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a range decrease over the last thousand years, surviving only in Central European forests with the last wild population going extinct in Bialowieza forest in 1921. Starting from 1929, reintroduction of animals from zoos allowed the species to recover in the wild. The historical range of Bison bonasus was limited to for...	{ "page_id": 59573391, "source": null, "title": "Conservation paleobiology" }
The analyses of the fossil record from past warm intervals of Earth's history (Paleogene-Eocene Thermal Maximum) provides an adequate comparison to test this hypothesis. Data shows that, during warmer climates, the frequency and diversity of insect damage to North American plants increased significantly, providing supp...	{ "page_id": 59573391, "source": null, "title": "Conservation paleobiology" }
In the Babylonian magico-medical tradition, Šulak is the lurker of the bathroom or the demon of the privy. Šulak appears in the Babylonian Diagnostic Handbook (Tablet XXVII), in which various diseases are described and attributed to the hand of a god, goddess, or spirit. A lurker is a type of demon who lies in wait in ...	{ "page_id": 22414479, "source": null, "title": "Šulak" }
long enough to walk half a mil, Stroke and epilepsy were closely related in ancient medicine. This law is not included in the Mishneh Torah. The "demon of the privy" is the type of unclean spirit that in the early Christian era was regarded as causing both physical and spiritual affliction. == See also == Triptych, May...	{ "page_id": 22414479, "source": null, "title": "Šulak" }
A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data are represented in a 3D plot they may be called waterfall displays. Spectrograms are used e...	{ "page_id": 263317, "source": null, "title": "Spectrogram" }
Spectrograms may be created from a time-domain signal in one of two ways: approximated as a filterbank that results from a series of band-pass filters (this was the only way before the advent of modern digital signal processing), or calculated from the time signal using the Fourier transform. These two methods actually...	{ "page_id": 263317, "source": null, "title": "Spectrogram" }
not possible to reverse the process and generate a copy of the original signal from a spectrogram, though in situations where the exact initial phase is unimportant it may be possible to generate a useful approximation of the original signal. The Analysis & Resynthesis Sound Spectrograph is an example of a computer pro...	{ "page_id": 263317, "source": null, "title": "Spectrogram" }
of phonetics and speech synthesis are often facilitated through the use of spectrograms. In deep learning-keyed speech synthesis, spectrogram (or spectrogram in mel scale) is first predicted by a seq2seq model, then the spectrogram is fed to a neural vocoder to derive the synthesized raw waveform. By reversing the proc...	{ "page_id": 263317, "source": null, "title": "Spectrogram" }
speech deficits in cochlear implant users and phoneme class recognition to extract phone-attribute features. In order to obtain a speaker's pronunciation characteristics, some researchers proposed a method based on an idea from bionics, which uses spectrogram statistics to achieve a characteristic spectrogram to give a...	{ "page_id": 263317, "source": null, "title": "Spectrogram" }
The Odonata Records Committee is the recognised national body which verifies records of rare vagrant dragonflies in Britain. It was set up in 1998 and consists of six members. Its chairman is Adrian Parr. Decisions on records are published in Atropos and the Journal of the British Dragonfly Society. == References ==	{ "page_id": 2294937, "source": null, "title": "Odonata Records Committee" }
Infinite Energy: The Magazine of New Energy Technology, more commonly referred to simply as Infinite Energy, is a bi-monthly magazine published in New Hampshire that details theories and experiments concerning alternative energy, new science and new physics. The phrase "new energy" in the subtitle is a euphemism for pe...	{ "page_id": 1115289, "source": null, "title": "Infinite Energy (magazine)" }
of promising research, resigned from MIT and became one of the most vocal defenders of cold fusion, or what became known in later years as low-energy nuclear reactions (LENR). He launched Infinite Energy to serve as a platform for the continued exploration of LENR, alternative energy technologies, and unconventional sc...	{ "page_id": 1115289, "source": null, "title": "Infinite Energy (magazine)" }
In botany, an evergreen is a plant which has foliage that remains green and functional throughout the year. This contrasts with deciduous plants, which lose their foliage completely during the winter or dry season. Consisting of many different species, the unique feature of evergreen plants lends itself to various envi...	{ "page_id": 66719, "source": null, "title": "Evergreen" }
or dry/wet season. Evergreen trees also lose leaves, but each tree loses its leaves gradually and not all at once. Most tropical rainforest plants are considered to be evergreens, replacing their leaves gradually throughout the year as the leaves age and fall, whereas species growing in seasonally arid climates may be ...	{ "page_id": 66719, "source": null, "title": "Evergreen" }
it is too cold for the organic matter in the soil to decay rapidly, so the nutrients in the soil are less easily available to plants, thus favoring evergreens. In temperate climates, evergreens can reinforce their own survival; evergreen leaf and needle litter has a higher carbon–nitrogen ratio than deciduous leaf litt...	{ "page_id": 66719, "source": null, "title": "Evergreen" }
The molecular formula C21H24N2O3 may refer to: Ajmalicine 16-Hydroxytabersonine Lochnericine Preakuammicine Raucaffrinoline Vobasine	{ "page_id": 26608799, "source": null, "title": "C21H24N2O3" }
In the fields of horticulture and botany, the term deciduous () means "falling off at maturity" and "tending to fall off", in reference to trees and shrubs that seasonally shed leaves, usually in the autumn; to the shedding of petals, after flowering; and to the shedding of ripe fruit. The antonym of deciduous in the b...	{ "page_id": 66722, "source": null, "title": "Deciduous" }
pollen for wind-pollinated plants and increases the visibility of the flowers to insects in insect-pollinated plants. This strategy is not without risks, as the flowers can be damaged by frost or, in dry season regions, result in water stress on the plant. Spring leafout and fall leaf drop are triggered by a combinatio...	{ "page_id": 66722, "source": null, "title": "Deciduous" }
they are produced in the foliage in late summer, when sugars are trapped in the leaves after the process of abscission begins. Parts of the world that have showy displays of bright autumn colors are limited to locations where days become short and nights are cool. The New England region of the United States and southea...	{ "page_id": 66722, "source": null, "title": "Deciduous" }
of the plant, the cells of the abscission layer remain connected; in autumn, or when under stress, the auxin flow from the leaf decreases or stops, triggering cellular elongation within the abscission layer. The elongation of these cells breaks the connection between the different cell layers, allowing the leaf to brea...	{ "page_id": 66722, "source": null, "title": "Deciduous" }
leaves in winter may reduce damage from insects; repairing leaves and keeping them functional may be more costly than just losing and regrowing them. Removing leaves also reduces cavitation which can damage xylem vessels in plants. This then allows deciduous plants to have xylem vessels with larger diameters and theref...	{ "page_id": 66722, "source": null, "title": "Deciduous" }
have great seasonable temperature variability. Growth occurs during warm summers, leaf drop in autumn, and dormancy during cold winters. These seasonally distinctive communities have diverse life forms that are impacted greatly by the seasonality of their climate, mainly temperature and precipitation rates. These varyi...	{ "page_id": 66722, "source": null, "title": "Deciduous" }
An alloy is a mixture of chemical elements of which in most cases at least one is a metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Metallic alloys often have properties that differ from those of the pure elements from which they are made. The va...	{ "page_id": 1187, "source": null, "title": "Alloy" }
silver (silver and copper), steel or silicon steel (iron with non-metallic carbon or silicon respectively), solder, brass, pewter, duralumin, bronze, and amalgams. Alloys are used in a wide variety of applications, from the steel alloys, used in everything from buildings to automobiles to surgical tools, to exotic tita...	{ "page_id": 1187, "source": null, "title": "Alloy" }
By adding chromium to steel, its resistance to corrosion can be enhanced, creating stainless steel, while adding silicon will alter its electrical characteristics, producing silicon steel. Like oil and water, a molten metal may not always mix with another element. For example, pure iron is almost completely insoluble w...	{ "page_id": 1187, "source": null, "title": "Alloy" }
its components. Steel was another common alloy. However, in ancient times, it could only be created as an accidental byproduct from the heating of iron ore in fires (smelting) during the manufacture of iron. Other ancient alloys include pewter, brass and pig iron. In the modern age, steel can be created in many forms. ...	{ "page_id": 1187, "source": null, "title": "Alloy" }
during the alloying process to remove excess impurities, using fluxes, chemical additives, or other methods of extractive metallurgy. == Theory == Alloying a metal is done by combining it with one or more other elements. The most common and oldest alloying process is performed by heating the base metal beyond its melti...	{ "page_id": 1187, "source": null, "title": "Alloy" }
The electrical and thermal conductivity of alloys is usually lower than that of the pure metals. The physical properties, such as density, reactivity, Young's modulus of an alloy may not differ greatly from those of its base element, but engineering properties such as tensile strength, ductility, and shear strength may...	{ "page_id": 1187, "source": null, "title": "Alloy" }
can be softened by annealing, which recrystallizes the alloy and repairs the defects, but not as many can be hardened by controlled heating and cooling. Many alloys of aluminium, copper, magnesium, titanium, and nickel can be strengthened to some degree by some method of heat treatment, but few respond to this to the s...	{ "page_id": 1187, "source": null, "title": "Alloy" }
change to its low temperature state, leaving those crystals very hard but much less ductile (more brittle). While the high strength of steel results when diffusion and precipitation is prevented (forming martensite), most heat-treatable alloys are precipitation hardening alloys, that depend on the diffusion of alloying...	{ "page_id": 1187, "source": null, "title": "Alloy" }
low weight, these alloys became widely used in many forms of industry, including the construction of modern aircraft. === Mechanisms === When a molten metal is mixed with another substance, there are two mechanisms that can cause an alloy to form, called atom exchange and the interstitial mechanism. The relative size o...	{ "page_id": 1187, "source": null, "title": "Alloy" }
could be forged from a red heat to make objects such as tools, weapons, and nails. In many cultures it was shaped by cold hammering into knives and arrowheads. They were often used as anvils. Meteoric iron was very rare and valuable, and difficult for ancient people to work. === Bronze and brass === Iron is usually fou...	{ "page_id": 1187, "source": null, "title": "Alloy" }
temperature). Amalgams have been used since 200 BC in China for gilding objects such as armor and mirrors with precious metals. The ancient Romans often used mercury-tin amalgams for gilding their armor. The amalgam was applied as a paste and then heated until the mercury vaporized, leaving the gold, silver, or tin beh...	{ "page_id": 1187, "source": null, "title": "Alloy" }
sometimes added individually in varying amounts, or added together, making a wide variety of objects, ranging from practical items such as dishes, surgical tools, candlesticks or funnels, to decorative items like ear rings and hair clips. The earliest examples of pewter come from ancient Egypt, around 1450 BC. The use ...	{ "page_id": 1187, "source": null, "title": "Alloy" }
widespread around 1200 BC, mainly because of interruptions in the trade routes for tin, the metal was much softer than bronze. However, very small amounts of steel, (an alloy of iron and around 1% carbon), was always a byproduct of the bloomery process. The ability to modify the hardness of steel by heat treatment had ...	{ "page_id": 1187, "source": null, "title": "Alloy" }
steel. Steel is an alloy of iron and carbon, but the term alloy steel usually only refers to steels that contain other elements— like vanadium, molybdenum, or cobalt—in amounts sufficient to alter the properties of the base steel. Since ancient times, when steel was used primarily for tools and weapons, the methods of ...	{ "page_id": 1187, "source": null, "title": "Alloy" }
silicon steel, launching the search for other possible alloys of steel. Robert Forester Mushet found that by adding tungsten to steel it could produce a very hard edge that would resist losing its hardness at high temperatures. "R. Mushet's special steel" (RMS) became the first high-speed steel. Mushet's steel was quic...	{ "page_id": 1187, "source": null, "title": "Alloy" }
alloy to construct the first airplane engine in 1903. During the time between 1865 and 1910, processes for extracting many other metals were discovered, such as chromium, vanadium, tungsten, iridium, cobalt, and molybdenum, and various alloys were developed. Prior to 1910, research mainly consisted of private individua...	{ "page_id": 1187, "source": null, "title": "Alloy" }
A Cypress forest is a western United States plant association typically dominated by one or more cypress species. Example species comprising the canopy include Cupressus macrocarpa. In some cases these forests have been severely damaged by goats, cattle and other grazing animals. While cypress species are clearly domin...	{ "page_id": 19989669, "source": null, "title": "Cypress forest" }
Blanche Muriel Bristol (21 April 1888 – 15 March 1950) was a British phycologist who worked at Rothamsted Research (then Rothamsted Experimental Station) in 1919. Her research focused on the mechanisms by which algae acquire nutrients. == Statistics and tea == One day at Rothamsted, Ronald Fisher offered Bristol a cup ...	{ "page_id": 5571750, "source": null, "title": "Muriel Bristol" }
Orotidine 5'-monophosphate (OMP), also known as orotidylic acid, is a pyrimidine nucleotide which is the last intermediate in the biosynthesis of uridine monophosphate. OMP is formed from orotate and phosphoribosyl pyrophosphate by the enzyme orotate phosphoribosyltransferase. In humans, the enzyme UMP synthase convert...	{ "page_id": 11273383, "source": null, "title": "Orotidine 5'-monophosphate" }
The molecular formula C25H29N3O3 may refer to: Adimolol BMS-202	{ "page_id": 26608808, "source": null, "title": "C25H29N3O3" }
Microwave digestion is a chemical technique used to decompose sample material into a solution suitable for quantitative elemental analysis. It is commonly used to prepare samples for analysis using inductively coupled plasma mass spectrometry (ICP-MS), atomic absorption spectroscopy, and atomic emission spectroscopy (i...	{ "page_id": 29623466, "source": null, "title": "Microwave digestion" }
fast sample heating, reducing digestion time to as little as one hour. Another common means to decompose samples for elemental analysis is dry-ashing, in which samples are incinerated in a muffle furnace. The resultant ash is then dissolved for analysis, usually into dilute nitric acid. While this method is simple, ine...	{ "page_id": 29623466, "source": null, "title": "Microwave digestion" }
Supermicelle is a hierarchical micelle structure (supramolecular assembly) where individual components are also micelles. Supermicelles are formed via bottom-up chemical approaches, such as self-assembly of long cylindrical micelles into radial cross-, star- or dandelion-like patterns in a specially selected solvent; s...	{ "page_id": 48759979, "source": null, "title": "Supermicelle" }
The molecular formula C15H21NO4 (molar mass: 279.33 g/mol, exact mass: 279.1471 u) may refer to: Afurolol Metalaxyl	{ "page_id": 26608813, "source": null, "title": "C15H21NO4" }
The molecular formula C19H22N2O3 (molar mass: 326.39 g/mol, exact mass: 326.1630 u) may refer to: Bumadizone Ervatinine 25CN-NBOMe	{ "page_id": 61211822, "source": null, "title": "C19H22N2O3" }
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, 'a measure'. Models can be divided into physical models (e.g. a ship model or a fashion model) and...	{ "page_id": 263343, "source": null, "title": "Model" }
(logic), a structure (a set of items, such as natural numbers 1, 2, 3,..., along with mathematical operations such as addition and multiplication, and relations, such as < {\displaystyle <} ) that satisfies a given system of axioms (basic truisms), i.e. that satisfies the statements of a given theory Model (CGI), a mat...	{ "page_id": 263343, "source": null, "title": "Model" }
the design of ductwork systems, pollution control equipment, food processing machines, and mixing vessels. Transparent flow models are used in this case to observe the detailed flow phenomenon. These models are scaled in terms of both geometry and important forces, for example, using Froude number or Reynolds number sc...	{ "page_id": 263343, "source": null, "title": "Model" }
surface of an object in three dimensions via specialized software Medical model, a proposed "set of procedures in which all doctors are trained" Mental model, in psychology, an internal representation of external reality Model (logic), a set along with a collection of finitary operations, and relations that are defined...	{ "page_id": 263343, "source": null, "title": "Model" }
between concrete and mathematical models and proposes computer simulations (computational models) as their own class of models. == Uses of models == According to Bruce Edmonds, there are at least 5 general uses for models: Prediction: reliably anticipating unknown data, including data within the domain of the training ...	{ "page_id": 263343, "source": null, "title": "Model" }
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and the proces...	{ "page_id": 1200, "source": null, "title": "Atomic physics" }
By this consideration, atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though both deal with very large numbers of atoms. == Electronic configuration == Electrons form notional shells around the nucleus. These are normally in a ground state but can be excited by the absorpt...	{ "page_id": 1200, "source": null, "title": "Atomic physics" }
are no such rules for excitation by collision processes. === Bohr Model of the Atom === The Bohr model, proposed by Niels Bohr in 1913, is a revolutionary theory describing the structure of the hydrogen atom. It introduced the idea of quantized orbits for electrons, combining classical and quantum physics. Key Postulat...	{ "page_id": 1200, "source": null, "title": "Atomic physics" }
emitted/absorbed radiation. • E f , E i : {\displaystyle E_{f},E_{i}:} Final and initial energy levels. == History and developments == One of the earliest steps towards atomic physics was the recognition that matter was composed of atoms. It forms a part of the texts written in 6th century BC to 2nd century BC, such as...	{ "page_id": 1200, "source": null, "title": "Atomic physics" }
occur which need different descriptions. == Significant atomic physicists == == See also == Particle physics Isomeric shift Atomism Ionisation Quantum Mechanics Electron Correlation Quantum Chemistry Bound State == Bibliography == Will Raven (2025). Atomic Physics for Everyone. Springer Nature. doi:10.1007/978-3-031-69...	{ "page_id": 1200, "source": null, "title": "Atomic physics" }
SqueezeNet is a deep neural network for image classification released in 2016. SqueezeNet was developed by researchers at DeepScale, University of California, Berkeley, and Stanford University. In designing SqueezeNet, the authors' goal was to create a smaller neural network with fewer parameters while achieving compet...	{ "page_id": 57410739, "source": null, "title": "SqueezeNet" }
computer network. However, it's important to note that SqueezeNet is not a "squeezed version of AlexNet." Rather, SqueezeNet is an entirely different DNN architecture than AlexNet. What SqueezeNet and AlexNet have in common is that both of them achieve approximately the same level of accuracy when evaluated on the Imag...	{ "page_id": 57410739, "source": null, "title": "SqueezeNet" }
Alais or Allais is the first carbonaceous chondrite meteorite identified. It fell near Alès in 1806 in multiple fragments which together weighed 6 kg (13 lb 4 oz), although only 0.26 kg (9.2 oz) remains. The meteorite contains a number of elements in similar proportions to the Solar System in its primordial state. It a...	{ "page_id": 63571124, "source": null, "title": "Alais meteorite" }
kg (13 lb 4 oz), it has been subject to substantial scientific examination and currently only 260 g (9.2 oz) remains. A fragment, weighing 39.3 g (1.39 oz) is held by the National Museum of Natural History, France. === Composition and classification === The meteorite is one of five known meteorites belonging to the CI ...	{ "page_id": 63571124, "source": null, "title": "Alais meteorite" }
London: The Geological Society. pp. 1–13. ISBN 978-1-86239-194-9. Kerridge, John F.; Macdougall, J. Douglas; Marti, K. (1979). "Clues to the origin of sulfide minerals in CI chondrites". Earth and Planetary Science Letters. 43 (3): 359–367. Bibcode:1979E&PSL..43..359K. doi:10.1016/0012-821X(79)90091-8. Lauretta, Dante ...	{ "page_id": 63571124, "source": null, "title": "Alais meteorite" }
BOP (benzotriazol-1-yloxytris(dimethylamino)phosphonium hexafluorophosphate) is a reagent commonly used for the synthesis of amides from carboxylic acids and amines in peptide synthesis. It can be prepared from 1-hydroxybenzotriazole and a chlorophosphonium reagent under basic conditions. This reagent has advantages in...	{ "page_id": 12649653, "source": null, "title": "BOP reagent" }
H2 producing hydrogenase may refer to: Ferredoxin hydrogenase, an enzyme Hydrogenase (acceptor), an enzyme	{ "page_id": 38339763, "source": null, "title": "H2 producing hydrogenase" }
In quantum mechanics, an atomic orbital ( ) is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nuc...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
electron configuration that is a product of simpler hydrogen-like atomic orbitals. The repeating periodicity of blocks of 2, 6, 10, and 14 elements within sections of periodic table arises naturally from total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher val...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
Electrons retain particle-like properties such as: each wave state has the same electric charge as its electron particle. Each wave state has a single discrete spin (spin up or spin down) depending on its superposition. Thus, electrons cannot be described simply as solid particles. An analogy might be that of a large a...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
n {\displaystyle n} and l {\displaystyle l} , but m l {\displaystyle m_{l}} would definitely be 1. Eigenstates make it easier to deal with the math. You can choose a different basis of eigenstates by superimposing eigenstates from any other basis (see Real orbitals below). === Formal quantum mechanical definition === A...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless, one has to keep in mind that electrons are fermions ruled by the Pauli exclusion principle and cannot be distinguished from each other. Moreover, it sometimes happens...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons: The hydrogen-like orbitals are derived from the exact solutions of the Schrödinger equation for one electron and a nucleus, for a hydrogen-like atom. The part of the function that depends on distanc...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
in 1897, it became clear that atoms were not the smallest building blocks of nature, but were rather composite particles. The newly discovered structure within atoms tempted many to imagine how the atom's constituent parts might interact with each other. Thomson theorized that multiple electrons revolve in orbit-like r...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
this), and more importantly explained the origin of spectral lines. After Bohr's use of Einstein's explanation of the photoelectric effect to relate energy levels in atoms with the wavelength of emitted light, the connection between the structure of electrons in atoms and the emission and absorption spectra of atoms be...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
In our current understanding of physics, the Bohr model is called a semi-classical model because of its quantization of angular momentum, not primarily because of its relationship with electron wavelength, which appeared in hindsight a dozen years after the Bohr model was proposed. The Bohr model was able to explain th...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. ...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
=== Orbital notation and subshells === Orbitals have been given names, which are usually given in the form: X t y p e {\displaystyle X\,\mathrm {type} \ } where X is the energy level corresponding to the principal quantum number n; type is a lower-case letter denoting the shape or subshell of the orbital, corresponding...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
the same form. In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy. They can be obtained analytically, meaning that the resulting orbitals are products of a polynomial series, and exponential and trigon...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers. These quantum numbers occur only in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the at...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
around that axis and the orbital contribution to the magnetic moment of an electron via the Ampèrian loop model. Within a subshell ℓ {\displaystyle \ell } , m ℓ {\displaystyle m_{\ell }} obtains the integer values in the range − ℓ ≤ m ℓ ≤ ℓ {\displaystyle -\ell \leq m_{\ell }\leq \ell } . The above results may be summa...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
would be no sense in distinguishing m = +1 from m = −1. As such, the model is most useful when applied to physical systems that share these symmetries. The Stern–Gerlach experiment—where an atom is exposed to a magnetic field—provides one such example. === Real orbitals === Instead of the complex orbitals described abo...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
for }}m>0\end{cases}}\\[4pt]&={\begin{cases}{\frac {i}{\sqrt {2}}}\left(\psi _{n,\ell ,-\|m\|}-(-1)^{m}\psi _{n,\ell ,\|m\|}\right)&{\text{ for }}m<0\\[2pt]\psi _{n,\ell ,\|m\|}&{\text{ for }}m=0\\[4pt]{\frac {1}{\sqrt {2}}}\left(\psi _{n,\ell ,-\|m\|}+(-1)^{m}\psi _{n,\ell ,\|m\|}\right)&{\text{ for }}m>0\end{cases}}\end{aligne...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
{\displaystyle 2{\text{p}}_{\pm 1}=\psi _{2,1,\pm 1}} ; the first symbol is the n quantum number, the second character is the symbol for that particular ℓ quantum number and the subscript is the m quantum number. As an example of how the full orbital names are generated for real orbitals, one may calculate ψ n , 1 , ± ...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
z. We then use the abbreviated polynomial as a subscript label for the atomic state, using the same nomenclature as above to indicate the n {\displaystyle n} and ℓ {\displaystyle \ell } quantum numbers. ψ n , 1 , − 1 real = n p y = i 2 ( n p − 1 + n p + 1 ) ψ n , 1 , 0 real = n p z = 2 p 0 ψ n , 1 , + 1 real = n p x = ...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
to be found. The diagrams cannot show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or contour surfaces where the probability dens...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
modes and the shape is spherically symmetric. Nodal planes and nodal spheres are surfaces on which the probability density vanishes. The number of nodal surfaces is controlled by the quantum numbers n and ℓ. An orbital with azimuthal quantum number ℓ has ℓ radial nodal planes passing through the origin. For example, th...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
radial, following a sinusoidal radial component as well). See illustration of a cross-section of these nested shells, at right. The s orbitals for all n numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular ...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
orbital consists of three regions of high probability density: a torus in between two pear-shaped regions placed symmetrically on its z axis. The overall total of 18 directional lobes point in every primary axis direction and between every pair. There are seven f orbitals, each with shapes more complex than those of th...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
resulting total density of all the atomic orbitals in that subshell (those with the same ℓ) is spherical. This is known as Unsöld's theorem. === Orbitals table === This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of a...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
the analogy, the mean vibrational displacement of each bit of drum membrane from the equilibrium point over many cycles (a measure of average drum membrane velocity and momentum at that point) must be considered relative to that point's distance from the center of the drum head. If this displacement is taken as being a...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
of which have no angular momentum, might perhaps be that of a Keplerian orbit with the orbital eccentricity of 1 but a finite major axis, not physically possible (because particles were to collide), but can be imagined as a limit of orbits with equal major axes but increasing eccentricity. Below, a number of drum membr...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
Such features again emphasize that the shapes of atomic orbitals are a direct consequence of the wave nature of electrons. p-type drum modes and wave functions d-type drum modes == Orbital energy == In atoms with one electron (hydrogen-like atom), the energy of an orbital (and, consequently, any electron in the orbital...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
\ell =2} , the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s orbital in the next higher shell; when ℓ = 3 {\displaystyle \ell =3} the energy is pushed into the shell two steps higher. The filling of the 3d orbitals does not occur until the 4s orbitals have...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as the spin magnetic quantum number ms. Thus, two electrons may occupy a single orbital, so long as they have different values of ms. Because ms takes one of only two values (⁠1/2⁠ or −⁠1/2⁠), at most two electrons ...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
is the order for filling the "subshell" orbitals, which also gives the order of the "blocks" in the periodic table: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p The "periodic" nature of the filling of orbitals, as well as emergence of the s, p, d, and f "blocks", is more obvious if this or...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
periodic table); this results in 6s valence electrons becoming lowered in energy. Examples of significant physical outcomes of this effect include the lowered melting temperature of mercury (which results from 6s electrons not being available for metal bonding) and the golden color of gold and caesium. In the Bohr mode...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
=== In late period 8 elements, a hybrid of 8p3/2 and 9p1/2 is expected to exist, where "3/2" and "1/2" refer to the total angular momentum quantum number. This "pp" hybrid may be responsible for the p-block of the period due to properties similar to p subshells in ordinary valence shells. Energy levels of 8p3/2 and 9p1...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
photons that are greater or lower in energy cannot be absorbed by the electron, because the electron can jump only to one of the orbitals, it cannot jump to a state between orbitals. The result is that only photons of a specific frequency will be absorbed by the atom. This creates a line in the spectrum, known as an ab...	{ "page_id": 1206, "source": null, "title": "Atomic orbital" }
The Eschweiler–Clarke reaction (also called the Eschweiler–Clarke methylation) is a chemical reaction whereby a primary (or secondary) amine is methylated using excess formic acid and formaldehyde. Reductive amination reactions such as this one will not produce quaternary ammonium salts, but instead will stop at the te...	{ "page_id": 2032822, "source": null, "title": "Eschweiler–Clarke reaction" }
The molecular formula C15H22N2O2 may refer to: Alprenoxime, a beta blocker and prodrug to alprenolol Mepindolol, a non-selective beta blocker used to treat glaucoma	{ "page_id": 26608825, "source": null, "title": "C15H22N2O2" }
A Brief History of Time is a 1991 biographical documentary film about the physicist Stephen Hawking, directed by Errol Morris. The title derives from Hawking's bestselling 1988 book A Brief History of Time, but, whereas the book is solely an explanation of cosmology, the film is also a biography of Hawking, featuring i...	{ "page_id": 1443000, "source": null, "title": "A Brief History of Time (film)" }
Hawking. He employed stylized interview sequences, graphic illustrations, and music written by Glass. Morris also included clips from Disney's The Black Hole (1979). Instead of Morris traveling around and filming the various interview subjects in their native surroundings, all of the interviews for this film were shot ...	{ "page_id": 1443000, "source": null, "title": "A Brief History of Time (film)" }

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