Metal ions in aqueous solutionA metal ion in aqueous solution or aqua ion is a cation, dissolved in water, of chemical formula [M(H2O)n]z+. The solvation number, n, determined by a variety of experimental methods is 4 for Li+ and Be2+ and 6 for most elements in periods 3 and 4 of the periodic table. Lanthanide and actinide aqua ions have higher solvation numbers (often 8 to 9), with the highest known being 11 for Ac3+. The strength of the bonds between the metal ion and water molecules in the primary solvation shell increases with the electrical charge, z, on the metal ion and decreases as its ionic radius, r, increases.
Apparent magnitudeApparent magnitude (m) is a measure of the brightness of a star or other astronomical object. An object's apparent magnitude depends on its intrinsic luminosity, its distance, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer. The word magnitude in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest).
Trans effectIn inorganic chemistry, the trans effect is the increased lability of ligands that are trans to certain other ligands, which can thus be regarded as trans-directing ligands. It is attributed to electronic effects and it is most notable in square planar complexes, although it can also be observed for octahedral complexes. The analogous cis effect is most often observed in octahedral transition metal complexes. In addition to this kinetic trans effect, trans ligands also have an influence on the ground state of the molecule, the most notable ones being bond lengths and stability.
Molecular engineeringMolecular engineering is an emerging field of study concerned with the design and testing of molecular properties, behavior and interactions in order to assemble better materials, systems, and processes for specific functions. This approach, in which observable properties of a macroscopic system are influenced by direct alteration of a molecular structure, falls into the broader category of “bottom-up” design.
Kepler conjectureThe Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is around 74.05%. In 1998, Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture.
Unpaired electronIn chemistry, an unpaired electron is an electron that occupies an orbital of an atom singly, rather than as part of an electron pair. Each atomic orbital of an atom (specified by the three quantum numbers n, l and m) has a capacity to contain two electrons (electron pair) with opposite spins. As the formation of electron pairs is often energetically favourable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively uncommon in chemistry, because an entity that carries an unpaired electron is usually rather reactive.
ElectrideAn electride is an ionic compound in which an electron is the anion. Solutions of alkali metals in ammonia are electride salts. In the case of sodium, these blue solutions consist of [Na(NH3)6]+ and solvated electrons: Na + 6 NH3 → [Na(NH3)6]+ + e− The cation [Na(NH3)6]+ is an octahedral coordination complex. Addition of a complexant like crown ether or [2.2.2]-cryptand to a solution of [Na(NH3)6]+e− affords [Na (crown ether)]+e− or [Na(2,2,2-crypt)]+e−.
László Fejes TóthLászló Fejes Tóth (Fejes Tóth László, ˈfɛjɛʃ ˈtoːt ˈlaːsloː 12 March 1915 – 17 March 2005) was a Hungarian mathematician who specialized in geometry. He proved that a lattice pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane (a generalization of Thue's theorem, a 2-dimensional analog of the Kepler conjecture). He also investigated the sphere packing problem. He was the first to show, in 1953, that proof of the Kepler conjecture can be reduced to a finite case analysis and, later, that the problem might be solved using a computer.
Kissing numberIn geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of spheres) in a given space, a kissing number can also be defined for each individual sphere as the number of spheres it touches. For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another.
Hour angleIn astronomy and celestial navigation, the hour angle is the angle between two planes: one containing Earth's axis and the zenith (the meridian plane), and the other containing Earth's axis and a given point of interest (the hour circle). It may be given in degrees, time, or rotations depending on the application. The angle may be expressed as negative east of the meridian plane and positive west of the meridian plane, or as positive westward from 0° to 360°. The angle may be measured in degrees or in time, with 24h = 360° exactly.
