Polonium is a chemical element with symbol Po and atomic number 84. A rare and radioactive metal with no stable isotopes, polonium is chemically similar to selenium and tellurium, though its metallic character resembles that of its horizontal neighbors in the periodic table: thallium and bismuth. Due to the short half-life of all its isotopes, its natural occurrence is limited to tiny traces of the fleeting polonium-210 in uranium ores, as it is the penultimate daughter of natural uranium-238. Though longer-lived isotopes exist, they are much more difficult to produce. Today, polonium is produced in milligram quantities by the neutron irradiation of bismuth. Due to its intense radioactivity, which results in the radiolysis of chemical bonds and radioactive self-heating, its chemistry has been investigated on the trace scale only. Polonium was discovered in 1898 by Marie and Pierre Curie, when it was extracted from the uranium ore pitchblende and identified by its strong radioactivity: it was the first element to be so discovered.
Polonium was named after Marie Curie's homeland of Poland. Polonium has few applications, those are related to its radioactivity: heaters in space probes, antistatic devices, sources of neutrons and alpha particles. Besides being radioactive, polonium is toxic. 210Po is an alpha emitter. A milligram of 210Po emits about as many alpha particles per second as 5 grams of 226Ra. A few curies of 210Po emit a blue glow, caused by ionisation of the surrounding air. About one in 100,000 alpha emissions causes an excitation in the nucleus which results in the emission of a gamma ray with a maximum energy of 803 keV. Polonium is a radioactive element; the alpha form is the only known example of a simple cubic crystal structure in a single atom basis at STP, with an edge length of 335.2 picometers. The structure of polonium has been characterized by X-ray diffraction and electron diffraction.210Po has the ability to become airborne with ease: if a sample is heated in air to 55 °C, 50% of it is vaporized in 45 hours to form diatomic Po2 molecules though the melting point of polonium is 254 °C and its boiling point is 962 °C.
More than one hypothesis exists for. The chemistry of polonium is similar to that of tellurium, although it shows some similarities to its neighbor bismuth due to its metallic character. Polonium dissolves in dilute acids but is only soluble in alkalis. Polonium solutions are first colored in pink by the Po2+ ions, but rapidly become yellow because alpha radiation from polonium ionizes the solvent and converts Po2+ into Po4+; this process is accompanied by bubbling and emission of heat and light by glassware due to the absorbed alpha particles. At pH about 1, polonium ions are hydrolyzed and complexed by acids such as oxalic acid, citric acid, tartaric acid. Polonium has no common compounds, all of its compounds are synthetically created; the most stable class of polonium compounds are polonides, which are prepared by direct reaction of two elements. Na2Po has the antifluorite structure, the polonides of Ca, Ba, Hg, Pb and lanthanides form a NaCl lattice, BePo and CdPo have the wurtzite and MgPo the nickel arsenide structure.
Most polonides decompose upon heating to about 600 °C, except for HgPo that decomposes at ~300 °C and the lanthanide polonides, which do not decompose but melt at temperatures above 1000 °C. For example, PrPo melts at 1250 °C and TmPo at 2200 °C. PbPo is one of the few occurring polonium compounds, as polonium alpha decays to form lead. Polonium hydride is a volatile liquid at room temperature prone to dissociation. Water is the only other known hydrogen chalcogenide, a liquid at room temperature; the two oxides PoO2 and PoO3 are the products of oxidation of polonium. Halides of the structure PoX2, PoX4 and PoF6 are known, they are soluble in the corresponding hydrogen halides, i.e. PoClX in HCl, PoBrX in HBr and PoI4 in HI. Polonium dihalides are formed by direct reaction of the elements or by reduction of PoCl4 with SO2 and with PoBr4 with H2S at room temperature. Tetrahalides can be obtained by reacting polonium dioxide with HCl, HBr or HI. Other polonium compounds include potassium polonite as a polonite, acetate, carbonate, chromate, cyanide and hydroxides, selenate, monosulfide, sulfate and sulfite.
Polonium has 33 known isotopes. They have atomic masses that range from 188 to 220 u. 210Po is the most available and is made via neutron capture by natural bismuth. The longer-lived 209Po and 208Po can be made through the alpha, proton, or deuteron bombardment of lead or bismuth in a cyclotron. Tentatively called "radium F", polonium was discovered by Marie and Pierre Curie in 1898, was named after Marie Curie's native land of Poland. Poland at the time was under Russian and Austro-Hungarian partition, did not exist as an independent country, it was Curie's hope that naming the element after her native land woul
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom. Molecular geometry influences several properties of a substance including its reactivity, phase of matter, color and biological activity; the angles between bonds that an atom forms depend only weakly on the rest of molecule, i.e. they can be understood as local and hence transferable properties. The molecular geometry can be determined by diffraction methods. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques. X-ray crystallography, neutron diffraction and electron diffraction can give molecular structure for crystalline solids based on the distance between nuclei and concentration of electron density.
Gas electron diffraction can be used for small molecules in the gas phase. NMR and FRET methods can be used to determine complementary information including relative distances, dihedral angles and connectivity. Molecular geometries are best determined at low temperature because at higher temperatures the molecular structure is averaged over more accessible geometries. Larger molecules exist in multiple stable geometries that are close in energy on the potential energy surface. Geometries can be computed by ab initio quantum chemistry methods to high accuracy; the molecular geometry can be different as a solid, in solution, as a gas. The position of each atom is determined by the nature of the chemical bonds by which it is connected to its neighboring atoms; the molecular geometry can be described by the positions of these atoms in space, evoking bond lengths of two joined atoms, bond angles of three connected atoms, torsion angles of three consecutive bonds. Since the motions of the atoms in a molecule are determined by quantum mechanics, one must define "motion" in a quantum mechanical way.
The overall quantum mechanical motions translation and rotation hardly change the geometry of the molecule. In addition to translation and rotation, a third type of motion is molecular vibration, which corresponds to internal motions of the atoms such as bond stretching and bond angle variation; the molecular vibrations are harmonic, the atoms oscillate about their equilibrium positions at the absolute zero of temperature. At absolute zero all atoms are in their vibrational ground state and show zero point quantum mechanical motion, so that the wavefunction of a single vibrational mode is not a sharp peak, but an exponential of finite width. At higher temperatures the vibrational modes may be thermally excited, but they oscillate still around the recognizable geometry of the molecule. To get a feeling for the probability that the vibration of molecule may be thermally excited, we inspect the Boltzmann factor β ≡ exp , where Δ E is the excitation energy of the vibrational mode, k the Boltzmann constant and T the absolute temperature.
At 298 K, typical values for the Boltzmann factor β are: β = 0.089 for ΔE = 500 cm−1. When an excitation energy is 500 cm−1 about 8.9 percent of the molecules are thermally excited at room temperature. To put this in perspective: the lowest excitation vibrational energy in water is the bending mode. Thus, at room temperature less than 0.07 percent of all the molecules of a given amount of water will vibrate faster than at absolute zero. As stated above, rotation hardly influences the molecular geometry. But, as a quantum mechanical motion, it is thermally excited at low temperatures. From a classical point of view it can be stated that at higher temperatures more molecules will rotate faster, which implies that they have higher angular velocity and angular momentum. In quantum mechanical language: more eigenstates of higher angular momentum become thermally populated with rising temperatures. Typical rotational excitation energies are on the order of a few cm−1; the results of many spectroscopic experiments are broadened because they involve an averaging over rotational states.
It is difficult to extract geometries from spectra at high temperatures, because the number of rotational states probed in the experimental averaging increases with increasing temperature. Thus, many spectroscopic observations can only be expected to yield reliable molecular geometries at temperatures close to absolute zero, because at higher temperatures too many higher rotational states are thermally populated. Molecules, by definition, are most held together with covalent bonds involving single, and/or triple bonds, where a "bond
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is one of the five Platonic solids, it has 6 faces, 12 edges, 8 vertices. The cube is a square parallelepiped, an equilateral cuboid and a right rhombohedron, it is a regular square prism in three orientations, a trigonal trapezohedron in four orientations. The cube is dual to the octahedron, it has octahedral symmetry. The cube is the only convex polyhedron; the cube has four special orthogonal projections, centered, on a vertex, edges and normal to its vertex figure. The first and third correspond to the B2 Coxeter planes; the cube can be represented as a spherical tiling, projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not lengths. Straight lines on the sphere are projected as circular arcs on the plane. For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian coordinates of the vertices are while the interior consists of all points with −1 < xi < 1 for all i.
In analytic geometry, a cube's surface with center and edge length of 2a is the locus of all points such that max = a. For a cube of edge length a: As the volume of a cube is the third power of its sides a × a × a, third powers are called cubes, by analogy with squares and second powers. A cube has the largest volume among cuboids with a given surface area. A cube has the largest volume among cuboids with the same total linear size. For a cube whose circumscribing sphere has radius R, for a given point in its 3-dimensional space with distances di from the cube's eight vertices, we have: ∑ i = 1 8 d i 4 8 + 16 R 4 9 = 2. Doubling the cube, or the Delian problem, was the problem posed by ancient Greek mathematicians of using only a compass and straightedge to start with the length of the edge of a given cube and to construct the length of the edge of a cube with twice the volume of the original cube, they were unable to solve this problem, in 1837 Pierre Wantzel proved it to be impossible because the cube root of 2 is not a constructible number.
The cube has three uniform colorings, named by the colors of the square faces around each vertex: 111, 112, 123. The cube has three classes of symmetry, which can be represented by vertex-transitive coloring the faces; the highest octahedral symmetry Oh has all the faces the same color. The dihedral symmetry D4h comes from the cube being a prism, with all four sides being the same color; the lowest symmetry D2h is a prismatic symmetry, with sides alternating colors, so there are three colors, paired by opposite sides. Each symmetry form has a different Wythoff symbol. A cube has eleven nets: that is, there are eleven ways to flatten a hollow cube by cutting seven edges. To color the cube so that no two adjacent faces have the same color, one would need at least three colors; the cube is the cell of the only regular tiling of three-dimensional Euclidean space. It is unique among the Platonic solids in having faces with an number of sides and it is the only member of that group, a zonohedron; the cube can be cut into six identical square pyramids.
If these square pyramids are attached to the faces of a second cube, a rhombic dodecahedron is obtained. The analogue of a cube in four-dimensional Euclidean space has a special name—a tesseract or hypercube. More properly, a hypercube is the analogue of the cube in n-dimensional Euclidean space and a tesseract is the order-4 hypercube. A hypercube is called a measure polytope. There are analogues of the cube in lower dimensions too: a point in dimension 0, a line segment in one dimension and a square in two dimensions; the quotient of the cube by the antipodal map yields the hemicube. If the original cube has edge length 1, its dual polyhedron has edge length 2 / 2; the cube is a special case in various classes of general polyhedra: The vertices of a cube can be grouped into two groups of four, each forming a regular tetrahedron. These two together form the stella octangula; the int
Galena called lead glance, is the natural mineral form of lead sulfide. It is an important source of silver. Galena is one of the most abundant and distributed sulfide minerals, it crystallizes in the cubic crystal system showing octahedral forms. It is associated with the minerals sphalerite and fluorite. Galena is the main ore of lead, used since ancient times; because of its somewhat low melting point, it was easy to liberate by smelting. It forms in low-temperature sedimentary deposits. In some deposits the galena contains about 1–2% silver, a byproduct that far outweighs the main lead ore in revenue. In these deposits significant amounts of silver occur as included silver sulfide mineral phases or as limited silver in solid solution within the galena structure; these argentiferous galenas have long been an important ore of silver. Galena deposits are found worldwide in various environments. Noted deposits include those at Freiberg in Saxony. In the United States, it occurs most notably in the Mississippi Valley type deposits of the Lead Belt in southeastern Missouri, in the Driftless Area of Illinois and Wisconsin.
Galena was a major mineral of the zinc-lead mines of the tri-state district around Joplin in southwestern Missouri and the adjoining areas of Kansas and Oklahoma. Galena is an important ore mineral in the silver mining regions of Colorado, Idaho and Montana. Of the latter, the Coeur d'Alene district of northern Idaho was most prominent. Galena is the official state mineral of the U. S. states of Wisconsin. The largest documented crystal of galena is composite cubo-octahedra from the Great Laxey Mine, Isle of Man, measuring 25 cm × 25 cm × 25 cm. Galena belongs to the octahedral sulfide group of minerals that have metal ions in octahedral positions, such as the iron sulfide pyrrhotite and the nickel arsenide niccolite; the galena group is named after its most common member, with other isometric members that include manganese bearing alabandite and niningerite. Divalent lead cations and sulfur anions form a close-packed cubic unit cell much like the mineral halite of the halide mineral group. Zinc, iron, antimony, arsenic and selenium occur in variable amounts in galena.
Selenium substitutes for sulfur in the structure constituting a solid solution series. The lead telluride mineral altaite has the same crystal structure as galena. Within the weathering or oxidation zone galena alters to cerussite. Galena exposed to acid mine drainage can be oxidized to anglesite by occurring bacteria and archaea, in a process similar to bioleaching. One of the oldest uses of galena was in the eye cosmetic kohl. In Ancient Egypt, this was applied around the eyes to reduce the glare of the desert sun and to repel flies, which were a potential source of disease. Galena is the primary ore of lead, used in making lead–acid batteries. Galena is mined for its silver content, such as at the Galena Mine in northern Idaho. Known as "potter's ore", galena is used in a green glaze applied to pottery. Galena is a semiconductor with a small band gap of about 0.4 eV, which found use in early wireless communication systems. It was used as the crystal in crystal radio receivers, in which it was used as a point-contact diode capable of rectifying alternating current to detect the radio signals.
The galena crystal was used with a sharp wire, known as a "cat's whisker" in contact with it. The operation of the radio required that the point of contact on the galena be shifted about to find a part of the crystal that acted as a rectifying diode. Making such wireless receivers was a popular home hobby in Britain and other European countries during the 1930s. Scientists associated with the investigation of the diode effect are Karl Ferdinand Braun and Jagadish Bose. In modern wireless communication systems, galena detectors have been replaced by more reliable semiconductor devices. List of minerals Lead smelter Klein, Cornelis. Manual of Mineralogy. Wiley. Pp. 274–276. ISBN 0-471-80580-7. Case Studies in Environmental Medicine: Lead Toxicity. ToxFAQs: Lead. Mineral Information Institute entry for lead
A crystal or crystalline solid is a solid material whose constituents are arranged in a ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations; the scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification; the word crystal derives from the Ancient Greek word κρύσταλλος, meaning both "ice" and "rock crystal", from κρύος, "icy cold, frost". Examples of large crystals include snowflakes and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Examples of polycrystals include most metals, rocks and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever.
Examples of amorphous solids include glass and many plastics. Despite the name, lead crystal, crystal glass, related products are not crystals, but rather types of glass, i.e. amorphous solids. Crystals are used in pseudoscientific practices such as crystal therapy, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements; the scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement.. Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a polycrystalline structure. In the final block of ice, each of the small crystals is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does not have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries.
Most macroscopic inorganic solids are polycrystalline, including all metals, ice, etc. Solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids called glassy, vitreous, or noncrystalline; these have no periodic order microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does. A crystal structure is characterized by its unit cell, a small imaginary box containing one or more atoms in a specific spatial arrangement; the unit cells are stacked in three-dimensional space to form the crystal. The symmetry of a crystal is constrained by the requirement that the unit cells stack with no gaps. There are 219 possible crystal symmetries, called crystallographic space groups; these are grouped into 7 crystal systems, such as hexagonal crystal system. Crystals are recognized by their shape, consisting of flat faces with sharp angles.
These shape characteristics are not necessary for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is present and easy to see. Euhedral crystals are those with well-formed flat faces. Anhedral crystals do not because the crystal is one grain in a polycrystalline solid; the flat faces of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of low Miller index. This occurs; as a crystal grows, new atoms attach to the rougher and less stable parts of the surface, but less to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, using them to infer the underlying crystal symmetry.
A crystal's habit is its visible external shape. This is determined by the crystal structure, the specific crystal chemistry and bonding, the conditions under which the crystal formed. By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock. Crystals found in rocks range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are found; as of 1999, the world's largest known occurring crystal is a crystal of beryl from Malakialina, Madagascar, 18 m long and 3.5 m in diameter, weighing 380,000 kg. Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock; the vast majority of igneous rocks are formed from molten magma and the degree of crystallization depends on the conditions under which they solidified. Such rocks as granite, which have cooled slowly and under great pressures, have crystallized.
In chemistry and materials science the'coordination number' called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand; this number is determined somewhat differently for molecules than for crystals. For molecules and polyatomic ions the coordination number of an atom is determined by counting the other atoms to which it is bonded. For example, − has Cr3+ as its central cation, which has a coordination number of 6 and is described as hexacoordinate; however the solid-state structures of crystals have less defined bonds, in these cases a count of neighboring atoms is employed. The simplest method is one used in materials science; the usual value of the coordination number for a given structure refers to an atom in the interior of a crystal lattice with neighbors in all directions. In contexts where crystal surfaces are important, such as materials science and heterogeneous catalysis, the number of neighbors of an interior atom is the bulk coordination number, while the number of surface neighbors of an atom at the surface of the crystal is the surface coordination number.
In chemistry, coordination number, defined in 1893 by Alfred Werner, is the total number of neighbors of a central atom in a molecule or ion. Although a carbon atom has four chemical bonds in most stable molecules, the coordination number of each carbon is four in methane, three in ethylene, two in acetylene. In effect we count the first bond to each neighboring atom, but not the other bonds. In coordination complexes, only the first or sigma bond between each ligand and the central atom counts, but not any pi bonds to the same ligands. In tungsten hexacarbonyl, W6, the coordination number of tungsten is counted as six although pi as well as sigma bonding is important in such metal carbonyls; the most common coordination number for d-block transition metal complexes is 6, with an octahedral geometry. The observed range is 2 to 9. Metals in the f-block can accommodate higher coordination number due to their greater ionic radii and availability of more orbitals for bonding. Coordination numbers of 8 to 12 are observed for f-block elements.
For example, with bidentate nitrate ions as ligands, CeIV and ThIV form the 12-coordinate ions 2− and 2−. When the surrounding ligands are much smaller than the central atom higher coordination numbers may be possible. One computational chemistry study predicted a stable PbHe2+15 ion composed of a central lead ion coordinated with no fewer than 15 helium atoms. At the opposite extreme, steric shielding can give rise to unusually low coordination numbers. An rare instance of a metal adopting a coordination number of 1 occurs in the terphenyl-based arylthallium complex 2,6-Tipp2C6H3Tl, where Tipp is the 2,4,6-triisopropylphenyl group. For π-electron ligands such as the cyclopentadienide ion −, alkenes and the cyclooctatetraenide ion 2−, the number of atoms in the π-electron system that bind to the central atom is termed the hapticity. In ferrocene the hapticity, η, of each cyclopentadienide anion is five, Fe2. There are various ways of assigning the contribution made to the coordination number of the central iron atom by each cyclopentadienide ligand.
The contribution could be assigned as one since there is one ligand, or as five since there are five neighbouring atoms, or as three since there are three electron pairs involved. The count of electron pairs is taken. In order to determine the coordination number of an atom in a crystal, the crystal structure has first to be determined; this is achieved using neutron or electron diffraction. Once the positions of the atoms within the unit cell of the crystal are known the coordination number of an atom can be determined. For molecular solids or coordination complexes the units of the polyatomic species can be detected and a count of the bonds can be performed. Solids with lattice structures which includes metals and many inorganic solids can have regular structures where coordinating atoms are all at the same distance and they form the vertices of a coordination polyhedron. However, there are many such solids where the structures are irregular. In materials science, the bulk coordination number of a given atom in the interior of a crystal lattice is the number of nearest neighbours to a given atom.
For an atom at a surface of a crystal, the surface coordination number is always less than the bulk coordination number. The surface coordination number is dependent on the Miller indices of the surface. In a body-centered cubic crystal, the bulk coordination number is 8, for the surface, the surface coordination number is 4.α-Aluminium has a regular cubic close packed structure, where each aluminium atom has 12 nearest neighbors, 6 in the same plane and 3 above and below and the coordination polyhedron is a cuboctahedron. Α-Iron has a body centered cubic structure where each iron atom has 8 nearest neighbors situated at the corners of a cube. The two most common allotropes of carbon have different coordination numbers. In diamond, each carbon atom is at the centre of a regular tetrahedron formed by four other carbon atoms, the coordination number is four, as for methane. Graphite is made of two-dimensional layers in which each carbon is covalently bonded to three other carbons.