# Atom

{{#invoke:Hatnote|hatnote}} {{ safesubst:#invoke:Unsubst||$N=Use dmy dates |date=__DATE__ |$B= }} Template:Pp-semi Template:Pp-move-indef Template:Infobox atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons (except in the case of hydrogen-1, which is the only stable nuclide with no neutrons). The electrons of an atom are bound to the nucleus by the electromagnetic force. Likewise, a group of atoms can remain bound to each other by chemical bonds based on the same force, forming a molecule. An atom containing an equal number of protons and electrons is electrically neutral, otherwise it is positively or negatively charged and is known as an ion. An atom is classified according to the number of protons and neutrons in its nucleus: the number of protons determines the chemical element, and the number of neutrons determines the isotope of the element.[1]

Chemical atoms, which in science now carry the simple name of "atom," are minuscule objects with diameters of a few tenths of a nanometer and tiny masses proportional to the volume implied by these dimensions. Atoms can only be observed individually using special instruments such as the scanning tunneling microscope. Over 99.94% of an atom's mass is concentrated in the nucleus,[note 1] with protons and neutrons having roughly equal mass. Each element has at least one isotope with an unstable nucleus that can undergo radioactive decay. This can result in a transmutation that changes the number of protons or neutrons in a nucleus.[2] Electrons that are bound to atoms possess a set of stable energy levels, or orbitals, and can undergo transitions between them by absorbing or emitting photons that match the energy differences between the levels. The electrons determine the chemical properties of an element, and strongly influence an atom's magnetic properties. The principles of quantum mechanics have been successfully used to model the observed properties of the atom.

## Etymology

The name atom comes from the Greek ἄτομος (atomos, "indivisible") from ἀ- (a-, "not") and τέμνω (temnō, "I cut"),[3] which means uncuttable, or indivisible, something that cannot be divided further.[4] The concept of an atom as an indivisible component of matter was first proposed by early Indian and Greek philosophers. In the 18th and 19th centuries, chemists provided a physical basis for this idea by showing that certain substances could not be further broken down by chemical methods, and they applied the ancient philosophical name of atom to the chemical entity. During the late 19th and early 20th centuries, physicists discovered subatomic components and structure inside the atom, thereby demonstrating that the chemical "atom" was divisible and that the name might not be appropriate.[5]Template:Sfn However, it was retained. This has led to some debate about whether the ancient philosophers, who intended to refer to fundamental individual objects with their concept of "atoms," were referring to modern chemical atoms, or something more like indivisible subatomic particles such as leptons or quarks, or even some more fundamental particle that has yet to be discovered.[6]

## History of atomic theory

{{#invoke:main|main}}

### Atomism

{{#invoke:main|main}} The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny quantities has been around for millennia, but these ideas were founded in abstract, philosophical reasoning rather than experimentation and empirical observation. The nature of atoms in philosophy varied considerably over time and between cultures and schools, and often had spiritual elements. Nevertheless, the basic idea of the atom was adopted by scientists thousands of years later because it elegantly explained new discoveries in the field of chemistry.Template:Sfn The ancient name of "atom" from atomism had already been nearly universally used to describe chemical atoms by that time, and it was therefore retained as a term, long after chemical atoms were found to be divisible, and even after smaller, truly indivisible particles were identified.

References to the concept of atoms date back to ancient Greece and India. In India, the Ājīvika, Jain, and Cārvāka schools of atomism may date back to the 6th century BCE.Template:Sfn The Nyaya and Vaisheshika schools later developed theories on how atoms combined into more complex objects.Template:Sfn In the West, the references to atoms emerged in the 5th century BCE with Leucippus, whose student, Democritus, systematized his views. In approximately 450 BCE, Democritus coined the term átomos (Greek: ἄτομος{{#invoke:Category handler|main}}), which means "uncuttable" or "the smallest indivisible particle of matter". Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained the name coined by Democritus.Template:Sfn

Corpuscularianism is the postulate, expounded in the 13th-century by the alchemist Pseudo-Geber (Geber),Template:Sfn sometimes identified with Paul of Taranto, that all physical bodies possess an inner and outer layer of minute particles or corpuscles.Template:Sfn Corpuscularianism is similar to the theory of atomism, except that where atoms were supposed to be indivisible, corpuscles could in principle be divided. In this manner, for example, it was theorized that mercury could penetrate into metals and modify their inner structure.[7] Corpuscularianism stayed a dominant theory over the next several hundred years.

In 1661, natural philosopher Robert Boyle published The Sceptical Chymist in which he argued that matter was composed of various combinations of different "corpuscules" or atoms, rather than the classical elements of air, earth, fire and water.Template:Sfn During the 1670s corpuscularianism was used by Isaac Newton in his development of the corpuscular theory of light.Template:Sfn[8]

### Origin of scientific theory

Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808), one of the earliest scientific works on atomic theory

Further progress in the understanding of atoms did not occur until the science of chemistry began to develop. In 1789, French nobleman and scientific researcher Antoine Lavoisier discovered the law of conservation of mass and defined an element as a basic substance that could not be further broken down by the methods of chemistry.[9]

In 1805, English instructor and natural philosopher John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers (the law of multiple proportions) and why certain gases dissolved better in water than others. He proposed that each element consists of atoms of a single, unique type, and that these atoms can join together to form chemical compounds.Template:SfnTemplate:Sfn Dalton is considered the originator of modern atomic theory.Template:Sfn

Dalton's atomic hypothesis did not specify the size of atoms. Common sense indicated they must be very small, but nobody knew how small. Therefore it was a major landmark when in 1865 Johann Josef Loschmidt measured the size of the molecules that make up air.

An additional line of reasoning in support of particle theory (and by extension atomic theory) began in 1827 when botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically—a phenomenon that became known as "Brownian motion". J. Desaulx suggested in 1877 that the phenomenon was caused by the thermal motion of water molecules, and in 1905 Albert Einstein produced the first mathematical analysis of the motion.[10]Template:Sfn[11] French physicist Jean Perrin used Einstein's work to experimentally determine the mass and dimensions of atoms, thereby conclusively verifying Dalton's atomic theory.[12]

Mendeleev's first periodic table (1869)

In 1869, building upon earlier discoveries by such scientists as Lavoisier, Dmitri Mendeleev published the first functional periodic table.[13] The table itself is a visual representation of the periodic law, which states that certain chemical properties of elements repeat periodically when arranged by atomic number.Template:Sfn

### Subcomponents and quantum theory

A generic atomic planetary model, or the Rutherford model

The physicist J. J. Thomson, through his work on cathode rays in 1897, discovered the electron, and concluded that they were a component of every atom. Thus he overturned the belief that atoms are the indivisible, ultimate particles of matter.[14] Thomson postulated that the low mass, negatively charged electrons were distributed throughout the atom, possibly rotating in rings, with their charge balanced by the presence of a uniform sea of positive charge. This later became known as the plum pudding model.

In 1909, Hans Geiger and Ernest Marsden, under the direction of physicist Ernest Rutherford, bombarded a sheet of gold foil with alpha rays—by then known to be positively charged helium atoms—and discovered that a small percentage of these particles were deflected through much larger angles than was predicted using Thomson's proposal. Rutherford interpreted the gold foil experiment as suggesting that the positive charge of a heavy gold atom and most of its mass was concentrated in a nucleus at the center of the atom—the Rutherford model.[15]

While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the periodic table.[16] The term isotope was coined by Margaret Todd as a suitable name for different atoms that belong to the same element. J.J. Thomson created a technique for separating atom types through his work on ionized gases, which subsequently led to the discovery of stable isotopes.[17]

A Bohr model of the hydrogen atom, showing an electron jumping between fixed orbits and emitting a photon of energy with a specific frequency

Meanwhile, in 1913, physicist Niels Bohr suggested that the electrons were confined into clearly defined, quantized orbits, and could jump between these, but could not freely spiral inward or outward in intermediate states.[18] An electron must absorb or emit specific amounts of energy to transition between these fixed orbits. When the light from a heated material was passed through a prism, it produced a multi-colored spectrum. The appearance of fixed lines in this spectrum was successfully explained by these orbital transitions.[19]

Later in the same year Henry Moseley provided additional experimental evidence in favor of Niels Bohr's theory. These results refined Ernest Rutherford's and Antonius Van den Broek's model, which proposed that the atom contains in its nucleus a number of positive nuclear charges that is equal to its (atomic) number in the periodic table. Until these experiments, atomic number was not known to be a physical and experimental quantity. That it is equal to the atomic nuclear charge remains the accepted atomic model today.Template:Sfn

Chemical bonds between atoms were now explained, by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons.[20] As the chemical properties of the elements were known to largely repeat themselves according to the periodic law,Template:Sfn in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells about the nucleus.[21]

The Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of the atom. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split based on the direction of an atom's angular momentum, or spin. As this direction is random, the beam could be expected to spread into a line. Instead, the beam was split into two parts, depending on whether the atomic spin was oriented up or down.[22]

In 1924, Louis de Broglie proposed that all particles behave to an extent like waves. In 1926, Erwin Schrödinger used this idea to develop a mathematical model of the atom that described the electrons as three-dimensional waveforms rather than point particles. A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926. In this concept, for a given accuracy in measuring a position one could only obtain a range of probable values for momentum, and vice versa. This model was able to explain observations of atomic behavior that previous models could not, such as certain structural and spectral patterns of atoms larger than hydrogen. Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.[23][24]

Schematic diagram of a simple mass spectrometer

The development of the mass spectrometer allowed the exact mass of atoms to be measured. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis William Aston used this instrument to show that isotopes had different masses. The atomic mass of these isotopes varied by integer amounts, called the whole number rule.[25] The explanation for these different isotopes awaited the discovery of the neutron, a neutral-charged particle with a mass similar to the proton, by the physicist James Chadwick in 1932. Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.[26]

### Fission, high-energy physics and condensed matter

In 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product.[27] A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental nuclear fission.[28][29] In 1944, Hahn received the Nobel prize in chemistry. Despite Hahn's efforts, the contributions of Meitner and Frisch were not recognized.[30]

In the 1950s, the development of improved particle accelerators and particle detectors allowed scientists to study the impacts of atoms moving at high energies.[31] Neutrons and protons were found to be hadrons, or composites of smaller particles called quarks. The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.[32]

### Subatomic particles

{{#invoke:main|main}} Though the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron; all three are fermions. However, the hydrogen-1 atom has no neutrons and the hydron ion has no electrons.

The electron is by far the least massive of these particles at Template:Val, with a negative electrical charge and a size that is too small to be measured using available techniques.Template:Sfn It is the lightest particle with a positive rest mass measured. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom have more or fewer electrons than its atomic number, then is become respectively negatively or positively charged as a whole; a charged atom is called ion. Electrons are known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.

Protons have a positive charge and a mass 1,836 times that of the electron, at Template:Val. The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920 he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton.

Neutrons have no electrical charge and have a free mass of 1,839 times the mass of the electron,Template:Sfn or Template:Val, the heaviest of the three constituent particles, but it can be reduced by the nuclear binding energy. Neutrons and protons (collectively known as nucleons) have comparable dimensions—on the order of Template:Val—although the 'surface' of these particles is not sharply defined.Template:Sfn The neutron was discovered in 1932 by the English physicist James Chadwick.

In the Standard Model of physics, electrons are truly elementary particles with no internal structure. However, both protons and neutrons are composite particles composed of elementary particles called quarks. There are two types of quarks in atoms, each having a fractional electric charge. Protons are composed of two up quarks (each with charge +Template:Frac) and one down quark (with a charge of −Template:Frac). Neutrons consist of one up quark and two down quarks. This distinction accounts for the difference in mass and charge between the two particles.[33][34]

The quarks are held together by the strong interaction (or strong force), which is mediated by gluons. The protons and neutrons, in turn, are held to each other in the nucleus by the nuclear force, which is a residuum of the strong force that has somewhat different range-properties (see the article on the nuclear force for more). The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.[33][34]

### Nucleus

{{#invoke:main|main}}

The binding energy needed for a nucleon to escape the nucleus, for various isotopes

All the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 Template:Radic fm, where A is the total number of nucleons.Template:Sfn This is much smaller than the radius of the atom, which is on the order of 105 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more powerful than the electrostatic force that causes positively charged protons to repel each other.Template:Sfn

Atoms of the same element have the same number of protons, called the atomic number. Within a single element, the number of neutrons may vary, determining the isotope of that element. The total number of protons and neutrons determine the nuclide. The number of neutrons relative to the protons determines the stability of the nucleus, with certain isotopes undergoing radioactive decay.[35]

The proton, the electron, and the neutron are classified as fermions. Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time. Thus, every proton in the nucleus must occupy a quantum state different from all other protons, and the same applies to all neutrons of the nucleus and to all electrons of the electron cloud. However, a proton and a neutron are allowed to occupy the same quantum state.[36]

For atoms with low atomic numbers, a nucleus that has more neutrons than protons tends to drop to a lower energy state through radioactive decay so that the neutron-proton ratio is closer to one. However, as the atomic number increases, a higher proportion of neutrons is required to offset the mutual repulsion of the protons. Thus, there are no stable nuclei with equal proton and neutron numbers above atomic number Z = 20 (calcium) and as Z increases, the neutron-proton ratio of stable isotopes increases.[36] The stable isotope with the highest proton-neutron ration is lead-208 (about 1.5).

Illustration of a nuclear fusion process that forms a deuterium nucleus, consisting of a proton and a neutron, from two protons. A positron (e+)—an antimatter electron—is emitted along with an electron neutrino.

The number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force. Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei. For example, at the core of the Sun protons require energies of 3–10 keV to overcome their mutual repulsion—the coulomb barrier—and fuse together into a single nucleus.[37] Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei—usually through radioactive decay. The nucleus can also be modified through bombardment by high energy subatomic particles or photons. If this modifies the number of protons in a nucleus, the atom changes to a different chemical element.[38][39]

If the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass–energy equivalence formula, E = mc2, where m is the mass loss and c is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.Template:Sfn

The fusion of two nuclei that create larger nuclei with lower atomic numbers than iron and nickel—a total nucleon number of about 60—is usually an exothermic process that releases more energy than is required to bring them together.[40] It is this energy-releasing process that makes nuclear fusion in stars a self-sustaining reaction. For heavier nuclei, the binding energy per nucleon in the nucleus begins to decrease. That means fusion processes producing nuclei that have atomic numbers higher than about 26, and atomic masses higher than about 60, is an endothermic process. These more massive nuclei can not undergo an energy-producing fusion reaction that can sustain the hydrostatic equilibrium of a star.[36]

### Electron cloud

{{#invoke:main|main}}

A potential well, showing, according to classical mechanics, the minimum energy V(x) needed to reach each position x. Classically, a particle with energy E is constrained to a range of positions between x1 and x2.

The electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.

Electrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured.[41] Only a discrete (or quantized) set of these orbitals exist around the nucleus, as other possible wave patterns rapidly decay into a more stable form.[42] Orbitals can have one or more ring or node structures, and they differ from each other in size, shape and orientation.[43]

Wave functions of the first five atomic orbitals. The three 2p orbitals each display a single angular node that has an orientation and a minimum at the center.

Each atomic orbital corresponds to a particular energy level of the electron. The electron can change its state to a higher energy level by absorbing a photon with sufficient energy to boost it into the new quantum state. Likewise, through spontaneous emission, an electron in a higher energy state can drop to a lower energy state while radiating the excess energy as a photon. These characteristic energy values, defined by the differences in the energies of the quantum states, are responsible for atomic spectral lines.[42]

The amount of energy needed to remove or add an electron—the electron binding energy—is far less than the binding energy of nucleons. For example, it requires only 13.6 eV to strip a ground-state electron from a hydrogen atom,[44] compared to 2.23 million eV for splitting a deuterium nucleus.[45] Atoms are electrically neutral if they have an equal number of protons and electrons. Atoms that have either a deficit or a surplus of electrons are called ions. Electrons that are farthest from the nucleus may be transferred to other nearby atoms or shared between atoms. By this mechanism, atoms are able to bond into molecules and other types of chemical compounds like ionic and covalent network crystals.Template:Sfn

## Properties

### Nuclear properties

{{#invoke:main|main}}

By definition, any two atoms with an identical number of protons in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of neutrons are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form,[46] also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element ununoctium.[47] All known isotopes of elements with atomic numbers greater than 82 are radioactive.Template:Sfn[48]

About 339 nuclides occur naturally on Earth,[49] of which 254 (about 75%) have not been observed to decay, and are referred to as "stable isotopes". However, only 90 of these nuclides are stable to all decay, even in theory. Another 164 (bringing the total to 254) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as "stable". An additional 34 radioactive nuclides have half-lives longer than 80 million years, and are long-lived enough to be present from the birth of the solar system. This collection of 288 nuclides are known as primordial nuclides. Finally, an additional 51 short-lived nuclides are known to occur naturally, as daughter products of primordial nuclide decay (such as radium from uranium), or else as products of natural energetic processes on Earth, such as cosmic ray bombardment (for example, carbon-14).[50][note 2]

For 80 of the chemical elements, at least one stable isotope exists. As a rule, there is only a handful of stable isotopes for each of these elements, the average being 3.2 stable isotopes per element. Twenty-six elements have only a single stable isotope, while the largest number of stable isotopes observed for any element is ten, for the element tin. Elements 43, 61, and all elements numbered 83 or higher have no stable isotopes.[51]Template:Page needed

Stability of isotopes is affected by the ratio of protons to neutrons, and also by the presence of certain "magic numbers" of neutrons or protons that represent closed and filled quantum shells. These quantum shells correspond to a set of energy levels within the shell model of the nucleus; filled shells, such as the filled shell of 50 protons for tin, confers unusual stability on the nuclide. Of the 254 known stable nuclides, only four have both an odd number of protons and odd number of neutrons: hydrogen-2 (deuterium), lithium-6, boron-10 and nitrogen-14. Also, only four naturally occurring, radioactive odd-odd nuclides have a half-life over a billion years: potassium-40, vanadium-50, lanthanum-138 and tantalum-180m. Most odd-odd nuclei are highly unstable with respect to beta decay, because the decay products are even-even, and are therefore more strongly bound, due to nuclear pairing effects.[51]Template:Page needed

### Mass

{{#invoke:main|main}}

The large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called "nucleons") in a given atom is called the mass number. The mass number is a simple whole number, and has units of "nucleons." An example of use of a mass number is "carbon-12," which has 12 nucleons (six protons and six neutrons).

The actual mass of an atom at rest is often expressed using the unified atomic mass unit (u), which is also called a dalton (Da). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately Template:Val.[52] Hydrogen-1, the lightest isotope of hydrogen and the atom with the lowest mass, has an atomic weight of 1.007825 u.[53] The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the mass of the atomic mass unit. However, this number will not be an exact whole number except in the case of carbon-12 (see below).[54] The heaviest stable atom is lead-208,Template:Sfn with a mass of Template:Val.[55]

As even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about [[Avogadro constant|Template:Val]]). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 u, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.[52]Template:Page needed

### Shape and size

{{#invoke:main|main}} Atoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus.{{ safesubst:#invoke:Unsubst||date=__DATE__ |\$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} However, this assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin.[56] On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right).[57] Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm.[58]

When subjected to external fields, like an electrical field, the shape of an atom may deviate from spherical symmetry. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystals, where large crystal-electrical fields may occur at low-symmetry lattice sites.[59] Significant ellipsoidal deformations have recently been shown to occur for sulfur ions in pyrite-type compounds.[60]

Atomic dimensions are thousands of times smaller than the wavelengths of light (400–700 nm) so they can not be viewed using an optical microscope. However, individual atoms can be observed using a scanning tunneling microscope. To visualize the minuteness of the atom, consider that a typical human hair is about 1 million carbon atoms in width.[61] A single drop of water contains about 2 sextillion (Template:Val) atoms of oxygen, and twice the number of hydrogen atoms.[62] A single carat diamond with a mass of Template:Val contains about 10 sextillion (1022) atoms of carbon.[note 3] If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple.Template:Sfn

{{#invoke:main|main}}

This diagram shows the half-life (T½) of various isotopes with Z protons and N neutrons.

Every element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm.[63]

The most common forms of radioactive decay are:Template:Sfn[64]

• Alpha decay: this process is caused when the nucleus emits an alpha particle, which is a helium nucleus consisting of two protons and two neutrons. The result of the emission is a new element with a lower atomic number.
• Beta decay (and electron capture): these processes are regulated by the weak force, and result from a transformation of a neutron into a proton, or a proton into a neutron. The neutron to proton transition is accompanied by the emission of an electron and an antineutrino, while proton to neutron transition (except in electron capture) causes the emission of a positron and a neutrino. The electron or positron emissions are called beta particles. Beta decay either increases or decreases the atomic number of the nucleus by one. Electron capture is more common than positron emission, because it requires less energy. In this type of decay, an electron is absorbed by the nucleus, rather than a positron emitted from the nucleus. A neutrino is still emitted in this process, and a proton changes to a neutron.
• Gamma decay: this process results from a change in the energy level of the nucleus to a lower state, resulting in the emission of electromagnetic radiation. The excited state of a nucleus which results in gamma emission usually occurs following the emission of an alpha or a beta particle. Thus, gamma decay usually follows alpha or beta decay.

Other more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or more than one beta particle. An analog of gamma emission which allows excited nuclei to lose energy in a different way, is internal conversion— a process that produces high-speed electrons that are not beta rays, followed by production of high-energy photons that are not gamma rays. A few large nuclei explode into two or more charged fragments of varying masses plus several neutrons, in a decay called spontaneous nuclear fission.

Each radioactive isotope has a characteristic decay time period—the half-life—that is determined by the amount of time needed for half of a sample to decay. This is an exponential decay process that steadily decreases the proportion of the remaining isotope by 50% every half-life. Hence after two half-lives have passed only 25% of the isotope is present, and so forth.[63]

### Magnetic moment

{{#invoke:main|main}}

Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or "spin-½". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.[65]

The magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field. However, the most dominant contribution comes from spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons pair up with each other, with one member of each pair in a spin up state and the other in the opposite, spin down state. Thus these spins cancel each other out, reducing the total magnetic dipole moment to zero in some atoms with even number of electrons.[66]

In ferromagnetic elements such as iron, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a process known as an exchange interaction. When the magnetic moments of ferromagnetic atoms are lined up, the material can produce a measurable macroscopic field. Paramagnetic materials have atoms with magnetic moments that line up in random directions when no magnetic field is present, but the magnetic moments of the individual atoms line up in the presence of a field.[66][67]

The nucleus of an atom can also have a net spin. Normally these nuclei are aligned in random directions because of thermal equilibrium. However, for certain elements (such as xenon-129) it is possible to polarize a significant proportion of the nuclear spin states so that they are aligned in the same direction—a condition called hyperpolarization. This has important applications in magnetic resonance imaging.[68]Template:Sfn

### Energy levels

These electron's energy levels (not to scale) are sufficient for ground states of atoms up to cadmium (5s2 4d10) inclusively. Do not forget that even the top of the diagram is lower than an unbound electron state.

The potential energy of an electron in an atom is negative, its dependence of its position reaches the minimum (the most absolute value) inside the nucleus, and vanishes when the distance from the nucleus goes to infinity, roughly in an inverse proportion to the distance. In the quantum-mechanical model, a bound electron can only occupy a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for theoretical explanation. An energy level can be measured by the amount of energy needed to unbind the electron from the atom, and is usually given in units of electronvolts (eV). The lowest energy state of a bound electron is called the ground state, i.e. stationary state, while an electron transition to a higher level results in an excited state.[69] The electron's energy raises when n increases because the (average) distance to the nucleus increases. Dependence of the energy on [[azimuthal quantum number|Template:Ell]] is caused not by electrostatic potential of the nucleus, but by interaction between electrons.

For an electron to transition between two different states, e.g. grounded state to first excited level (ionization), it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to Niels Bohr model, what can be precisely calculated by the Schrödinger equation. Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon; see Electron properties.

The energy of an emitted photon is proportional to its frequency, so these specific energy levels appear as distinct bands in the electromagnetic spectrum.[70] Each element has a characteristic spectrum that can depend on the nuclear charge, subshells filled by electrons, the electromagnetic interactions between the electrons and other factors.[71]

An example of absorption lines in a spectrum

When a continuous spectrum of energy is passed through a gas or plasma, some of the photons are absorbed by atoms, causing electrons to change their energy level. Those excited electrons that remain bound to their atom spontaneously emit this energy as a photon, traveling in a random direction, and so drop back to lower energy levels. Thus the atoms behave like a filter that forms a series of dark absorption bands in the energy output. (An observer viewing the atoms from a view that does not include the continuous spectrum in the background, instead sees a series of emission lines from the photons emitted by the atoms.) Spectroscopic measurements of the strength and width of atomic spectral lines allow the composition and physical properties of a substance to be determined.[72]

Close examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron.[73] When an atom is in an external magnetic field, spectral lines become split into three or more components; a phenomenon called the Zeeman effect. This is caused by the interaction of the magnetic field with the magnetic moment of the atom and its electrons. Some atoms can have multiple electron configurations with the same energy level, which thus appear as a single spectral line. The interaction of the magnetic field with the atom shifts these electron configurations to slightly different energy levels, resulting in multiple spectral lines.[74] The presence of an external electric field can cause a comparable splitting and shifting of spectral lines by modifying the electron energy levels, a phenomenon called the Stark effect.Template:Sfn

If a bound electron is in an excited state, an interacting photon with the proper energy can cause stimulated emission of a photon with a matching energy level. For this to occur, the electron must drop to a lower energy state that has an energy difference matching the energy of the interacting photon. The emitted photon and the interacting photon then move off in parallel and with matching phases. That is, the wave patterns of the two photons are synchronized. This physical property is used to make lasers, which can emit a coherent beam of light energy in a narrow frequency band.[75]

### Valence and bonding behavior

{{#invoke:main|main}}

The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in that shell are called valence electrons. The number of valence electrons determines the bonding behavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells.[76] For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts. However, many elements display multiple valences, or tendencies to share differing numbers of electrons in different compounds. Thus, chemical bonding between these elements takes many forms of electron-sharing that are more than simple electron transfers. Examples include the element carbon and the organic compounds.[77]

The chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) The elements at the far right of the table have their outer shell completely filled with electrons, which results in chemically inert elements known as the noble gases.[78][79]

### States

{{#invoke:main|main}}

Snapshots illustrating the formation of a Bose–Einstein condensate

Quantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas. Template:Sfn Within a state, a material can also exist in different allotropes. An example of this is solid carbon, which can exist as graphite or diamond.[80] Gaseous allotropes exist as well, such as dioxygen and ozone.

At temperatures close to absolute zero, atoms can form a Bose–Einstein condensate, at which point quantum mechanical effects, which are normally only observed at the atomic scale, become apparent on a macroscopic scale.Template:Sfn[81] This super-cooled collection of atoms then behaves as a single super atom, which may allow fundamental checks of quantum mechanical behavior.[82]

## Identification

Scanning tunneling microscope image showing the individual atoms making up this gold (100) surface. Reconstruction causes the surface atoms to deviate from the bulk crystal structure and arrange in columns several atoms wide with pits between them.

The scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would normally be insurmountable. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely packed energy levels—the Fermi level local density of states.[83][84]

An atom can be ionized by removing one of its electrons. The electric charge causes the trajectory of an atom to bend when it passes through a magnetic field. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses this principle to measure the mass-to-charge ratio of ions. If a sample contains multiple isotopes, the mass spectrometer can determine the proportion of each isotope in the sample by measuring the intensity of the different beams of ions. Techniques to vaporize atoms include inductively coupled plasma atomic emission spectroscopy and inductively coupled plasma mass spectrometry, both of which use a plasma to vaporize samples for analysis.[85]

A more area-selective method is electron energy loss spectroscopy, which measures the energy loss of an electron beam within a transmission electron microscope when it interacts with a portion of a sample. The atom-probe tomograph has sub-nanometer resolution in 3-D and can chemically identify individual atoms using time-of-flight mass spectrometry.[86]

Spectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same element.[87] Helium was discovered in this way in the spectrum of the Sun 23 years before it was found on Earth.[88]

## Origin and current state

Atoms form about 4% of the total energy density of the observable Universe, with an average density of about 0.25 atoms/m3.[89] Within a galaxy such as the Milky Way, atoms have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 105 to 109 atoms/m3.Template:Sfn The Sun is believed to be inside the Local Bubble, a region of highly ionized gas, so the density in the solar neighborhood is only about 103 atoms/m3.[90] Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium. Up to 95% of the Milky Way's atoms are concentrated inside stars and the total mass of atoms forms about 10% of the mass of the galaxy.Template:Sfn (The remainder of the mass is an unknown dark matter.)[91]

### Formation

Electrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron.[92][93][94]

Ubiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma – a gas of positively-charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically favorable. Atoms (complete with bound electrons) became to dominate over charged particles 380,000 years after the Big Bang—an epoch called recombination, when the expanding Universe cooled enough to allow electrons to become attached to nuclei.[95]

Since the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple alpha process) the sequence of elements from carbon up to iron;[96] see stellar nucleosynthesis for details.

Isotopes such as lithium-6, as well as some beryllium and boron are generated in space through cosmic ray spallation.[97] This occurs when a high-energy proton strikes an atomic nucleus, causing large numbers of nucleons to be ejected.

Elements heavier than iron were produced in supernovae through the r-process and in AGB stars through the s-process, both of which involve the capture of neutrons by atomic nuclei.[98] Elements such as lead formed largely through the radioactive decay of heavier elements.[99]

### Earth

Most of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating.Template:Sfn[100] Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay.[101]

There are a few trace atoms on Earth that were not present at the beginning (i.e., not "primordial"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere.[102] Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors or explosions.[103][104] Of the transuranic elements—those with atomic numbers greater than 92—only plutonium and neptunium occur naturally on Earth.[105][106] Transuranic elements have radioactive lifetimes shorter than the current age of the EarthTemplate:Sfn and thus identifiable quantities of these elements have long since decayed, with the exception of traces of plutonium-244 possibly deposited by cosmic dust.Template:Sfn Natural deposits of plutonium and neptunium are produced by neutron capture in uranium ore.[107]

The Earth contains approximately Template:Val atoms.[108] Although small numbers of independent atoms of noble gases exist, such as argon, neon, and helium, 99% of the atmosphere is bound in the form of molecules, including carbon dioxide and diatomic oxygen and nitrogen. At the surface of the Earth, an overwhelming majority of atoms combine to form various compounds, including water, salt, silicates and oxides. Atoms can also combine to create materials that do not consist of discrete molecules, including crystals and liquid or solid metals.[109][110] This atomic matter forms networked arrangements that lack the particular type of small-scale interrupted order associated with molecular matter.Template:Sfn

### Rare and theoretical forms

#### Superheavy elements

{{#invoke:main|main}}

While isotopes with atomic numbers higher than lead (82) are known to be radioactive, an "island of stability" has been proposed for some elements with atomic numbers above 103. These superheavy elements may have a nucleus that is relatively stable against radioactive decay.[111] The most likely candidate for a stable superheavy atom, unbihexium, has 126 protons and 184 neutrons.[112]

#### Exotic matter

{{#invoke:main|main}}

Each particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature.[113][114] However, in 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva.[115][116]

Other exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test the fundamental predictions of physics.[117][118][119] Template:Category see also

## Notes

1. In the case of hydrogen-1, with a single electron and nucleon, the proton is ${\displaystyle {\begin{smallmatrix}{\frac {1836}{1837}}\approx 0.99946\end{smallmatrix}}}$, or 99.946% of the total atomic mass. All other nuclides (isotopes of hydrogen and all other elements) have more nucleons than electrons, so the fraction of mass taken by the nucleus is significantly closer to 100% for all of these types of atoms, than for hydrogen-1.
2. For more recent updates see Interactive Chart of Nuclides (Brookhaven National Laboratory).
3. A carat is 200 milligrams. By definition, carbon-12 has 0.012 kg per mole. The Avogadro constant defines Template:Val atoms per mole.

## References

1. {{#invoke:citation/CS1|citation |CitationClass=book }}
2. Template:Cite web
3. Template:Cite web
4. Template:Cite web
5. Template:Cite web
6. {{#invoke:citation/CS1|citation |CitationClass=book }} Lederman provides an excellent discussion of this point, and this debate.
7. Template:Cite web
8. Template:Cite web
9. Template:Cite web
10. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
11. Template:Cite web
12. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
13. Template:Cite web
14. Template:Cite web
15. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
16. Template:Cite web
17. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
18. Template:Cite web
19. Template:Cite web
20. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
21. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
22. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
23. Template:Cite web
24. Template:Cite web
25. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
26. Template:Cite web
27. Template:Cite web
28. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
29. Template:Cite web
30. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
31. Template:Cite web
32. Template:Cite web
33. Template:Cite web
34. Template:Cite web
35. Template:Cite web
36. Template:Cite web
37. Template:Cite web
38. Template:Cite web
39. Template:Cite web
40. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
41. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
42. Template:Cite web
43. Template:Cite web
44. Template:Cite web
45. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
46. Template:Cite web
47. Template:Cite news
48. Template:Cite news
49. Template:Cite web
50. Template:Cite web
51. CRC Handbook (2002).
52. Mills et al. (1993).
53. Template:Cite web
54. Template:Cite web
55. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
56. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
57. Template:Cite web
58. Zumdahl (2002).
59. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
60. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
61. Template:Cite web—describes the width of a human hair as Template:Val and 10 carbon atoms as spanning 1 nm.
62. Padilla et al. (2002:32)—"There are 2,000,000,000,000,000,000,000 (that's 2 sextillion) atoms of oxygen in one drop of water—and twice as many atoms of hydrogen."
63. Template:Cite web
64. Template:Cite web
65. Template:Cite web
66. Template:Cite web
67. Template:Cite web
68. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
69. Template:Cite web
70. Fowles (1989:227–233).
71. Template:Cite web
72. Template:Cite web
73. Template:Cite web
74. Template:Cite web
75. Template:Cite web
76. Template:Cite web
77. Template:Cite web
78. Template:Cite web
79. Template:Cite web
80. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
81. Template:Cite news
82. Template:Cite web
83. Template:Cite web
84. Template:Cite web—in particular, see the Nobel lecture by G. Binnig and H. Rohrer.
85. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
86. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
87. Template:Cite web
88. Template:Cite web
89. Template:Cite web
90. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
91. Template:Cite web
92. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
93. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
94. Template:Cite web
95. Template:Cite web
96. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
97. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
98. Template:Cite arXiv
99. Template:Cite web
100. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
101. Template:Cite web
102. Template:Cite news
103. Template:Cite news
104. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
105. Template:Cite web
106. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
107. Template:Cite web
108. Template:Cite web
109. Template:Cite web
110. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
111. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
112. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
113. Template:Cite news
114. Template:Cite news
115. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
116. Template:Cite news
117. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
118. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
119. Template:Cite web

### Book references

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }} Template:Refend