1 7s2 is not very stable in the +3 oxidation state either, preferring +4 and +6.

The electron-shell configuration of elements beyond hassium has not yet been empirically verified, but they are expected to follow Madelung's rule without exceptions until element 120. Element 121 should have the anomalous configuration [Og] 8s2 5g0 6f0 7d0 8p1, having a p rather than a g electron. Electron configurations beyond this are tentative and predictions differ between models, but Madelung's rule is expected to break down due to the closeness in energy of the 5g, 6f, 7d, and 8p1/2 orbitals. That said, the filling sequence 8s, 5g, 6f, 7d, 8p is predicted to hold approximately, with perturbations due to the huge spin-orbit splitting of the 8p and 9p shells, and the huge relativistic stabilisation of the 9s shell.

Open and closed shells

In the context of atomic orbitals, an open shell is a valence shell which is not completely filled with electrons or that has not given all of its valence electrons through chemical bonds with other atoms or molecules during a chemical reaction. Conversely a closed shell is obtained with a completely filled valence shell. This configuration is very stable.

For molecules, "open shell" signifies that there are unpaired electrons. In molecular orbital theory, this leads to molecular orbitals that are singly occupied. In computational chemistry implementations of molecular orbital theory, open-shell molecules have to be handled by either the restricted open-shell Hartree–Fock method or the unrestricted Hartree–Fock method. Conversely a closed-shell configuration corresponds to a state where all molecular orbitals are either doubly occupied or empty (a singlet state). Open shell molecules are more difficult to study computationally.

Noble gas configuration

Noble gas configuration is the electron configuration of noble gases. The basis of all chemical reactions is the tendency of chemical elements to acquire stability. Main-group atoms generally obey the octet rule, while transition metals generally obey the 18-electron rule. The noble gases (He, Ne, Ar, Kr, Xe, Rn) are less reactive than other elements because they already have a noble gas configuration. Oganesson is predicted to be more reactive due to relativistic effects for heavy atoms.

Period Element Configuration
1 He 1s2





2 Ne 1s2 2s2 2p6




3 Ar 1s2 2s2 2p6 3s2 3p6



4 Kr 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6


5 Xe 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6

6 Rn 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6
7 Og 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6

Every system has the tendency to acquire the state of stability or a state of minimum energy, and so chemical elements take part in chemical reactions to acquire a stable electronic configuration similar to that of its nearest noble gas. An example of this tendency is two hydrogen (H) atoms reacting with one oxygen (O) atom to form water (H2O). Neutral atomic hydrogen has 1 electron in the valence shell, and on formation of water it acquires a share of a second electron coming from oxygen, so that its configuration is similar to that of its nearest noble gas helium with 2 electrons in the valence shell. Similarly, neutral atomic oxygen has 6 electrons in the valence shell, and acquires a share of two electrons from the two hydrogen atoms, so that its configuration is similar to that of its nearest noble gas neon with 8 electrons in the valence shell.

Electron configuration in molecules

In molecules, the situation becomes more complex, as each molecule has a different orbital structure. The molecular orbitals are labelled according to their symmetry, rather than the atomic orbital labels used for atoms and monatomic ions: hence, the electron configuration of the dioxygen molecule, O2, is written 1σg2 1σu2 2σg2 2σu2 3σg2 1πu4 1πg2, or equivalently 1σg2 1σu2 2σg2 2σu2 1πu4 3σg2 1πg2. The term 1πg2 represents the two electrons in the two degenerate π*-orbitals (antibonding). From Hund's rules, these electrons have parallel spins in the ground state, and so dioxygen has a net magnetic moment (it is paramagnetic). The explanation of the paramagnetism of dioxygen was a major success for molecular orbital theory.

The electronic configuration of polyatomic molecules can change without absorption or emission of a photon through vibronic couplings.

Electron configuration in solids

In a solid, the electron states become very numerous. They cease to be discrete, and effectively blend into continuous ranges of possible states (an electron band). The notion of electron configuration ceases to be relevant, and yields to band theory.

Applications

The most widespread application of electron configurations is in the rationalization of chemical properties, in both inorganic and organic chemistry. In effect, electron configurations, along with some simplified form of molecular orbital theory, have become the modern equivalent of the valence concept, describing the number and type of chemical bonds that an atom can be expected to form.

This approach is taken further in computational chemistry, which typically attempts to make quantitative estimates of chemical properties. For many years, most such calculations relied upon the "linear combination of atomic orbitals" (LCAO) approximation, using an ever-larger and more complex basis set of atomic orbitals as the starting point. The last step in such a calculation is the assignment of electrons among the molecular orbitals according to the Aufbau principle. Not all methods in calculational chemistry rely on electron configuration: density functional theory (DFT) is an important example of a method that discards the model.

For atoms or molecules with more than one electron, the motion of electrons are correlated and such a picture is no longer exact. A very large number of electronic configurations are needed to exactly describe any multi-electron system, and no energy can be associated with one single configuration. However, the electronic wave function is usually dominated by a very small number of configurations and therefore the notion of electronic configuration remains essential for multi-electron systems.

A fundamental application of electron configurations is in the interpretation of atomic spectra. In this case, it is necessary to supplement the electron configuration with one or more term symbols, which describe the different energy levels available to an atom. Term symbols can be calculated for any electron configuration, not just the ground-state configuration listed in tables, although not all the energy levels are observed in practice. It is through the analysis of atomic spectra that the ground-state electron configurations of the elements were experimentally determined.

Atmospheric optics

From Wikipedia, the free encyclopedia
 
A colorful sky is often due to indirect sunlight being scattered off oxygen molecules and particulates, like smog, soot, and cloud droplets, as shown in this photo of a sunset during the October 2007 California wildfires.

Atmospheric optics is "the study of the optical characteristics of the atmosphere or products of atmospheric processes .... [including] temporal and spatial resolutions beyond those discernible with the naked eye". Meteorological optics is "that part of atmospheric optics concerned with the study of patterns observable with the naked eye". Nevertheless, the two terms are sometimes used interchangeably.

Meteorological optical phenomena, as described in this article, are concerned with how the optical properties of Earth's atmosphere cause a wide range of optical phenomena and visual perception phenomena.

Examples of meteorological phenomena include:

  • The blue color of the sky. This is from Rayleigh scattering, which redirects higher frequency/shorter wavelength (blue) sunlight back into the field of view of the observer.
  • The reddish color of the Sun when it is observed through a thick atmosphere, as during a sunrise or sunset. This is because red light is scattered less than blue light. The red light reaches the observer's eye, whereas the blue light is scattered out of the line of sight.
  • Other colours in the sky, such as glowing skies at dusk and dawn. These are from additional particulate matter in the sky that scatter different colors at different angles.
  • Halos, afterglows, coronas, and sun dogs. These are from scattering, or refraction, by ice crystals and from other particles in the atmosphere. They depend on different particle sizes and geometries.
  • Mirages. These are optical phenomena in which light rays are bent due to thermal variations in the refractive index of air, producing displaced or heavily distorted images of distant objects. Other optical phenomena associated with this include the Novaya Zemlya effect, where the Sun appears to rise earlier or set later than predicted with a distorted shape. A spectacular form of refraction, called the Fata Morgana, occurs with a temperature inversion, in which objects on the horizon or even beyond the horizon (e.g. islands, cliffs, ships, and icebergs) appear elongated and elevated, like "fairy tale castles".
  • Rainbows. These result from a combination of internal reflection and dispersive refraction of light in raindrops. Because rainbows are seen on the opposite side of the sky from the sun, rainbows are more visible the closer the sun is to the horizon. For example, if the sun is overhead, any possible rainbow appears near an observer's feet, making it hard to see, and involves very few raindrops between the observer's eyes and the ground, making any rainbow very sparse.

Other phenomena that are remarkable because they are forms of visual illusions include:

History

A book on meteorological optics was published in the sixteenth century, but there have been numerous books on the subject since about 1950. The topic was popularised by the wide circulation of a book by Marcel Minnaert, Light and Color in the Open Air, in 1954. 

Sun and Moon size

Comparison between the relative sizes of the Moon and a cloud at different points in the sky
 

In the Book of Optics (1011–22 AD), Ibn al-Haytham argued that vision occurs in the brain, and that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. Arguing against Ptolemy's refraction theory for why people perceive the Sun and Moon larger at the horizon than when they are higher in the sky, he redefined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. With the Moon, however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century. For over 100 years, research on the Moon illusion has been conducted by vision scientists who invariably have been psychologists specializing in human perception. After reviewing the many different explanations in their 2002 book The Mystery of the Moon Illusion, Ross and Plug conclude "No single theory has emerged victorious".

Sky coloration

When seen from a high altitude, as here from an airplane, the sky's color varies from pale to dark at elevations toward the zenith.

Light from the sky is a result of the Rayleigh scattering of sunlight, which results in a blue color perceived by the human eye. On a sunny day, Rayleigh scattering gives the sky a blue gradient, where it is darkest around the zenith and bright near the horizon. Light rays incoming from overhead encounters 138 of the air mass than those coming along a horizontal path encounter. Hence, fewer particles scatter the zenithal sunbeam, and thus the light remains a darker blue. The blueness is at the horizon because the blue light coming from great distances is also preferentially scattered. This results in a red shift of the distant light sources that is compensated by the blue hue of the scattered light in the line of sight. In other words, the red light scatters also; if it does so at a point a great distance from the observer it has a much higher chance of reaching the observer than blue light. At distances nearing infinity, the scattered light is therefore white. Distant clouds or snowy mountaintops will seem yellow for that reason; that effect is not obvious on clear days, but very pronounced when clouds are covering the line of sight reducing the blue hue from scattered sunlight.

The scattering due to molecule sized particles (as in air) is greater in the forward and backward directions than it is in the lateral direction. Individual water droplets exposed to white light will create a set of colored rings. If a cloud is thick enough, scattering from multiple water droplets will wash out the set of colored rings and create a washed out white color. Dust from the Sahara moves around the southern periphery of the subtropical ridge moves into the southeastern United States during the summer, which changes the sky from a blue to a white appearance and leads to an increase in red sunsets. Its presence negatively impacts air quality during the summer since it adds to the count of airborne particulates.

Purple sky on the La Silla Observatory.

The sky can turn a multitude of colors such as red, orange, pink and yellow (especially near sunset or sunrise) and black at night. Scattering effects also partially polarize light from the sky, most pronounced at an angle 90° from the sun.

Sky luminance distribution models have been recommended by the International Commission on Illumination (CIE) for the design of daylighting schemes. Recent developments relate to “all sky models” for modelling sky luminance under weather conditions ranging from clear sky to overcast.

Cloud coloration

An occurrence of altocumulus and cirrocumulus cloud iridescence
 
Sunset reflecting shades of pink onto grey stratocumulus clouds.

The color of a cloud, as seen from the Earth, tells much about what is going on inside the cloud. Dense deep tropospheric clouds exhibit a high reflectance (70% to 95%) throughout the visible spectrum. Tiny particles of water are densely packed and sunlight cannot penetrate far into the cloud before it is reflected out, giving a cloud its characteristic white color, especially when viewed from the top. Cloud droplets tend to scatter light efficiently, so that the intensity of the solar radiation decreases with depth into the gases. As a result, the cloud base can vary from a very light to very dark grey depending on the cloud's thickness and how much light is being reflected or transmitted back to the observer. Thin clouds may look white or appear to have acquired the color of their environment or background. High tropospheric and non-tropospheric clouds appear mostly white if composed entirely of ice crystals and/or supercooled water droplets.

As a tropospheric cloud matures, the dense water droplets may combine to produce larger droplets, which may combine to form droplets large enough to fall as rain. By this process of accumulation, the space between droplets becomes increasingly larger, permitting light to penetrate farther into the cloud. If the cloud is sufficiently large and the droplets within are spaced far enough apart, it may be that a percentage of the light which enters the cloud is not reflected back out before it is absorbed. A simple example of this is being able to see farther in heavy rain than in heavy fog. This process of reflection/absorption is what causes the range of cloud color from white to black.

Other colors occur naturally in clouds. Bluish-grey is the result of light scattering within the cloud. In the visible spectrum, blue and green are at the short end of light's visible wavelengths, while red and yellow are at the long end. The short rays are more easily scattered by water droplets, and the long rays are more likely to be absorbed. The bluish color is evidence that such scattering is being produced by rain-sized droplets in the cloud. A cumulonimbus cloud emitting green is a sign that it is a severe thunderstorm, capable of heavy rain, hail, strong winds and possible tornadoes. The exact cause of green thunderstorms is still unknown, but it could be due to the combination of reddened sunlight passing through very optically thick clouds. Yellowish clouds may occur in the late spring through early fall months during forest fire season. The yellow color is due to the presence of pollutants in the smoke. Yellowish clouds caused by the presence of nitrogen dioxide are sometimes seen in urban areas with high air pollution levels.

Red, orange and pink clouds occur almost entirely at sunrise and sunset and are the result of the scattering of sunlight by the atmosphere. When the angle between the sun and the horizon is less than 10 percent, as it is just after sunrise or just prior to sunset, sunlight becomes too red due to refraction for any colors other than those with a reddish hue to be seen. The clouds do not become that color; they are reflecting long and unscattered rays of sunlight, which are predominant at those hours. The effect is much like if one were to shine a red spotlight on a white sheet. In combination with large, mature thunderheads this can produce blood-red clouds. Clouds look darker in the near-infrared because water absorbs solar radiation at those wavelengths.

Halos

A man in front of a complex halo display at the Amundsen-Scott South Pole Station.

A halo (ἅλως; also known as a nimbus, icebow or gloriole) is an optical phenomenon produced by the interaction of light from the sun or moon with ice crystals in the atmosphere, resulting in colored or white arcs, rings or spots in the sky. Many halos are positioned near the sun or moon, but others are elsewhere and even in the opposite part of the sky. They can also form around artificial lights in very cold weather when ice crystals called diamond dust are floating in the nearby air.

There are many types of ice halos. They are produced by the ice crystals in cirrus or cirrostratus clouds high in the upper troposphere, at an altitude of 5 kilometres (3.1 mi) to 10 kilometres (6.2 mi), or, during very cold weather, by ice crystals called diamond dust drifting in the air at low levels. The particular shape and orientation of the crystals are responsible for the types of halo observed. Light is reflected and refracted by the ice crystals and may split into colors because of dispersion. The crystals behave like prisms and mirrors, refracting and reflecting sunlight between their faces, sending shafts of light in particular directions. For circular halos, the preferred angular distance are 22 and 46 degrees from the ice crystals which create them. Atmospheric phenomena such as halos have been used as part of weather lore as an empirical means of weather forecasting, with their presence indicating an approach of a warm front and its associated rain.

Sun dogs

Very bright sundogs in Fargo, North Dakota. Note the halo arcs passing through each sun dog.
 

Sun dogs are a common type of halo, with the appearance of two subtly-colored bright spots to the left and right of the sun, at a distance of about 22° and at the same elevation above the horizon. They are commonly caused by plate-shaped hexagonal ice crystals. These crystals tend to become horizontally aligned as they sink through the air, causing them to refract the sunlight to the left and right, resulting in the two sun dogs.

As the sun rises higher, the rays passing through the crystals are increasingly skewed from the horizontal plane. Their angle of deviation increases and the sundogs move further from the sun. However, they always stay at the same elevation as the sun. Sun dogs are red-colored at the side nearest the sun. Farther out the colors grade to blue or violet. However, the colors overlap considerably and so are muted, rarely pure or saturated. The colors of the sun dog finally merge into the white of the parhelic circle (if the latter is visible).

It is theoretically possible to predict the forms of sun dogs as would be seen on other planets and moons. Mars might have sundogs formed by both water-ice and CO2-ice. On the giant gas planets — Jupiter, Saturn, Uranus and Neptune — other crystals form the clouds of ammonia, methane, and other substances that can produce halos with four or more sundogs.

Glory

Solar glory at the steam from a hot spring
 

A common optical phenomenon involving water droplets is the glory. A glory is an optical phenomenon, appearing much like an iconic Saint's halo about the head of the observer, produced by light backscattered (a combination of diffraction, reflection and refraction) towards its source by a cloud of uniformly sized water droplets. A glory has multiple colored rings, with red colors on the outermost ring and blue/violet colors on the innermost ring.

The angular distance is much smaller than a rainbow, ranging between 5° and 20°, depending on the size of the droplets. The glory can only be seen when the observer is directly between the sun and cloud of refracting water droplets. Hence, it is commonly observed while airborne, with the glory surrounding the airplane's shadow on clouds (this is often called The Glory of the Pilot). Glories can also be seen from mountains and tall buildings, when there are clouds or fog below the level of the observer, or on days with ground fog. The glory is related to the optical phenomenon anthelion.

Rainbow

Double rainbow and supernumerary rainbows on the inside of the primary arc. The shadow of the photographer's head marks the centre of the rainbow circle (antisolar point).

A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when sunlight shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicolored arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun, but originate no further than 42 degrees above the horizon for observers on the ground. To see them at higher angles, an observer would need to be in an airplane or near a mountaintop since the rainbow would otherwise be below the horizon. The bigger the droplets which formed the rainbow, the brighter it will be. Rainbows are most common near afternoon thunderstorms during the summer.

A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Within the "primary rainbow" (the lowest, and also normally the brightest rainbow) the arc of a rainbow shows red on the outer (or upper) part of the arc, and violet on the inner section. This rainbow is caused by light being reflected once in droplets of water. In a double rainbow, a second arc may be seen above and outside the primary arc, and has the order of its colors reversed (red faces inward toward the other rainbow, in both rainbows). This second rainbow is caused by light reflecting twice inside water droplets. The region between a double rainbow is dark. The reason for this dark band is that, while light below the primary rainbow comes from droplet reflection, and light above the upper (secondary) rainbow also comes from droplet reflection, there is no mechanism for the region between a double rainbow to show any light reflected from water drops, at all.

A rainbow spans a continuous spectrum of colors; the distinct bands (including the number of bands) are an artifact of human color vision, and no banding of any type is seen in a black-and-white photograph of a rainbow (only a smooth gradation of intensity to a maxima, then fading to a minima at the other side of the arc). For colors seen by a normal human eye, the most commonly cited and remembered sequence, in English, is Isaac Newton's sevenfold red, orange, yellow, green, blue, indigo and violet (popularly memorized by mnemonics like Roy G. Biv).

Mirage

Various kinds of mirages in one location taken over the course of six minutes. The uppermost inset frame shows an inferior mirage of the Farallon Islands. The second inset frame shows a green flash on the left-hand side. The two lower frames and the main frame all show superior mirages of the Farallon Islands. In these three frames, the superior mirage evolves from a 3-image mirage to a 5-image mirage, and back to a 2-image mirage. Such a display is consistent with a Fata Morgana.

A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at". This is the same root as for "mirror" and "to admire". Also, it has its roots in the Arabic mirage.

In contrast to a hallucination, a mirage is a real optical phenomenon which can be captured on camera, since light rays actually are refracted to form the false image at the observer's location. What the image appears to represent, however, is determined by the interpretive faculties of the human mind. For example, inferior images on land are very easily mistaken for the reflections from a small body of water.

Mirages can be categorized as "inferior" (meaning lower), "superior" (meaning higher) and "Fata Morgana", one kind of superior mirage consisting of a series of unusually elaborate, vertically stacked images, which form one rapidly changing mirage.

Green flashes and green rays are optical phenomena that occur shortly after sunset or before sunrise, when a green spot is visible, usually for no more than a second or two, above the sun, or a green ray shoots up from the sunset point. Green flashes are actually a group of phenomena stemming from different causes, and some are more common than others. Green flashes can be observed from any altitude (even from an aircraft). They are usually seen at an unobstructed horizon, such as over the ocean, but are possible over cloud tops and mountain tops as well.

A green flash from the moon and bright planets at the horizon, including Venus and Jupiter, can also be observed.

Fata Morgana

A Fata Morgana of a boat
 

This optical phenomenon occurs because rays of light are strongly bent when they pass through air layers of different temperatures in a steep thermal inversion where an atmospheric duct has formed. A thermal inversion is an atmospheric condition where warmer air exists in a well-defined layer above a layer of significantly cooler air. This temperature inversion is the opposite of what is normally the case; air is usually warmer close to the surface, and cooler higher up. In calm weather, a layer of significantly warmer air can rest over colder dense air, forming an atmospheric duct which acts like a refracting lens, producing a series of both inverted and erect images.

A Fata Morgana is an unusual and very complex form of mirage, a form of superior mirage, which, like many other kinds of superior mirages, is seen in a narrow band right above the horizon. It is an Italian phrase derived from the vulgar Latin for "fairy" and the Arthurian sorcerer Morgan le Fay, from a belief that the mirage, often seen in the Strait of Messina, were fairy castles in the air, or false land designed to lure sailors to their death created by her witchcraft. Although the term Fata Morgana is sometimes incorrectly applied to other, more common kinds of mirages, the true Fata Morgana is not the same as an ordinary superior mirage, and is certainly not the same as an inferior mirage.

Fata Morgana mirages tremendously distort the object or objects which they are based on, such that the object often appears to be very unusual, and may even be transformed in such a way that it is completely unrecognizable. A Fata Morgana can be seen on land or at sea, in polar regions or in deserts. This kind of mirage can involve almost any kind of distant object, including such things as boats, islands, and coastline.

A Fata Morgana is not only complex, but also rapidly changing. The mirage comprises several inverted (upside down) and erect (right side up) images that are stacked on top of one another. Fata Morgana mirages also show alternating compressed and stretched zones.

Novaya Zemlya effect

The Novaya Zemlya effect is a polar mirage caused by high refraction of sunlight between atmospheric thermoclines. The Novaya Zemlya effect will give the impression that the sun is rising earlier or setting later than it actually should (astronomically speaking). Depending on the meteorological situation the effect will present the Sun as a line or a square (which is sometimes referred to as the "rectangular sun"), made up of flattened hourglass shapes. The mirage requires rays of sunlight to have an inversion layer for hundreds of kilometres, and depends on the inversion layer's temperature gradient. The sunlight must bend to the Earth's curvature at least 400 kilometres (250 mi) to allow an elevation rise of 5 degrees for sight of the sun disk.

The first person to record the phenomenon was Gerrit de Veer, a member of Willem Barentsz' ill-fated third expedition into the polar region. Novaya Zemlya, the archipelago where de Veer first observed the phenomenon, lends its name to the effect.

Crepuscular rays

Crepuscular rays, taken in Taipei, Taiwan.
 

Crepuscular rays are near-parallel rays of sunlight moving through the Earth's atmosphere, but appear to diverge because of linear perspective. They often occur when objects such as mountain peaks or clouds partially shadow the Sun's rays like a cloud cover. Various airborne compounds scatter the sunlight and make these rays visible, due to diffraction, reflection, and scattering.

Crepuscular rays can also occasionally be viewed underwater, particularly in arctic areas, appearing from ice shelves or cracks in the ice. Also they are also viewed in days when the sun hits the clouds in a perfect angle shining upon the area.

There are three primary forms of crepuscular rays:

  • Rays of light penetrating holes in low clouds (also called "Jacob's Ladder").
  • Beams of light diverging from behind a cloud.
  • Pale, pinkish or reddish rays that radiate from below the horizon. These are often mistaken for light pillars.

They are commonly seen near sunrise and sunset, when tall clouds such as cumulonimbus and mountains can be most effective at creating these rays.

Anticrepuscular rays

Anticrepuscular rays while parallel in reality are sometimes visible in the sky in the direction opposite the sun. They appear to converge again at the distant horizon.

Atmospheric refraction

Diagram showing displacement of the Sun's image at sunrise and sunset
 

Atmospheric refraction influences the apparent position of astronomical and terrestrial objects, usually causing them to appear higher than they actually are. For this reason navigators, astronomers, and surveyors observe positions when these effects are minimal. Sailors will only shoot a star when 20° or more above the horizon, astronomers try to schedule observations when an object is highest in the sky, and surveyors try to observe in the afternoon when refraction is minimum.

Atmospheric diffraction

Atmospheric diffraction is a visual effect caused when sunlight is bent by particles suspended in the air.

Natural science

From Wikipedia, the free encyclopedia https://en.wikipedia.org/w...