Atoms in the context of Quantum mechanics

In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles. In everyday as well as scientific usage, matter generally includes atoms and anything made up of them, and any particles (or combination of particles) that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or heat. Matter exists in various states (also known as phases). These include classical everyday phases such as solid, liquid, and gas – for example water exists as ice, liquid water, and gaseous steam – but other states are possible, including plasma, Bose–Einstein condensates, fermionic condensates, and quark–gluon plasma.

Usually atoms can be imagined as a nucleus of protons and neutrons, and a surrounding "cloud" of orbiting electrons which "take up space". However, this is only somewhat correct because subatomic particles and their properties are governed by their quantum nature, which means they do not act as everyday objects appear to act – they can act like waves as well as particles, and they do not have well-defined sizes or positions. In the Standard Model of particle physics, matter is not a fundamental concept because the elementary constituents of atoms are quantum entities which do not have an inherent "size" or "volume" in any everyday sense of the word. Due to the exclusion principle and other fundamental interactions, some "point particles" known as fermions (quarks, leptons), and many composites and atoms, are effectively forced to keep a distance from other particles under everyday conditions; this creates the property of matter which appears to us as matter taking up space.

Atomism (from Ancient Greek ἄτομον (atomon) 'uncuttable, indivisible') is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms.

References to the concept of atomism and its atoms appeared in both ancient Greek and ancient Indian philosophical traditions. Leucippus is the earliest figure whose commitment to atomism is well attested and he is usually credited with inventing atomism. He and other ancient Greek atomists theorized that nature consists of two fundamental principles: atom and void. Clusters of different shapes, arrangements, and positions give rise to the various macroscopic substances in the world.

Plagioclase (/ˈplædʒ(i)əˌkleɪs, ˈpleɪdʒ-, -ˌkleɪz/ PLAJ-(ee)-ə-klayss, PLAYJ-, -⁠klayz) is a series of tectosilicate (framework silicate) minerals within the feldspar group. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a continuous solid solution series, more properly known as the plagioclase feldspar series. This was first shown by the German mineralogist Johann Friedrich Christian Hessel (1796–1872) in 1826. The series ranges from albite to anorthite endmembers (with respective compositions NaAlSi₃O₈ to CaAl₂Si₂O₈), where sodium and calcium atoms can substitute for each other in the mineral's crystal lattice structure. Plagioclase in hand samples is often identified by its polysynthetic crystal twinning or "record-groove" effect.

Plagioclase is a major constituent mineral in Earth's crust and is consequently an important diagnostic tool in petrology for identifying the composition, origin and evolution of igneous rocks. Plagioclase is also a major constituent of rock in the highlands of the Moon. Analysis of thermal emission spectra from the surface of Mars suggests that plagioclase is the most abundant mineral in the crust of Mars.

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of Coulomb's law for electricity and Ampère's force law for magnetism; the Lorentz force describes microscopic charged particles.

The electromagnetic force is responsible for many of the chemical and physical phenomena observed in daily life. The electrostatic attraction between atomic nuclei and their electrons holds atoms together. Electric forces also allow different atoms to combine into molecules, including the macromolecules such as proteins that form the basis of life. Meanwhile, magnetic interactions between the spin and angular momentum magnetic moments of electrons also play a role in chemical reactivity; such relationships are studied in spin chemistry. Electromagnetism also plays several crucial roles in modern technology: electrical energy production, transformation and distribution; light, heat, and sound production and detection; fiber optic and wireless communication; sensors; computation; electrolysis; electroplating; and mechanical motors and actuators.

In physics, a state of matter or phase of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma.

Different states are distinguished by the ways the component particles (atoms, molecules, ions and electrons) are arranged, and how they behave collectively. In a solid, the particles are tightly packed and held in fixed positions, giving the material a definite shape and volume. In a liquid, the particles remain close together but can move past one another, allowing the substance to maintain a fixed volume while adapting to the shape of its container. In a gas, the particles are far apart and move freely, allowing the substance to expand and fill both the shape and volume of its container. Plasma is similar to a gas, but it also contains charged particles (ions and free electrons) that move independently and respond to electric and magnetic fields.

Solid is a state of matter in which atoms are closely packed and are difficult to move past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree of resistance being dependent upon the specific material under consideration. Solids also always possess the least amount of kinetic energy per atom/molecule relative to other phases or, equivalently stated, solids are formed when matter in the liquid / gas phase is cooled below a certain temperature. This temperature is called the melting point of the substance and is an intrinsic property; i.e. independent of how much of the matter there is. The vast majority of substances, when in the solid state, can be arranged in one of a few ubiquitous structures.

Solids are characterized by structural rigidity and resistance to applied external forces and pressure. Unlike liquids, solids do not flow to take on the shape of their container, nor do they expand to fill the entire available volume like a gas. Much like the other three fundamental phases, solids also expand when heated, the thermal energy put into increasing the distance and reducing the potential energy between atoms. However, solids do this to a much lesser extent. When heated to their melting point or sublimation point, solids melt into a liquid or sublimate directly into a gas, respectively. For solids that directly sublimate into a gas, the melting point is replaced by the sublimation point. As a rule of thumb, melting will occur if the subjected pressure is higher than the substance's triple point pressure, and sublimation will occur otherwise. Melting and melting points refer exclusively to transitions between solids and liquids. Melting occurs across a great extent of temperatures, ranging from 0.10 K for helium-3 under 30 bars (3 MPa) of pressure, to around 4,100 K at 1 atm for the composite refractory material hafnium carbonitride.

Gas is a state of matter with neither fixed volume nor fixed shape. It is a compressible form of fluid, in contrast to a liquid. A pure gas consists of individual atoms (e.g. a noble gas like neon), or molecules (e.g. oxygen (O₂) or carbon dioxide). Pure gases can also be mixed together such as in the air. What distinguishes gases from liquids and solids is the vast separation of the individual gas particles. This separation can make some gases invisible to the human observer.

The gaseous state of matter occurs between the liquid and plasma states, the latter of which provides the upper-temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention.High-density atomic gases super-cooled to very low temperatures are classified by their statistical behavior as either Bose gases or Fermi gases. For a comprehensive listing of these exotic states of matter, see list of states of matter.

Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid (the absorbate) is dissolved by or permeates a liquid or solid (the absorbent). While adsorption does often precede absorption, which involves the transfer of the absorbate into the volume of the absorbent material, alternatively, adsorption is distinctly a surface phenomenon, wherein the adsorbate does not penetrate through the material surface and into the bulk of the adsorbent. The term sorption encompasses both adsorption and absorption, and desorption is the reverse of sorption.

Like surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent or metallic) of the constituent atoms of the material are fulfilled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption (characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding). It may also occur due to electrostatic attraction. The nature of the adsorption can affect the structure of the adsorbed species. For example, polymer physisorption from solution can result in squashed structures on a surface.

The fallacy of composition is an informal fallacy that arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber; therefore, the vehicle of which it is a part is also made of rubber." That is fallacious, because vehicles are made with a variety of parts, most of which are not made of rubber. The fallacy of composition can apply even when a fact is true of every proper part of a greater entity, though. A more complicated example might be: "No atoms are alive. Therefore, nothing made of atoms is alive." This is a statement most people would consider incorrect, due to emergence, where the whole possesses properties not present in any of the parts.

The fallacy of composition is related to the fallacy of hasty generalization, in which an unwarranted inference is made from a statement about a sample to a statement about the population from which the sample is drawn. The fallacy of composition is the converse of the fallacy of division.

The atomic ratio is a measure of the ratio of atoms of one kind (i) to another kind (j). A closely related concept is the atomic percent (or at.%), which gives the percentage of one kind of atom relative to the total number of atoms. The molecular equivalents of these concepts are the molar fraction, or molar percent.

Semiconductor materials are nominally small band gap insulators. The defining property of a semiconductor material is that it can be compromised by doping it with impurities that alter its electronic properties in a controllable way. Because of their application in the computer and photovoltaic industry—in devices such as transistors, lasers, and solar cells—the search for new semiconductor materials and the improvement of existing materials is an important field of study in materials science.

Most commonly used semiconductor materials are crystalline inorganic solids. These materials are classified according to the periodic table groups of their constituent atoms.

Ammonium is a modified form of ammonia that has an extra hydrogen atom. It is a positively charged (cationic) molecular ion with the chemical formula NH+4 or [NH₄]. It is formed by the addition of a proton (a hydrogen nucleus) to ammonia (NH₃). Ammonium is also a general name for positively charged (protonated) substituted amines and quaternary ammonium cations ([NR₄]), where one or more hydrogen atoms are replaced by organic or other groups (indicated by R). Not only is ammonium a source of nitrogen and a key metabolite for many living organisms, but it is an integral part of the global nitrogen cycle. As such, human impact in recent years could have an effect on the biological communities that depend on it.

Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. MD simulations are widely applied in chemical physics, materials science, and biophysics.

Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated.

A sesquioxide is an oxide of an element (or radical), where the ratio between the number of atoms of that element and the number of atoms of oxygen is 2:3. For example, aluminium oxide Al₂O₃ and phosphorus(III) oxide P₄O₆ are sesquioxides.Many sesquioxides contain a metal in the +3 oxidation state and the oxide ion O, e.g., aluminium oxide Al₂O₃, lanthanum(III) oxide La₂O₃ and iron(III) oxide Fe₂O₃. Sesquioxides of iron and aluminium are found in soil. The alkali metal sesquioxides are exceptions because they contain both peroxide O2−2 and superoxide O−2 ions, e.g., rubidium sesquioxide Rb₄O₆ is formulated (Rb)₄(O2−2)(O−2)₂. Sesquioxides of metalloids and nonmetals are better formulated as covalent, e.g. boron trioxide B₂O₃, dinitrogen trioxide N₂O₃ and phosphorus(III) oxide P₄O₆; chlorine trioxide Cl₂O₃ and bromine trioxide Br₂O₃ do not have oxidation state +3 on the halogen.

Many transition metal oxides crystallize in the corundum structure type, with space group R3c. Sesquioxides of rare earth elements crystalize into one or more of three crystal structures: hexagonal (type A, space group P3m1), monoclinic (type B, space group C2/m), or body-centered cubic (type C, space group Ia3).

In physics, the proton-to-electron mass ratio (symbol μ or β) is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely:

The number in parentheses is the measurement uncertainty on the last two digits, corresponding to a relative standard uncertainty of 1.7×10.