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Buckminsterfullerene

Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a football. Each of its 60 carbon atoms is bonded to its three neighbors.

Buckminsterfullerene is a black solid that dissolves in hydrocarbon solvents to produce a violet solution. The substance was discovered in 1985 and has received intense study, although few real world applications have been found.

Molecules of buckminsterfullerene (or of fullerenes in general) are commonly nicknamed buckyballs.

Occurrence
Buckminsterfullerene is the most common naturally occurring fullerene. Small quantities of it can be found in soot.

It also exists in space. Neutral C60 has been observed in planetary nebulae and several types of star. The ionised form, C60+, has been identified in the interstellar medium, where it is the cause of several absorption features known as diffuse interstellar bands in the near-infrared.

History
Theoretical predictions of buckminsterfullerene molecules appeared in the late 1960s and early 1970s. It was first generated in 1984 by Eric Rohlfing, Donald Cox, and Andrew Kaldor using a laser to vaporize carbon in a supersonic helium beam, although the group did not realize that buckminsterfullerene had been produced. In 1985 their work was repeated by Harold Kroto, James R. Heath, Sean C. O'Brien, Robert Curl, and Richard Smalley at Rice University, who recognized the structure of C60 as buckminsterfullerene.

Concurrent but unconnected to the Kroto-Smalley work, astrophysicists were working with spectroscopists to study infrared emissions from giant red carbon stars. Smalley and team were able to use a laser vaporization technique to create carbon clusters which could potentially emit infrared at the same wavelength as had been emitted by the red carbon star. Hence, the inspiration came to Smalley and team to use the laser technique on graphite to generate fullerenes.

Using laser evaporation of graphite the Smalley team found Cn clusters (where n > 20 and even) of which the most common were C60 and C70. A solid rotating graphite disk was used as the surface from which carbon was vaporized using a laser beam creating hot plasma that was then passed through a stream of high-density helium gas. The carbon species were subsequently cooled and ionized resulting in the formation of clusters. Clusters ranged in molecular masses, but Kroto and Smalley found predominance in a C60 cluster that could be enhanced further by allowing the plasma to react longer. They also discovered that C60 is a cage-like molecule, a regular truncated icosahedron.

The experimental evidence, a strong peak at 720 atomic mass units, indicated that a carbon molecule with 60 carbon atoms was forming, but provided no structural information. The research group concluded after reactivity experiments, that the most likely structure was a spheroidal molecule. The idea was quickly rationalized as the basis of an icosahedral symmetry closed cage structure.

Kroto, Curl, and Smalley were awarded the 1996 Nobel Prize in Chemistry for their roles in the discovery of buckminsterfullerene and the related class of molecules, the fullerenes.

In 1989 physicists Wolfgang Krätschmer, Konstantinos Fostiropoulos, and Donald R. Huffman observed unusual optical absorptions in thin films of carbon dust (soot). The soot had been generated by an arc-process between two graphite electrodes in a helium atmosphere where the electrode material evaporates and condenses forming soot in the quenching atmosphere. Among other features, the IR spectra of the soot showed four discrete bands in close agreement to those proposed for C60.

Another paper on the characterization and verification of the molecular structure followed on in the same year (1990) from their thin film experiments, and detailed also the extraction of an evaporable as well as benzene-soluble material from the arc-generated soot. This extract had TEM and X-ray crystal analysis consistent with arrays of spherical C60 molecules, approximately 1.0 nm in van der Waals diameter as well as the expected molecular mass of 720 Da for C60 (and 840 Da for C70) in their mass spectra. The method was simple and efficient to prepare the material in gram amounts per day (1990) which has boosted the fullerene research and is even today applied for the commercial production of fullerenes.

The discovery of practical routes to C60 led to the exploration of a new field of chemistry involving the study of fullerenes.

Etymology
The discoverers of the allotrope named the newfound molecule after American architect R. Buckminster Fuller, who designed many geodesic dome structures that look similar to C60 and who had died in 1983, the year before discovery. Another common name for buckminsterfullerene is "buckyballs".

Synthesis
Soot is produced by laser ablation of graphite or pyrolysis of aromatic hydrocarbons. Fullerenes are extracted from the soot with organic solvents using a Soxhlet extractor. This step yields a solution containing up to 75% of C60, as well as other fullerenes. These fractions are separated using chromatography. Generally, the fullerenes are dissolved in a hydrocarbon or halogenated hydrocarbon and separated using alumina columns.

Structure
Buckminsterfullerene is a truncated icosahedron with 60 vertices, 32 faces (20 hexagons and 12 pentagons where no pentagons share a vertex), and 90 edges (60 edges between 5-membered & 6-membered rings and 30 edges are shared between 6-membered & 6-membered rings), with a carbon atom at the vertices of each polygon and a bond along each polygon edge. The van der Waals diameter of a molecule is about 1.01 nanometers (nm). The nucleus to nucleus diameter of a molecule is about 0.71 nm. The molecule has two bond lengths. The 6:6 ring bonds (between two hexagons) can be considered "double bonds" and are shorter than the 6:5 bonds (between a hexagon and a pentagon). Its average bond length is 0.14 nm. Each carbon atom in the structure is bonded covalently with 3 others. A carbon atom in the can be substituted by a nitrogen or boron atom yielding a  or C59B respectively.

Properties
For a time buckminsterfullerene was the largest known molecule observed to exhibit wave–particle duality. In 2020 the dye molecule phthalocyanine exhibited the duality that is more famously attributed to light, electrons and other small particles and molecules.

Solution

Fullerenes are sparingly soluble in aromatic solvents and carbon disulfide, but insoluble in water. Solutions of pure C60 have a deep purple color which leaves a brown residue upon evaporation. The reason for this color change is the relatively narrow energy width of the band of molecular levels responsible for green light absorption by individual C60 molecules. Thus individual molecules transmit some blue and red light resulting in a purple color. Upon drying, intermolecular interaction results in the overlap and broadening of the energy bands, thereby eliminating the blue light transmittance and causing the purple to brown color change.

crystallises with some solvents in the lattice ("solvates"). For example, crystallization of C60 from benzene solution yields triclinic crystals with the formula C60·4C6H6. Like other solvates, this one readily releases benzene to give the usual face-centred cubic C60. Millimeter-sized crystals of C60 and can be grown from solution both for solvates and for pure fullerenes.

Solid
In solid buckminsterfullerene, the C60 molecules adopt the fcc (face-centered cubic) motif. They start rotating at about −20 °C. This change is associated with a first-order phase transition to an fcc structure and a small, yet abrupt increase in the lattice constant from 1.411 to 1.4154 nm.

solid is as soft as graphite, but when compressed to less than 70% of its volume it transforms into a superhard form of diamond (see aggregated diamond nanorod). films and solution have strong non-linear optical properties; in particular, their optical absorption increases with light intensity (saturable absorption).

forms a brownish solid with an optical absorption threshold at ≈1.6 eV. It is an n-type semiconductor with a low activation energy of 0.1–0.3 eV; this conductivity is attributed to intrinsic or oxygen-related defects. Fcc C60 contains voids at its octahedral and tetrahedral sites which are sufficiently large (0.6 and 0.2 nm respectively) to accommodate impurity atoms. When alkali metals are doped into these voids, C60 converts from a semiconductor into a conductor or even superconductor.

Redox (electron-transfer reactions)
undergoes six reversible, one-electron reductions, ultimately generating. Its oxidation is irreversible. The first reduction occurs at ≈-1.0 V (Fc/), showing that C60 is a reluctant electron acceptor. tends to avoid having double bonds in the pentagonal rings, which makes electron delocalization poor, and results in not being "superaromatic". C60 behaves like an electron deficient alkene. For example, it reacts with some nucleophiles.

Hydrogenation
C60 exhibits a small degree of aromatic character, but it still reflects localized double and single C–C bond characters. Therefore, C60 can undergo addition with hydrogen to give polyhydrofullerenes. C60 also undergoes Birch reduction. For example, C60 reacts with lithium in liquid ammonia, followed by tert-butanol to give a mixture of polyhydrofullerenes such as C60H18, C60H32, C60H36, with C60H32 being the dominating product. This mixture of polyhydrofullerenes can be re-oxidized by 2,3-dichloro-5,6-dicyano-1,4-benzoquinone to give C60 again.

A selective hydrogenation method exists. Reaction of C60 with 9,9′,10,10′-dihydroanthracene under the same conditions, depending on the time of reaction, gives C60H32 and C60H18 respectively and selectively.

Halogenation
Addition of fluorine, chlorine, and bromine occurs for C60. Fluorine atoms are small enough for a 1,2-addition, while Cl2 and Br2 add to remote C atoms due to steric factors. For example, in C60Br8 and C60Br24, the Br atoms are in 1,3- or 1,4-positions with respect to each other. Under various conditions a vast number of halogenated derivatives of C60 can be produced, some with an extraordinary selectivity on one or two isomers over the other possible ones. Addition of fluorine and chlorine usually results in a flattening of the C60 framework into a drum-shaped molecule.

Addition of oxygen atoms
Solutions of C60 can be oxygenated to the epoxide C60O. Ozonation of C60 in 1,2-xylene at 257K gives an intermediate ozonide C60O3, which can be decomposed into 2 forms of C60O. Decomposition of C60O3 at 296 K gives the epoxide, but photolysis gives a product in which the O atom bridges a 5,6-edge.

Cycloadditions
The Diels–Alder reaction is commonly employed to functionalize C60. Reaction of C60 with appropriate substituted diene gives the corresponding adduct.

The Diels–Alder reaction between C60 and 3,6-diaryl-1,2,4,5-tetrazines affords C62. The C62 has the structure in which a four-membered ring is surrounded by four six-membered rings.

The C60 molecules can also be coupled through a [2+2] cycloaddition, giving the dumbbell-shaped compound C120. The coupling is achieved by high-speed vibrating milling of C60 with a catalytic amount of KCN. The reaction is reversible as C120 dissociates back to two C60 molecules when heated at 450 K. Under high pressure and temperature, repeated [2+2] cycloaddition between C60 results in polymerized fullerene chains and networks. These polymers remain stable at ambient pressure and temperature once formed, and have remarkably interesting electronic and magnetic properties, such as being ferromagnetic above room temperature.

Free radical reactions
Reactions of C60 with free radicals readily occur. When C60 is mixed with a disulfide RSSR, the radical C60SR• forms spontaneously upon irradiation of the mixture.

Stability of the radical species C60Y• depends largely on steric factors of Y. When tert-butyl halide is photolyzed and allowed to react with C60, a reversible inter-cage C–C bond is formed:

Cyclopropanation (Bingel reaction)
Cyclopropanation (the Bingel reaction) is another common method for functionalizing C60. Cyclopropanation of C60 mostly occurs at the junction of 2 hexagons due to steric factors.

The first cyclopropanation was carried out by treating the β-bromomalonate with C60 in the presence of a base. Cyclopropanation also occur readily with diazomethanes. For example, diphenyldiazomethane reacts readily with C60 to give the compound C61Ph2. Phenyl-C61-butyric acid methyl ester derivative prepared through cyclopropanation has been studied for use in organic solar cells.

C60 anions
The LUMO in C60 is triply degenerate, with the HOMO–LUMO separation relatively small. This small gap suggests that reduction of C60 should occur at mild potentials leading to fulleride anions, [C60]n− (n = 1–6). The midpoint potentials of 1-electron reduction of buckminsterfullerene and its anions is given in the table below:

C60 forms a variety of charge-transfer complexes, for example with tetrakis(dimethylamino)ethylene:
 * C60 + C2(NMe2)4 → [C2(NMe2)4]+[C60]−

This salt exhibits ferromagnetism at 16 K.

C60 cations
C60 oxidizes with difficulty. Three reversible oxidation processes have been observed by using cyclic voltammetry with ultra-dry methylene chloride and a supporting electrolyte with extremely high oxidation resistance and low nucleophilicity, such as [nBu4N] [AsF6].

Metal complexes
C60 forms complexes akin to the more common alkenes. Complexes have been reported molybdenum, tungsten, platinum, palladium, iridium, and titanium. The pentacarbonyl species are produced by photochemical reactions.

 * M(CO)6 + C60 → M(η2-C60)(CO)5 + CO (M = Mo, W)

In the case of platinum complex, the labile ethylene ligand is the leaving group in a thermal reaction:
 * Pt(η2-C2H4)(PPh3)2 + C60 → Pt(η2-C60)(PPh3)2 + C2H4

Titanocene complexes have also been reported:
 * (η5-Cp)2Ti(η2-(CH3)3SiC≡CSi(CH3)3) + C60 → (η5-Cp)2Ti(η2-C60) + (CH3)3SiC≡CSi(CH3)3

Coordinatively unsaturated precursors, such as Vaska's complex, for adducts with C60:

 * trans-Ir(CO)Cl(PPh3)2 + C60 → Ir(CO)Cl(η2-C60)(PPh3)2

One such iridium complex, [Ir(η2-C60)(CO)Cl(Ph2CH2C6H4OCH2Ph)2] has been prepared where the metal center projects two electron-rich 'arms' that embrace the C60 guest.

Endohedral fullerenes
Metal atoms or certain small molecules such as H2 and noble gas can be encapsulated inside the C60 cage. These endohedral fullerenes are usually synthesized by doping in the metal atoms in an arc reactor or by laser evaporation. These methods gives low yields of endohedral fullerenes, and a better method involves the opening of the cage, packing in the atoms or molecules, and closing the opening using certain organic reactions. This method, however, is still immature and only a few species have been synthesized this way.

Endohedral fullerenes show distinct and intriguing chemical properties that can be completely different from the encapsulated atom or molecule, as well as the fullerene itself. The encapsulated atoms have been shown to perform circular motions inside the C60 cage, and their motion has been followed using NMR spectroscopy.

Potential applications in technology
The optical absorption properties of C60 match the solar spectrum in a way that suggests that C60-based films could be useful for photovoltaic applications. Because of its high electronic affinity it is one of the most common electron acceptors used in donor/acceptor based solar cells. Conversion efficiencies up to 5.7% have been reported in C60–polymer cells.

Ingestion and risks
C60 is sensitive to light, so leaving C60 under light exposure causes it to degrade, becoming dangerous. The ingestion of C60 solutions that have been exposed to light could lead to developing cancer (tumors). So the management of C60 products for human ingestion requires cautionary measures such as: elaboration in very dark environments, encasing into bottles of great opacity, and storing in dark places, and others like consumption under low light conditions and using labels to warn about the problems with light.

Solutions of C60 dissolved in olive oil or water, as long as they are preserved from light, have been found nontoxic to rodents.

Otherwise, a study found that C60 remains in the body for a longer time than usual, especially in the liver, where it tends to be accumulated, and therefore has the potential to induce detrimental health effects.

Oils with C60 and risks
An experiment in 2011–2012 administered a solution of C60 in olive oil to rats, achieving a major prolongation of their lifespan. Since then, many oils with C60 have been sold as antioxidant products, but it does not avoid the problem of their sensitivity to light, that can turn them toxic. A later research confirmed that exposure to light degrades solutions of C60 in oil, making it toxic and leading to a "massive" increase of the risk of developing cancer (tumors) after its consumption.

To avoid the degradation by effect of light, C60 oils must be made in very dark environments, encased into bottles of great opacity, and kept in darkness, consumed under low light conditions and accompanied by labels to warn about the dangers of light for C60.

Some producers have been able to dissolve C60 in water to avoid possible problems with oils, but that would not protect C60 from light, so the same cautions are needed.

title: Buckminsterfullerene


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Baire category theorem

The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space (a topological space such that the intersection of countably many dense open sets is still dense). It is used in the proof of results in many areas of analysis and geometry, including some of the fundamental theorems of functional analysis.

Versions of the Baire category theorem were first proved independently in 1897 by Osgood for the real line $$\R$$ and in 1899 by Baire for Euclidean space $$\R^n$$. The more general statement for completely metrizable spaces was first shown by Hausdorff in 1914.

Statement
A Baire space is a topological space $$X$$ in which every countable intersection of open dense sets is dense in $$X.$$ See the corresponding article for a list of equivalent characterizations, as some are more useful than others depending on the application.

 * (BCT1) Every complete pseudometric space is a Baire space. In particular, every completely metrizable topological space is a Baire space.
 * (BCT2) Every locally compact regular space is a Baire space. In particular, every locally compact Hausdorff space is a Baire space.

Neither of these statements directly implies the other, since there are complete metric spaces that are not locally compact (the irrational numbers with the metric defined below; also, any Banach space of infinite dimension), and there are locally compact Hausdorff spaces that are not metrizable (for instance, any uncountable product of non-trivial compact Hausdorff spaces is such; also, several function spaces used in functional analysis; the uncountable Fort space). See Steen and Seebach in the references below.

Relation to the axiom of choice
The proof of BCT1 for arbitrary complete metric spaces requires some form of the axiom of choice; and in fact BCT1 is equivalent over ZF to the axiom of dependent choice, a weak form of the axiom of choice.

A restricted form of the Baire category theorem, in which the complete metric space is also assumed to be separable, is provable in ZF with no additional choice principles. This restricted form applies in particular to the real line, the Baire space $$\omega^{\omega},$$ the Cantor space $$2^{\omega},$$ and a separable Hilbert space such as the $L^p$-space $$L^2(\R^n)$$.

Uses
BCT1 is used in functional analysis to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle.

BCT1 also shows that every nonempty complete metric space with no isolated point is uncountable. (If $$X$$ is a nonempty countable metric space with no isolated point, then each singleton $$\{x\}$$ in $$X$$ is nowhere dense, and $$X$$ is meagre in itself.) In particular, this proves that the set of all real numbers is uncountable.

BCT1 shows that each of the following is a Baire space:
 * The space $$\R$$ of real numbers
 * The irrational numbers, with the metric defined by $$d(x, y) = \tfrac{1}{n+1},$$ where $$n$$ is the first index for which the continued fraction expansions of $$x$$ and $$y$$ differ (this is a complete metric space)
 * The Cantor set

By BCT2, every finite-dimensional Hausdorff manifold is a Baire space, since it is locally compact and Hausdorff. This is so even for non-paracompact (hence nonmetrizable) manifolds such as the long line.

BCT is used to prove Hartogs's theorem, a fundamental result in the theory of several complex variables.

BCT1 is used to prove that a Banach space cannot have countably infinite dimension.

Proof
(BCT1) The following is a standard proof that a complete pseudometric space $$X$$ is a Baire space.

Let $$U_1, U_2, \ldots$$ be a countable collection of open dense subsets. It remains to show that the intersection $$U_1 \cap U_2 \cap \ldots$$ is dense. A subset is dense if and only if every nonempty open subset intersects it. Thus to show that the intersection is dense, it suffices to show that any nonempty open subset $$W$$ of $$X$$ has some point $$x$$ in common with all of the $$U_n$$. Because $$U_1$$ is dense, $$W$$ intersects $$U_1;$$ consequently, there exists a point $$x_1$$ and a number $$0 < r_1 < 1$$ such that: $$\overline{B}\left(x_1, r_1\right) \subseteq W \cap U_1$$ where $$B(x, r)$$ and $$\overline{B}(x, r)$$ denote an open and closed ball, respectively, centered at $$x$$ with radius $$r.$$ Since each $$U_n$$ is dense, this construction can be continued recursively to find a pair of sequences $$x_n$$ and $$0 < r_n < \tfrac{1}{n}$$ such that: $$\overline{B}\left(x_n, r_n\right) \subseteq B\left(x_{n-1}, r_{n-1}\right) \cap U_n.$$

(This step relies on the axiom of choice and the fact that a finite intersection of open sets is open and hence an open ball can be found inside it centered at $$x_n$$.) The sequence $$\left(x_n\right)$$ is Cauchy because $$x_n \in B\left(x_m, r_m\right)$$ whenever $$n > m,$$ and hence $$\left(x_n\right)$$ converges to some limit $$x$$ by completeness. If $$n$$ is a positive integer then $$x \in \overline{B}\left(x_n, r_n\right)$$ (because this set is closed). Thus $$x \in W$$ and $$x \in U_n$$ for all $$n.$$ $$\blacksquare$$

There is an alternative proof using Choquet's game.

(BCT2) The proof that a locally compact regular space $$X$$ is a Baire space is similar. It uses the facts that (1) in such a space every point has a local base of closed compact neighborhoods; and (2) in a compact space any collection of closed sets with the finite intersection property has nonempty intersection. The result for locally compact Hausdorff spaces is a special case, as such spaces are regular.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Baire category theorem


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Bushranger

Bushrangers were armed robbers who hid from authorities in the bush of the British colonies in Australia. The earliest use of the term applied to escaped convicts in the early years of the British settlements in Australia. By the 1820s, the term had evolved to refer to those who took up "robbery under arms" as a way of life, using bases in the bush.

Bushranging thrived during the gold rush years of the 1850s and 1860s when the likes of Ben Hall, Bluecap, and Captain Thunderbolt roamed the country districts of New South Wales. These "Wild Colonial Boys", mostly Australian-born sons of convicts, were roughly analogous to British "highwaymen" and outlaws of the American Old West, and their crimes typically included robbing small-town banks and coach services. In certain cases, such as that of Dan Morgan, the Clarke brothers, and Australia's best-known bushranger, Ned Kelly, numerous policemen were murdered. The number of bushrangers declined due to better policing and improvements in rail transport and communication technology, such as telegraphy. Although bushrangers appeared sporadically into the early 20th century, most historians regard Kelly's capture and execution in 1880 as effectively representing the end of the bushranging era.

Bushranging exerted a powerful influence in Australia, lasting for over a century and predominating in the eastern colonies. Its origins in a convict system bred a unique kind of desperado, most frequently with an Irish political background. Native-born bushrangers also expressed nascent Australian nationalist views and are recognised as "the first distinctively Australian characters to gain general recognition." As such, a number of bushrangers became folk heroes and symbols of rebellion against the authorities, admired for their bravery, rough chivalry and colourful personalities. However, in stark contrast to romantic portrayals in the arts and popular culture, bushrangers tended to lead lives that were "nasty, brutish and short", with some earning notoriety for their cruelty and bloodthirst. Australian attitudes toward bushrangers remain complex and ambivalent.

Etymology
The earliest documented use of the term appears in a February 1805 issue of The Sydney Gazette, which reports that a cart had been stopped between Sydney and Hawkesbury by three men "whose appearance sanctioned the suspicion of their being bush-rangers". John Bigge described bushranging in 1821 as "absconding in the woods and living upon plunder and the robbery of orchards." Charles Darwin likewise recorded in 1835 that a bushranger was "an open villain who subsists by highway robbery, and will sooner be killed than taken alive".

History
Over 2,000 bushrangers are estimated to have roamed the Australian countryside, beginning with the convict bolters and drawing to a close after Ned Kelly's last stand at Glenrowan.

Convict era (1780s–1840s)
Bushranging began soon after British settlement with the establishment of New South Wales as a penal colony in 1788. The majority of early bushrangers were convicts who had escaped prison, or from the properties of landowners to whom they had been assigned as servants. These bushrangers, also known as "bolters", preferred the hazards of wild, unexplored bushland surrounding Sydney to the deprivation and brutality of convict life. The first notable bushranger, African convict John Caesar, robbed settlers for food, and had a brief, tempestuous alliance with Aboriginal resistance fighters during Pemulwuy's War. While other bushrangers would go on to fight alongside Indigenous Australians in frontier conflicts with the colonial authorities, the Government tried to bring an end to any such collaboration by rewarding Aborigines for returning convicts to custody. Aboriginal trackers would play a significant role in the hunt for bushrangers.

Colonel Godfrey Mundy described convict bushrangers as "desperate, hopeless, fearless; rendered so, perhaps, by the tyranny of a gaoler, of an overseer, or of a master to whom he has been assigned." Edward Smith Hall, editor of early Sydney newspaper The Monitor, agreed that the convict system was a breeding-ground for bushrangers due to its savagery, with starvation and acts of torture being rampant. "Liberty or Death!" was the cry of convict bushrangers, and in large numbers they roamed beyond Sydney, some hoping to reach China, which was commonly believed to be connected by an overland route. Some bolters seized boats and set sail for foreign lands, but most were hunted down and brought back to Australia. Others attempted to inspire an overhaul of the convict system, or simply sought revenge on their captors. This latter desire found expression in the convict ballad "Jim Jones at Botany Bay", in which Jones, the narrator, plans to join bushranger Jack Donahue and "gun the floggers down".

Donahue was the most notorious of the early New South Wales bushrangers, terrorising settlements outside Sydney from 1827 until he was fatally shot by a trooper in 1830. That same year, west of the Blue Mountains, convict Ralph Entwistle sparked a bushranging insurgency known as the Bathurst Rebellion. He and his gang raided farms, liberating assigned convicts by force in the process, and within a month, his personal army numbered 80 men. Following gun battles with vigilante posses, mounted policemen and soldiers of the 39th and 57th Regiment of Foot, he and nine of his men were captured and executed.

Convict bushrangers were particularly prevalent in the penal colony of Van Diemen's Land (now the state of Tasmania), established in 1803. The island's most powerful bushranger, the self-styled "Lieutenant Governor of the Woods", Michael Howe, led a gang of up to one hundred members "in what amounted to a civil war" with the colonial government. His control over large swathes of the island prompted elite squatters from Hobart and Launceston to collude with him, and for six months in 1815, Lieutenant-Governor Thomas Davey, fearing a convict uprising, declared martial law in an effort to suppress Howe's influence. Most of the gang had either been captured or killed by 1818, the year Howe was clubbed to death by a soldier. Vandemonian bushranging peaked in the 1820s with hundreds of bolters at large, among the most notorious being Matthew Brady's gang, cannibal serial killers Alexander Pearce and Thomas Jeffrey, and tracker-turned-resistance leader Musquito. Jackey Jackey (alias of William Westwood) was sent from New South Wales to Van Diemen's Land in 1842 after attempting to escape Cockatoo Island. In 1843, he escaped Port Arthur, and took up bushranging in Tasmania's mountains, but was recaptured and sent to Norfolk Island, where, as leader of the 1846 Cooking Pot Uprising, he murdered three constables, and was hanged along with sixteen of his men.

The era of convict bushrangers gradually faded with the decline in penal transportations to Australia in the 1840s. It had ceased by the 1850s to all colonies except Western Australia, which accepted convicts between 1850 and 1868. The best-known convict bushranger of the colony was the prolific escapee Moondyne Joe.

Gold rush era (1850s–1860s)
The bushrangers' heyday was the Gold Rush years of the 1850s and 1860s as the discovery of gold gave bushrangers access to great wealth that was portable and easily converted to cash. Their task was assisted by the isolated location of the goldfields and a police force decimated by troopers abandoning their duties to join the gold rush.

George Melville was hanged in front of a large crowd for robbing the McIvor gold escort near Castlemaine in 1853.

Bushranging numbers flourished in New South Wales with the rise of the colonial-born sons of poor, often ex-convict squatters who were drawn to a more glamorous life than mining or farming.

Much of the activity in this era was in the Lachlan Valley, around Forbes, Yass and Cowra.

The Gardiner–Hall gang, led by Frank Gardiner and Ben Hall and counting John Dunn, John Gilbert and Fred Lowry among its members, was responsible for some of the most daring robberies of the 1860s, including the 1862 Escort Rock robbery, Australia's largest ever gold heist. The gang also engaged in many shootouts with the police, resulting in deaths on both sides. Other bushrangers active in New South Wales during this period, such as Dan Morgan, and the Clarke brothers and their associates, murdered multiple policemen.

As bushranging continued to escalate in the 1860s, the Parliament of New South Wales passed a bill, the Felons Apprehension Act 1865, that effectively allowed anyone to shoot outlawed bushrangers on sight. By the time that the Clarke brothers were captured and hanged in 1867, organised gang bushranging in New South Wales had effectively ceased.

Captain Thunderbolt (alias of Frederick Ward) robbed inns and mail-coaches across northern New South Wales for six and a half years, one of the longest careers of any bushranger. He sometimes operated alone; at other times, he led gangs, and was accompanied by his Aboriginal 'wife', Mary Ann Bugg, who is credited with helping extend his career.

Decline and the Kelly gang (1870s–1880s)
The increasing push of settlement, increased police efficiency, improvements in rail transport and communications technology, such as telegraphy, made it more difficult for bushrangers to evade capture. In 1870, Captain Thunderbolt was fatally shot by a policeman, and with his death, the New South Wales bushranging epidemic that began in the early 1860s came to an end.

The scholarly, but eccentric Captain Moonlite (alias of Andrew George Scott) worked as an Anglican lay reader before turning to bushranging. Imprisoned in Ballarat for an armed bank robbery on the Victorian goldfields, he escaped, but was soon recaptured and received a ten-year sentence in HM Prison Pentridge. Within a year of his release in 1879, he and his gang held up the town of Wantabadgery in the Riverina. Two of the gang (including Moonlite's "soulmate" and alleged lover, James Nesbitt) and one trooper were killed when the police attacked. Scott was found guilty of murder and hanged along with one of his accomplices on 20 January 1880.

Among the last bushrangers was the Kelly gang in Victoria, led by Ned Kelly, Australia's most famous bushranger. After murdering three policemen in a shootout in 1878, the gang was outlawed, and after raiding towns and robbing banks into 1879, earned the distinction of having the largest reward ever placed on the heads of bushrangers. In 1880, after failing to derail and ambush a police train, the gang, clad in bulletproof armour they had devised, engaged in a shootout with the police. Ned Kelly, the only gang member to survive, was hanged at the Melbourne Gaol on 11 November 1880.

Isolated outbreaks (1890s–1900s)
In July 1900, the Governor brothers—a trio group consisting of an Aboriginal fencing contractor named Jimmy Governor and his associates, Joe Governor and Jack Underwood—perpetrated the Breelong Massacre, wounding one and killing five members of the Mawbey family.

The massacre sparked the Governor brothers to engage in a crime spree across northern New South Wales, triggering one of the largest manhunts in Australian history, with 2,000 armed civilians and police covering 3,000 km of northern New South Wales in a search for the brothers. The Governor brothers were pursued by authorities for a total of three months, consequently being brought down on 27 October with the arrest of Jimmy Governor by a group of armed locals in Bobin, NSW, and the death of his brother, Joe Governor, near Singleton, NSW a few days later.

Jack Underwood (who had been caught shortly after the Breelong Massacre) was hanged in Dubbo Gaol on 14 January 1901, and Jimmy Governor was hanged in Darlinghurst Gaol on 18 January 1901.

"Boy bushrangers" (1910s–1920s)
The final phase of bushranging was sustained by the so-called "boy bushrangers"—youths who sought to commit crimes, mostly armed robberies, modelled on the exploits of their bushranging "heroes". The majority were captured alive without any fatalities.

Public perception
In Australia, bushrangers often attract public sympathy (cf. the concept of social bandits). In Australian history and iconography bushrangers are held in some esteem in some quarters due to the harshness and anti-Catholicism of the colonial authorities whom they embarrassed, and the romanticism of the lawlessness they represented. Some bushrangers, most notably Ned Kelly in his Jerilderie letter, and in his final raid on Glenrowan, explicitly represented themselves as political rebels. Attitudes to Kelly, by far the most well-known bushranger, exemplify the ambivalent views of Australians regarding bushranging.

Legacy
The impact of bushrangers upon the areas in which they roamed is evidenced in the names of many geographical features in Australia, including Brady's Lookout, Moondyne Cave, the township of Codrington, Mount Tennent, Thunderbolts Way and Ward's Mistake. The districts of North East Victoria are unofficially known as Kelly Country.

Some bushrangers made a mark on Australian literature. While running from soldiers in 1818, Michael Howe dropped a knapsack containing a self-made book of kangaroo skin and written in kangaroo blood. In it was a dream diary and plans for a settlement he intended to found in the bush. Sometime bushranger Francis MacNamara, also known as Frank the Poet, wrote some of the best-known poems of the convict era. Several convict bushrangers also wrote autobiographies, including Jackey Jackey, Martin Cash and Owen Suffolk.

Cultural depictions
Jack Donahue was the first bushranger to have inspired bush ballads, including "Bold Jack Donahue" and "The Wild Colonial Boy". Ben Hall and his gang were the subject of several bush ballads, including "Streets of Forbes".

Michael Howe inspired the earliest play set in Tasmania, ''Michael Howe: The Terror! of Van Diemen's Land'', which premiered at The Old Vic in London in 1821. Other early plays about bushrangers include David Burn's The Bushrangers (1829), William Leman Rede's Faith and Falsehood; or, The Fate of the Bushranger (1830), William Thomas Moncrieff's Van Diemen's Land: An Operatic Drama (1831), The Bushrangers; or, Norwood Vale (1834) by Henry Melville, and The Bushrangers; or, The Tregedy of Donohoe (1835) by Charles Harpur.

In the late 19th century, E. W. Hornung and Hume Nisbet created popular bushranger novels within the conventions of the European "noble bandit" tradition. First serialised in The Sydney Mail in 1882–83, Rolf Boldrewood's bushranging novel Robbery Under Arms is considered a classic of Australian colonial literature. It also cited as an important influence on the American writer Owen Wister's 1902 novel The Virginian, widely regarded as the first Western.

Bushrangers were a favoured subject of colonial artists such as S. T. Gill, Frank P. Mahony and William Strutt. Tom Roberts, one of the leading figures of the Heidelberg School (also known as Australian Impressionism), depicted bushrangers in some of his history paintings, including In a corner on the Macintyre (1894) and Bailed Up (1895), both set in Inverell, the area where Captain Thunderbolt was once active.

Film
Although not the first Australian film with a bushranging theme, The Story of the Kelly Gang (1906)—the world's first feature-length narrative film—is regarded as having set the template for the genre. On the back of the film's success, its producers released one of two 1907 film adaptations of Boldrewood's Robbery Under Arms (the other being Charles MacMahon's version). Entering the first "golden age" of Australian cinema (1910–12), director John Gavin released two fictionalised accounts of real-life bushrangers: Moonlite (1910) and Thunderbolt (1910). The genre's popularity with audiences led to a spike of production unprecedented in world cinema. Dan Morgan (1911) is notable for portraying its title character as an insane villain rather than a figure of romance. Ben Hall, Frank Gardiner, Captain Starlight, and numerous other bushrangers also received cinematic treatments at this time.

Alarmed by what they saw as the glorification of outlawry, state governments imposed a ban on bushranger films in 1912, effectively removing "the entire folklore relating to bushrangers ... from the most popular form of cultural expression." It is seen as a major reason for the collapse of a booming Australian film industry. One of the few Australian films to escape the ban before it was lifted in the 1940s is the 1920 adaptation of Robbery Under Arms. Also during this lull appeared American takes on the bushranger genre, including The Bushranger (1928), Stingaree (1934) and Captain Fury (1939).

Ned Kelly (1970) starred Mick Jagger in the title role. Dennis Hopper portrayed Dan Morgan in Mad Dog Morgan (1976). More recent bushranger films include Ned Kelly (2003), starring Heath Ledger, The Proposition (2005), written by Nick Cave, The Outlaw Michael Howe (2013), and The Legend of Ben Hall (2016).

title: Bushranger


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High-energy astronomy

High-energy astronomy is the study of astronomical objects that release electromagnetic radiation of highly energetic wavelengths. It includes X-ray astronomy, gamma-ray astronomy, extreme UV astronomy, neutrino astronomy, and studies of cosmic rays. The physical study of these phenomena is referred to as high-energy astrophysics.

Astronomical objects commonly studied in this field may include black holes, neutron stars, active galactic nuclei, supernovae, kilonovae, supernova remnants, and gamma-ray bursts.

Missions
Some space and ground-based telescopes that have studied high energy astronomy include the following:

 * AGILE
 * AMS-02
 * AUGER
 * CALET
 * Chandra
 * Fermi
 * HAWC
 * H.E.S.S.
 * IceCube
 * INTEGRAL
 * MAGIC
 * NuSTAR
 * Proton
 * Swift
 * TA
 * XMM-Newton
 * VERITAS

title: High-energy astronomy


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Larrea tridentata

Larrea tridentata, called creosote bush and greasewood as a plant, chaparral as a medicinal herb, and gobernadora (Spanish for "governess") in Mexico, due to its ability to secure more water by inhibiting the growth of nearby plants. In Sonora, it is more commonly called hediondilla; Spanish hediondo = "smelly".

It is a flowering plant in the family Zygophyllaceae. The specific name tridentata refers to its three-toothed leaves.

Distribution
Larrea tridentata is a prominent species in the Mojave, Sonoran, and Chihuahuan Deserts of western North America, and its range includes those and other regions in portions of southeastern California, Arizona, southern Nevada, southwestern Utah, New Mexico, and Texas in the United States, and Chihuahua, Sonora, Coahuila, Nuevo León, Zacatecas, Durango and San Luis Potosì in Mexico. The species grows as far east as Zapata County, Texas, along the Rio Grande southeast of Laredo near the 99th meridian west.

Description
Larrea tridentata is an evergreen shrub growing to 1 to 3 m tall, rarely 4 m. The light gray stems of the plant bear resinous, dark green leaves with two opposite lanceolate leaflets joined at the base, with a deciduous awn between them, each leaflet 7 to 18 mm long and 4 to 8.5 mm broad. The flowers are up to 25 mm in diameter, with five yellow petals. The fruit is a brown-burgundy spherical, fuzzy capsule, which separates into five individual carpels each containing one seed. Galls may form by the activity of the creosote gall midge. The whole plant exhibits a characteristic odor of creosote, from which the common name derives. In the regions where it grows, its smell is often associated with the "smell of rain".

Ecology
These animals eat creosote bush:
 * Leaves: Of mammals, only the jackrabbit, and only when it can find no other food, as the leaves are bitter; desert iguanas, and the chuckwalla.
 * Seeds: desert woodrats and kangaroo rats
 * Flowers: 22 species of bees, as pollinators, the chuckwalla, desert iguanas, etc
 * Many species of insect

The Arabian camel, brought to the area by the United States Camel Corps, readily ate creosote bush. It is thought that this meeting reestablished a biological relationship that was broken when the American camels became extinct in the Quaternary Extinction Event, making it an evolutionary anachronism.

Oldest plants

As the creosote bush grows older, its oldest branches eventually die and its crown splits into separate crowns. This normally happens when the plant is 30 to 90 years old. Eventually, the old crown dies and the new ones become a clonal colony from the previous plant, composed of many separate stems all from the same seed. The cloned individuals sometimes form a "ring" around the original plant, which may no longer be visible.

King Clone
The "King Clone" creosote ring is one of the oldest living organisms on Earth. It has been alive an estimated 11,700 years, in the central Mojave Desert near present-day Lucerne Valley, California. This single clonal colony plant of L. tridentata reaches up to 67 ft in diameter, with an average diameter of 45 ft.

King Clone was identified and its age estimated by Frank Vasek, a professor at the University of California, Riverside. Measurements of the plant, as well as radiocarbon dating of wood fragments, were used to determine the plant's mean annual growth rate outward from the center of the ring. By measuring the diameter of the ring, its total age could be estimated. It is within the Creosote Rings Preserve of the Lucerne Valley and Johnson Valley.

Habitat
Creosote bush is most common on the well-drained soils of alluvial fans and flats. In parts of its range, it may cover large areas in practically pure stands, though it usually occurs in association with Ambrosia dumosa (burro bush or bur-sage). Chemicals found in creosote bush roots have been shown to inhibit the growth of burro bush roots, but as of 2013, much of their relationship remains unexplained.

Creosote bush stands tend to display an evenly spaced distribution of plants. Originally, it was assumed that the plant produced a water-soluble inhibitor that prevented the growth of other bushes near mature, healthy bushes. Now, however, it has been shown that the root systems of mature creosote plants are simply so efficient at absorbing water that fallen seeds nearby cannot accumulate enough water to germinate, effectively creating dead zones around every plant.

Desert adaptation

Owing to the harshness of the germination environment above mature root systems, young creosote bushes are much more susceptible to drought stress than established plants. Germination is quite active during wet periods, but most of the young plants die very quickly unless water conditions are optimal. Ground heat compounds the young plants' susceptibility to water stress, and ground temperatures can reach upwards of 70 °C (160 °F). To become established, the young plant apparently must experience three to five years of abnormally cool and moist weather during and after germination. From this, it can be inferred that all the plants inside a stand are of equal age.

Mature plants, however, can tolerate extreme drought stress. In terms of negative water potential, creosote bushes can operate fully at −50 bars of water potential and have been found living down to −120 bars, although the practical average floor is around −70 bars, where the plant's need for cellular respiration generally exceeds the level that the water-requiring process of photosynthesis can provide. Cell division can occur during these times of water stress, and new cells commonly quickly absorb water after rainfall. This rapid uptake causes branches to grow several centimeters at the end of a wet season.

Water loss is reduced by the resinous waxy coating of the leaves, and by their small size, which prevents them from heating above air temperature (which would increase the vapor pressure deficit between the leaf and the air, thus increasing water loss). Plants drop some leaves heading into summer, but if all leaves are lost, the plant will not recover. Accumulation of fallen leaves, as well as other detritus caught from the passing wind, creates an ecological community specific to the creosote bush canopy, including beetles, millipedes, pocket mice, and kangaroo rats.

Native American medicinals
Native Americans in the Southwest held beliefs that it treated many maladies, including sexually transmitted diseases, tuberculosis, chicken pox, dysmenorrhea, and snakebite. The Coahuilla Indians used the plant for intestinal complaints and tuberculosis. The Pima drank a decoction of the leaves as an emetic, and applied the boiled leaves as poultices to wounds or sores. Tohono O'odham Indians prepared it medicinally for stiff limbs, snake bites, and menstrual cramps. The shrub is still widely used as an herbal medicine in Mexico.

In other uses, the reddish-colored lac that exudes from the plant was used by the Tohono O'odham, after boiling, to make a mending glue on broken pottery.

Herbal supplements and toxicity
Larrea tridentata is often referred to as chaparral when used as a herbal remedy and supplement; however, it does not grow in the synonymous plant community chaparral. The United States Food and Drug Administration has issued warnings about the health hazards of ingesting chaparral or using it as an internal medicine, and discourages its use. In 2005, Health Canada issued a warning to consumers to avoid using the leaves of Larrea species because of the risk of damage to the liver and kidneys.

Cancer Research UK states: "We don't recommend that you take chaparral to treat or prevent any type of cancer."

title: Larrea tridentata


text:
Compton scattering

Compton scattering (or the Compton effect) is the quantum theory of high frequency photons scattering following an interaction with a charged particle, usually an electron. Specifically, when the photon hits electrons, it releases loosely bound electrons from the outer valence shells of atoms or molecules.

The effect was discovered in 1923 by Arthur Holly Compton while researching the scattering of X-rays by light elements, and earned him the Nobel Prize for Physics in 1927. The Compton effect significantly deviated from dominating classical theories, using both special relativity and quantum mechanics to explain the interaction between high frequency photons and charged particles.

Photons can interact with matter at the atomic level (e.g. photoelectric effect and Rayleigh scattering), at the nucleus, or with just an electron. Pair production and the Compton effect occur at the level of the electron. When a high frequency photon scatters due to an interaction with a charged particle, there is a decrease in the energy of the photon (and thus, an increase in its wavelength.) This is the Compton effect. Because of conservation of energy the lost energy from the photon is transferred to the recoiling particle (such an electron would be called a "Compton Recoil electron").

This implies that if the recoiling particle lost energy, the reverse would occur. This is known as inverse Compton scattering, in which the scattered photon increases in energy.

Introduction

In Compton's original experiment (see Fig. 1), the energy of the X ray photon (≈17 keV) was significantly larger than the binding energy of the atomic electron, so the electrons could be treated as being free after scattering. The amount by which the light's wavelength changes is called the Compton shift. Although nucleus Compton scattering exists, Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following. Compton was awarded the 1927 Nobel Prize in Physics for the discovery.

The effect is significant because it demonstrates that light cannot be explained purely as a wave phenomenon. Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain shifts in wavelength at low intensity: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength. Thus, if we are to explain low-intensity Compton scattering, light must behave as if it consists of particles. Or the assumption that the electron can be treated as free is invalid resulting in the effectively infinite electron mass equal to the nuclear mass (see e.g. the comment below on elastic scattering of X-rays being from that effect). Compton's experiment convinced physicists that light can be treated as a stream of particle-like objects (quanta called photons), whose energy is proportional to the light wave's frequency.

As shown in Fig. 2, the interaction between an electron and a photon results in the electron being given part of the energy (making it recoil), and a photon of the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is also conserved. The process may be repeated. In this scenario, the electron is treated as free or loosely bound. Experimental verification of momentum conservation in individual Compton scattering processes by Bothe and Geiger as well as by Compton and Simon has been important in disproving the BKS theory.

Compton scattering is commonly described as inelastic scattering, because the energy in the scattered photon is less than the energy of the incident photon. Energy of the incident photon is transferred to the recoil particle, but only as kinetic energy. The electron gains no internal energy, respective masses remain the same, the mark of an elastic collision. From this perspective, Compton scattering could be considered elastic because the internal state of the electron does not change during the scattering process. Whether Compton scattering is considered elastic or inelastic depends on the specific definition of these terms being used.

Compton scattering is one of four competing processes when photons interact with matter. At energies of a few eV to a few keV, corresponding to visible light through soft X-rays, a photon can be completely absorbed and its energy can eject an electron from its host atom, a process known as the photoelectric effect. High-energy photons of $1.022 MeV$ and above may bombard the nucleus and cause an electron and a positron to be formed, a process called pair production; even-higher-energy photons (beyond a threshold energy of at least $1.67 MeV$, depending on the nuclei involved), can eject a nucleon or alpha particle from the nucleus in a process called photodisintegration. Compton scattering is the most important interaction in the intervening energy region, at photon energies greater than those typical of the photoelectric effect but less than the pair-production threshold.

Description of the phenomenon
By the early 20th century, research into the interaction of X-rays with matter was well under way. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle $$\theta$$ and emerge at a different wavelength related to $$\theta$$. Although classical electromagnetism predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.

In 1923, Compton published a paper in the Physical Review that explained the X-ray shift by attributing particle-like momentum to light quanta (Einstein had proposed light quanta in 1905 in explaining the photo-electric effect, but Compton did not build on Einstein's work). The energy of light quanta depends only on the frequency of the light. In his paper, Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments which verified his derived relation: $$\lambda' - \lambda = \frac{h}{m_e c}(1 - \cos{\theta}),$$ where
 * $$\lambda$$ is the initial wavelength,
 * $$\lambda'$$ is the wavelength after scattering,
 * $$h$$ is the Planck constant,
 * $$m_e$$ is the electron rest mass,
 * $$c$$ is the speed of light, and
 * $$\theta$$ is the scattering angle.

The quantity $h⁄m_{e}c$ is known as the Compton wavelength of the electron; it is equal to $2.43 m$. The wavelength shift λ′ − λ is at least zero (for θ = 0°) and at most twice the Compton wavelength of the electron (for θ = 180°).

Compton found that some X-rays experienced no wavelength shift despite being scattered through large angles; in each of these cases the photon failed to eject an electron. Thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10000 times smaller. This is known as "coherent" scattering off the entire atom since the atom remains intact, gaining no internal excitation.

In Compton's original experiments the wavelength shift given above was the directly measurable observable. In modern experiments it is conventional to measure the energies, not the wavelengths, of the scattered photons. For a given incident energy $$E_\gamma = hc/\lambda$$, the outgoing final-state photon energy, $$E_{\gamma^\prime}$$, is given by $$E_{\gamma^\prime} = \frac{E_\gamma}{1 + (E_\gamma/m_e c^2)(1-\cos\theta)}.$$

Derivation of the scattering formula
A photon $γ$  with wavelength $λ$   collides with an electron $e$ in an atom, which is treated as being at rest. The collision causes the electron to recoil, and a new photon $γ$'  with wavelength $λ$'   emerges at angle $θ$  from the photon's incoming path. Let $e$' denote the electron after the collision. Compton allowed for the possibility that the interaction would sometimes accelerate the electron to speeds sufficiently close to the velocity of light as to require the application of Einstein's special relativity theory to properly describe its energy and momentum.

At the conclusion of Compton's 1923 paper, he reported results of experiments confirming the predictions of his scattering formula, thus supporting the assumption that photons carry momentum as well as quantized energy. At the start of his derivation, he had postulated an expression for the momentum of a photon from equating Einstein's already established mass-energy relationship of $$E=mc^2$$ to the quantized photon energies of $$h f$$, which Einstein had separately postulated. If $$mc^2 = hf$$, the equivalent photon mass must be $$hf/c^2$$. The photon's momentum is then simply this effective mass times the photon's frame-invariant velocity $c$. For a photon, its momentum $$p=hf/c$$, and thus $hf$ can be substituted for $pc$   for all photon momentum terms which arise in course of the derivation below. The derivation which appears in Compton's paper is more terse, but follows the same logic in the same sequence as the following derivation.

The conservation of energy $$E$$ merely equates the sum of energies before and after scattering.
 * $$E_\gamma + E_e = E_{\gamma'} + E_{e'}.$$

Compton postulated that photons carry momentum; thus from the conservation of momentum, the momenta of the particles should be similarly related by
 * $$\mathbf{p}_\gamma = \mathbf{p}_{\gamma'} + \mathbf{p}_{e'},$$

in which ($${p_e}$$) is omitted on the assumption it is effectively zero.

The photon energies are related to the frequencies by
 * $$E_{\gamma} = hf$$
 * $$E_{\gamma'} = hf'$$

where h is Planck's constant.

Before the scattering event, the electron is treated as sufficiently close to being at rest that its total energy consists entirely of the mass-energy equivalence of its (rest) mass $$ m_e $$,
 * $$E_e = m_ec^2.$$

After scattering, the possibility that the electron might be accelerated to a significant fraction of the speed of light, requires that its total energy be represented using the relativistic energy–momentum relation
 * $$E_{e'} = \sqrt{(p_{e'}c)^2 + (m_ec^2)^2} ~.$$

Substituting these quantities into the expression for the conservation of energy gives
 * $$hf + m_e c^2 = hf' + \sqrt{(p_{e'}c)^2 + (m_e c^2)^2}.$$

This expression can be used to find the magnitude of the momentum of the scattered electron,

 * Note that this magnitude of the momentum gained by the electron (formerly zero) exceeds the energy/c lost by the photon,
 * $$\frac{1}{c}\sqrt{(hf - hf' + m_{e}c^2)^2-m_{e}^2c^4} > \frac{hf - hf'}{c}~. $$

Equation (1) relates the various energies associated with the collision. The electron's momentum change involves a relativistic change in the energy of the electron, so it is not simply related to the change in energy  occurring in classical physics. The change of the magnitude of the momentum of the photon is not just related to the change of its energy; it also involves a change in direction.

Solving the conservation of momentum expression for the scattered electron's momentum gives
 * $$\mathbf{p}_{e'} = \mathbf{p}_\gamma - \mathbf{p}_{\gamma'}.$$

Making use of the scalar product yields the square of its magnitude,
 * $$\begin{align}

p_{e'}^{\, 2} &= \mathbf{p}_{e'}\cdot\mathbf{p}_{e'} = (\mathbf{p}_\gamma - \mathbf{p}_{\gamma'}) \cdot (\mathbf{p}_\gamma - \mathbf{p}_{\gamma'}) \\ &= p_{\gamma}^{\, 2} + p_{\gamma'}^{\, 2} - 2 p_{\gamma}\, p_{\gamma'} \cos\theta. \end{align}$$ In anticipation of $$p_{\gamma}c$$ being replaced with $$h f$$, multiply both sides by $$c^2$$,
 * $$p_{e'}^{\, 2}c^2 = p_{\gamma}^{\, 2}c^2 + p_{\gamma'}^{\, 2}c^2 - 2c^2 p_{\gamma}\, p_{\gamma'} \cos\theta.$$

After replacing the photon momentum terms with $$h f/c$$, we get a second expression for the magnitude of the momentum of the scattered electron,

Equating the alternate expressions for this momentum gives
 * $$ (hf - hf' + m_e c^2)^2 - m_e^{\, 2}c^4 = \left(h f\right)^2 + \left(h f'\right)^2 - 2h^2 ff'\cos{\theta},$$

which, after evaluating the square and canceling and rearranging terms, further yields
 * $$ 2 h f m_e c^2-2 h f' m_e c^2  = 2 h^2 f f' \left( 1 - \cos \theta \right).  $$

Dividing both sides by $2 h f f' m_e c$ yields
 * $$ \frac{c}{f'} - \frac{c}{f} = \frac{h}{m_ec}\left(1-\cos \theta \right).  $$

Finally, since $fλ$ =  $f ' λ'$ = $$,

It can further be seen that the angle $$ of the outgoing electron with the direction of the incoming photon is specified by

Compton scattering
Compton scattering is of prime importance to radiobiology, as it is the most probable interaction of gamma rays and high energy X-rays with atoms in living beings and is applied in radiation therapy.

Compton scattering is an important effect in gamma spectroscopy which gives rise to the Compton edge, as it is possible for the gamma rays to scatter out of the detectors used. Compton suppression is used to detect stray scatter gamma rays to counteract this effect.

Magnetic Compton scattering
Magnetic Compton scattering is an extension of the previously mentioned technique which involves the magnetisation of a crystal sample hit with high energy, circularly polarised photons. By measuring the scattered photons' energy and reversing the magnetisation of the sample, two different Compton profiles are generated (one for spin up momenta and one for spin down momenta). Taking the difference between these two profiles gives the magnetic Compton profile (MCP), given by $$J_{\text{mag}}(\mathbf{p}_z)$$ – a one-dimensional projection of the electron spin density.

$$J_{\text{mag}}(\mathbf{p}_z) = \frac{1}{\mu}\iint_{-\infty}^\infty (n_{\uparrow} (\mathbf{p}) - n_{\downarrow}(\mathbf{p})) d\mathbf{p}_x d\mathbf{p}_y$$ where $$\mu$$ is the number of spin-unpaired electrons in the system, $$n_\uparrow(\mathbf{p})$$ and $$n_\downarrow(\mathbf{p})$$ are the three-dimensional electron momentum distributions for the majority spin and minority spin electrons respectively.

Since this scattering process is incoherent (there is no phase relationship between the scattered photons), the MCP is representative of the bulk properties of the sample and is a probe of the ground state. This means that the MCP is ideal for comparison with theoretical techniques such as density functional theory. The area under the MCP is directly proportional to the spin moment of the system and so, when combined with total moment measurements methods (such as SQUID magnetometry), can be used to isolate both the spin and orbital contributions to the total moment of a system. The shape of the MCP also yields insight into the origin of the magnetism in the system.

Inverse Compton scattering
Inverse Compton scattering is important in astrophysics. In X-ray astronomy, the accretion disk surrounding a black hole is presumed to produce a thermal spectrum. The lower energy photons produced from this spectrum are scattered to higher energies by relativistic electrons in the surrounding corona. This is surmised to cause the power law component in the X-ray spectra (0.2–10 keV) of accreting black holes.

The effect is also observed when photons from the cosmic microwave background (CMB) move through the hot gas surrounding a galaxy cluster. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the Sunyaev–Zel'dovich effect. Observations of the Sunyaev–Zel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters.

Some synchrotron radiation facilities scatter laser light off the stored electron beam. This Compton backscattering produces high energy photons in the MeV to GeV range subsequently used for nuclear physics experiments.

Non-linear inverse Compton scattering
Non-linear inverse Compton scattering (NICS) is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon (X-ray or gamma ray) during the interaction with a charged particle, such as an electron. It is also called non-linear Compton scattering and multiphoton Compton scattering. It is the non-linear version of inverse Compton scattering in which the conditions for multiphoton absorption by the charged particle are reached due to a very intense electromagnetic field, for example the one produced by a laser.

Non-linear inverse Compton scattering is an interesting phenomenon for all applications requiring high-energy photons since NICS is capable of producing photons with energy comparable to the charged particle rest energy and higher. As a consequence NICS photons can be used to trigger other phenomena such as pair production, Compton scattering, nuclear reactions, and can be used to probe non-linear quantum effects and non-linear QED.

title: Compton scattering


text:
Talk:Consumer protection

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 29 September 2020 and 4 December 2020. Further details are available on the course page. Student editor(s): Shenglintan.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 19:28, 17 January 2022 (UTC)

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 28 January 2020 and 27 April 2020. Further details are available on the course page. Student editor(s): Nikhilgupta1.

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title: Talk:Consumer protection


text:
Talk:Bird

Number of bird species
The beginning of the article reads "There are over 11,000 living species" without any reference. This is true according to BirdLife taxonomy, but not according to BirdTree, which recognize only about 10,000 species.

A more accurate description is given later in the text: "The number of known living bird species is around 11,000 [56][57] although sources may differ in their precise numbers". The numbers in the references are slightly above or below 11,000. I suggest changing the sentence in the beginning to "There are around 11,000 living species", with the two references given later in the text, also adding a reference to the BirdTree taxonomy: https://birdtree.org/ or https://doi.org/10.1038/nature11631 Yuvalr (talk) 12:08, 18 April 2024 (UTC)
 * All three regularly updated checklists are now over 11,000 species. HBW/Birdlife (11,195 species) has been for several years and eBird/Clements (11,017) and the IOC (11,032 extant and 162 extinct) have recently passed 11,000. Refs 56 and 57 can be updated for the new ones. The Howard & Moore checklist recognises less species, but hadn't been updated in ten years (although an update is in progress). The Birdtree number is based on a combination BirdLife v3 (2010) and IOC v2.7 (~2010). So "around 11,000 living species" is a safe statement. —  Jts1882 | talk 13:05, 18 April 2024 (UTC)

Missing birds
I'm hesistant to make any big bold changes to an FA but is it possible that this source may be of use somewhere? It states that the North America bird population "is down by 2.9 billion breeding adults". Seems like the sort of thing that may be worth noting. Europe is also missing some birds. If it were to be added, this section seems like it would make the most sense. I'm sure if one went digging they could find information about other continents as well. Clovermoss 🍀 (talk) 13:27, 4 May 2024 (UTC)
 * A couple of sentences seem appropriate. In addition to your sentence on North America, a sentence saying a similar fall has been observed in Europe (25% in 40 years) and that these falls have been attributed to intensive farming and habitat loss. It may be hard to find similar surveys for other continents, although you'd expect similar declines in other intensively farmed regions. —  Jts1882 | talk 15:59, 5 May 2024 (UTC)

title: Talk:Bird


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Hypersonic speed

In aerodynamics, a hypersonic speed is one that exceeds five times the speed of sound, often stated as starting at speeds of Mach 5 and above.

The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization) occur at different speeds; these effects collectively become important around Mach 5-10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with the temperature of the flow as kinetic energy of the moving object is converted into heat.

Characteristics of flow
While the definition of hypersonic flow can be quite vague and is generally debatable (especially due to the absence of discontinuity between supersonic and hypersonic flows), a hypersonic flow may be characterized by certain physical phenomena that can no longer be analytically discounted as in supersonic flow. The peculiarities in hypersonic flows are as follows:
 * 1) Shock layer
 * 2) Aerodynamic heating
 * 3) Entropy layer
 * 4) Real gas effects
 * 5) Low density effects
 * 6) Independence of aerodynamic coefficients with Mach number.

Small shock stand-off distance
As a body's Mach number increases, the density behind a bow shock generated by the body also increases, which corresponds to a decrease in volume behind the shock due to conservation of mass. Consequently, the distance between the bow shock and the body decreases at higher Mach numbers.

Entropy layer
As Mach numbers increase, the entropy change across the shock also increases, which results in a strong entropy gradient and highly vortical flow that mixes with the boundary layer.

Viscous interaction
A portion of the large kinetic energy associated with flow at high Mach numbers transforms into internal energy in the fluid due to viscous effects. The increase in internal energy is realized as an increase in temperature. Since the pressure gradient normal to the flow within a boundary layer is approximately zero for low to moderate hypersonic Mach numbers, the increase of temperature through the boundary layer coincides with a decrease in density. This causes the bottom of the boundary layer to expand, so that the boundary layer over the body grows thicker and can often merge with the shock wave near the body leading edge.

High-temperature flow
High temperatures due to a manifestation of viscous dissipation cause non-equilibrium chemical flow properties such as vibrational excitation and dissociation and ionization of molecules resulting in convective and radiative heat-flux.

Classification of Mach regimes
Although "subsonic" and "supersonic" usually refer to speeds below and above the local speed of sound respectively, aerodynamicists often use these terms to refer to particular ranges of Mach values. When an aircraft approaches transonic speeds (around Mach 1), it enters a special regime. The usual approximations based on the Navier–Stokes equations, which work well for subsonic designs, start to break down because, even in the freestream, some parts of the flow locally exceed Mach 1. So, more sophisticated methods are needed to handle this complex behavior.

The "supersonic regime" usually refers to the set of Mach numbers for which linearised theory may be used; for example, where the (air) flow is not chemically reacting and where heat transfer between air and vehicle may be reasonably neglected in calculations. Generally, NASA defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Among the spacecraft operating in these regimes are returning Soyuz and Dragon space capsules; the previously-operated Space Shuttle; various reusable spacecraft in development such as SpaceX Starship and Rocket Lab Electron; and (theoretical) spaceplanes.

In the following table, the "regimes" or "ranges of Mach values" are referenced instead of the usual meanings of "subsonic" and "supersonic".

Similarity parameters
The categorization of airflow relies on a number of similarity parameters, which allow the simplification of a nearly infinite number of test cases into groups of similarity. For transonic and compressible flow, the Mach and Reynolds numbers alone allow good categorization of many flow cases.

Hypersonic flows, however, require other similarity parameters. First, the analytic equations for the oblique shock angle become nearly independent of Mach number at high (~>10) Mach numbers. Second, the formation of strong shocks around aerodynamic bodies means that the freestream Reynolds number is less useful as an estimate of the behavior of the boundary layer over a body (although it is still important). Finally, the increased temperature of hypersonic flow mean that real gas effects become important. Research in hypersonics is therefore often called aerothermodynamics, rather than aerodynamics.

The introduction of real gas effects means that more variables are required to describe the full state of a gas. Whereas a stationary gas can be described by three variables (pressure, temperature, adiabatic index), and a moving gas by four (flow velocity), a hot gas in chemical equilibrium also requires state equations for the chemical components of the gas, and a gas in nonequilibrium solves those state equations using time as an extra variable. This means that for nonequilibrium flow, something between 10 and 100 variables may be required to describe the state of the gas at any given time. Additionally, rarefied hypersonic flows (usually defined as those with a Knudsen number above 0.1) do not follow the Navier–Stokes equations.

Hypersonic flows are typically categorized by their total energy, expressed as total enthalpy (MJ/kg), total pressure (kPa-MPa), stagnation pressure (kPa-MPa), stagnation temperature (K), or flow velocity (km/s).

Wallace D. Hayes developed a similarity parameter, similar to the Whitcomb area rule, which allowed similar configurations to be compared.

Regimes
Hypersonic flow can be approximately separated into a number of regimes. The selection of these regimes is rough, due to the blurring of the boundaries where a particular effect can be found.

Perfect gas
In this regime, the gas can be regarded as an ideal gas. Flow in this regime is still Mach number dependent. Simulations start to depend on the use of a constant-temperature wall, rather than the adiabatic wall typically used at lower speeds. The lower border of this region is around Mach 5, where ramjets become inefficient, and the upper border around Mach 10-12.

Two-temperature ideal gas
This is a subset of the perfect gas regime, where the gas can be considered chemically perfect, but the rotational and vibrational temperatures of the gas must be considered separately, leading to two temperature models. See particularly the modeling of supersonic nozzles, where vibrational freezing becomes important.

Dissociated gas
In this regime, diatomic or polyatomic gases (the gases found in most atmospheres) begin to dissociate as they come into contact with the bow shock generated by the body. Surface catalysis plays a role in the calculation of surface heating, meaning that the type of surface material also has an effect on the flow. The lower border of this regime is where any component of a gas mixture first begins to dissociate in the stagnation point of a flow (which for nitrogen is around 2000 K). At the upper border of this regime, the effects of ionization start to have an effect on the flow.

Ionized gas
In this regime the ionized electron population of the stagnated flow becomes significant, and the electrons must be modeled separately. Often the electron temperature is handled separately from the temperature of the remaining gas components. This region occurs for freestream flow velocities around 3-4 km/s. Gases in this region are modeled as non-radiating plasmas.

Radiation-dominated regime
Above around 12 km/s, the heat transfer to a vehicle changes from being conductively dominated to radiatively dominated. The modeling of gases in this regime is split into two classes: The modeling of optically thick gases is extremely difficult, since, due to the calculation of the radiation at each point, the computation load theoretically expands exponentially as the number of points considered increases.
 * 1) Optically thin: where the gas does not re-absorb radiation emitted from other parts of the gas
 * 2) Optically thick: where the radiation must be considered a separate source of energy.

title: Hypersonic speed