document_title: Honey bee

question_text: when were honey bees brought to north america

text: Honey bee

text: Etymology and name[edit]

text: The genus name Apis is Latin for "bee".[3]

text: Although modern dictionaries may refer to Apis as either honey bee or honeybee, entomologist Robert Snodgrass asserts that correct usage requires two words, i.e. honey bee, as it is a kind or type of bee, whereas it is incorrect to run the two words together as in dragonfly or butterfly, because the latter are not flies.[4] Honey bee, not honeybee, is the listed common name in the Integrated Taxonomic Information System, the Entomological Society of America Common Names of Insects Database, and the Tree of Life Web Project.[5][6][7] Nonetheless, compounds gradually solidify in the orthography of natural languages in ways that do not always comply with prescription.

text: Origin, systematics and distribution[edit]

text: Honey bees appear to have their center of origin in South and Southeast Asia (including the Philippines), as all the extant species except Apis mellifera are native to that region. Notably, living representatives of the earliest lineages to diverge (Apis florea and Apis andreniformis) have their center of origin there.[8]

text: The first Apis bees appear in the fossil record at the Eocene-Oligocene boundary (34 mya), in European deposits. The origin of these prehistoric honey bees does not necessarily indicate Europe as the place of origin of the genus, only that the bees were present in Europe by that time. Few fossil deposits are known from South Asia, the suspected region of honey bee origin, and fewer still have been thoroughly studied.

text: No Apis species existed in the New World during human times before the introduction of A. mellifera by Europeans. Only one fossil species is documented from the New World, Apis nearctica, known from a single 14 million-year-old specimen from Nevada.[9]

text: The close relatives of modern honey bees – e.g. bumblebees and stingless bees – are also social to some degree, and social behavior seems a plesiomorphic trait that predates the origin of the genus. Among the extant members of Apis, the more basal species make single, exposed combs, while the more recently evolved species nest in cavities and have multiple combs, which has greatly facilitated their domestication.

text: Most species have historically been cultured or at least exploited for honey and beeswax by humans indigenous to their native ranges. Only two species have been truly domesticated: Apis mellifera and Apis cerana indica. A. mellifera has been cultivated at least since the time of the building of the Egyptian pyramids, and only that species has been moved extensively beyond its native range.

text: Honey bees are the only extant members of the tribe Apini. Today's honey bees constitute three clades: Micrapis (dwarf honey bees), Megapis (giant honey bee), and Apis (domestic honey bees and close relatives).[1][10]

text: Genetics[edit]

text: The genome of Apis has been mapped.

text: The chromosome counts of female bees for the three clades are:

text:
Clade
2 N

Micrapis
16

Megapis
16

Apis
32

text: Drones (males) are produced from unfertilized eggs, so they represent only the DNA of the queen that laid the eggs, i.e. have only a mother. Drones of all bee genera have 1 N chromosome counts – half of those shown above.

text: Workers and queens (both female) result from fertilized eggs, so have both a mother and a father. Arrhenotokous parthenogenesis, a modified form of parthenogenesis, controls sex differentiation. The sex allele is polymorphic, and so long as two different variants are present, a female bee results. If both sex alleles are identical, diploid drones are produced. Honey bees detect and destroy diploid drones after the eggs hatch.

text: Queens typically mate with multiple drones on more than one mating flight. Once mated, they lay eggs and fertilize them as needed from sperm stored in the spermatheca. Since the number of sex alleles is limited at a regional level, a queen will most likely mate with one or more drones having sex alleles identical with one of the sex alleles in the queen. The queen, then, typically produces a percentage of diploid drone eggs.[a]

text: Micrapis[edit]

text: Apis florea and Apis andreniformis are small honey bees of southern and southeastern Asia. They make very small, exposed nests in trees and shrubs. Their stings are often incapable of penetrating human skin, so the hive and swarms can be handled with minimal protection. They occur largely sympatrically, though they are very distinct evolutionarily and are probably the result of allopatric speciation, their distribution later converging.

text: Given that A. florea is more widely distributed and A. andreniformis is considerably more aggressive, honey is, if at all, usually harvested from the former only. They are the most ancient extant lineage of honey bees, maybe diverging in the Bartonian (some 40 million years ago or slightly later) from the other lineages, but do not seem to have diverged from each other a long time before the Neogene.[10] Apis florea have smaller wing spans than its sister species.[12] Apis florea are also completely yellow with the exception of the scutellum of workers, which is black.[12]

text: Megapis[edit]

text: One species is recognized in the subgenus Megapis. It usually builds single or a few exposed combs on high tree limbs, on cliffs, and sometimes on buildings. They can be very fierce. Periodically robbed of their honey by human "honey hunters", colonies are easily capable of stinging a human being to death if provoked.

text:
Apis dorsata, the giant honey bee, is native and widespread across most of South and Southeast Asia.

A. d. binghami, the Indonesian giant honey bee, is classified as the Indonesian subspecies of the giant honey bee or a distinct species; in the latter case, A. d. breviligula and / or other lineages would probably also have to be considered species.[13]
A. d. laboriosa, the Himalayan giant honey bee, was initially described as a distinct species. Later, it was included in A. dorsata as a subspecies[1] based on the biological species concept, though authors applying a genetic species concept have suggested it should be considered a separate species.[10] Essentially restricted to the Himalayas, it differs little from the giant honey bee in appearance, but has extensive behavioral adaptations that enable it to nest in the open at high altitudes despite low ambient temperatures. It is the largest living honey bee.

text: Apis[edit]

text: Eastern Apis species include three or four species, including A. koschevnikovi and A. cerana. The genetics of the western honey bee A. mellifera are unclear. The domesticated species are A. cerana indica and A. mellifera

text: Borneo honey bee[edit]

text: The reddish Koschevnikov's bee (Apis koschevnikovi) from Borneo is clearly a distinct species; it probably derives from the first colonization of the island by cave-nesting honey bees.

text: Eastern honey bee[edit]

text: Apis cerana, the eastern honey bee proper, is the traditional honey bee of southern and eastern Asia. It was domesticated as subspecies A. c. indica and kept in hives in a fashion similar to A. mellifera, though on a more limited, regional scale.

text: It has not been possible yet to resolve its relationship to the Bornean A. c. nuluensis and Apis nigrocincta from the Philippines to satisfaction; the most recent hypothesis is that these are indeed distinct species, but that A. cerana is still paraphyletic, consisting of several separate species.[10]

text: Western honey bee[edit]

text: A. mellifera, the most common domesticated[14] species, was the third insect to have its genome mapped. It seems to have originated in eastern tropical Africa and spread from there to Northern Europe and eastwards into Asia to the Tien Shan range. It is variously called the European, western, or common honey bee in different parts of the world. Many subspecies have adapted to the local geographic and climatic environments; in addition, hybrid strains, such as the Buckfast bee, have been bred. Behavior, color, and anatomy can be quite different from one subspecies or even strain to another.

text: A. mellifera phylogeny is the most enigmatic of all honey bee species. It seems to have diverged from its eastern relatives only during the Late Miocene. This would fit the hypothesis that the ancestral stock of cave-nesting honey bees was separated into the western group of East Africa and the eastern group of tropical Asia by desertification in the Middle East and adjacent regions, which caused declines of food plants and trees that provided nest sites, eventually causing gene flow to cease.

text: The diversity of A. mellifera subspecies is probably the product of a largely Early Pleistocene radiation aided by climate and habitat changes during the last ice age. That the western honey bee has been intensively managed by humans for many millennia – including hybridization and introductions – has apparently increased the speed of its evolution and confounded the DNA sequence data to a point where little of substance can be said about the exact relationships of many A. mellifera subspecies.[10]

text: Apis mellifera is not native to the Americas, so was not present upon the arrival of the European explorers and colonists. However, other native bee species were kept and traded by indigenous peoples. In 1622, European colonists brought the dark bee (A. m. mellifera) to the Americas, followed later by Italian bees (A. m. ligustica) and others. Many of the crops that depend on honey bees for pollination have also been imported since colonial times. Escaped swarms (known as “wild” bees, but actually feral) spread rapidly as far as the Great Plains, usually preceding the colonists. Honey bees did not naturally cross the Rocky Mountains; they were transported by the Mormon pioneers to Utah in the late 1840s, and by ship to California in the early 1850s.[15]

text: Africanized bee[edit]

text: Africanized bees (known colloquially as "killer bees") are hybrids between European stock and one of the African subspecies A. m. scutellata; they are often more aggressive than European bees and do not create as much of a honey surplus, but are more resistant to disease and are better foragers.[citation needed] Originating by accident in Brazil, they have spread to North America and constitute a pest in some regions. However, these strains do not overwinter well, so are not often found in the colder, more northern parts of North America. The original breeding experiment for which the African bees were brought to Brazil in the first place has continued (though not as intended). Novel hybrid strains of domestic and redomesticated Africanized bees combine high resilience to tropical conditions and good yields. They are popular among beekeepers in Brazil.

text: Living and fossil honey bees (Apini: Apis)[edit]

text: Tribe Apini Latreille[16]

text: Genus Apis Linnaeus (s. lato)

text:
henshawi species group (†Priorapis Engel, †Synapis Cockerell)

†A. vetusta Engel
†A. henshawi Cockerell
†A. petrefacta (Říha)
†A. miocenica Hong
†A. “longtibia” Zhang
†A. “Miocene 1”

armbrusteri species group (†Cascapis Engel)

†A. armbrusteri Zeuner
†A. nearctica, sp. Nov.

florea species group (Micrapis Ashmead)

A. florea Fabricius
A. andreniformis Smith

dorsata species group (Megapis Ashmead)

†A. lithohermaea Engel
A. dorsata Fabricius

mellifera species group (Apis Linnaeus s. stricto)

mellifera subgroup

A. mellifera Linnaeus (Apis Linnaeus s. strictissimo)

cerana subgroup (Sigmatapis Maa)

A. cerana Fabricius
A. nigrocincta Smith
A. koschevnikovi Enderlein

text: Life cycle[edit]

text: As in a few other types of eusocial bees, a colony generally contains one queen bee, a fertile female; seasonally up to a few thousand drone bees, or fertile males;[17] and tens of thousands of sterile female worker bees. Details vary among the different species of honey bees, but common features include:

text:
Eggs are laid singly in a cell in a wax honeycomb, produced and shaped by the worker bees. Using her spermatheca, the queen can choose to fertilize the egg she is laying, usually depending on into which cell she is laying. Drones develop from unfertilised eggs and are haploid, while females (queens and worker bees) develop from fertilised eggs and are diploid. Larvae are initially fed with royal jelly produced by worker bees, later switching to honey and pollen. The exception is a larva fed solely on royal jelly, which will develop into a queen bee. The larva undergoes several moultings before spinning a cocoon within the cell, and pupating.
Young worker bees, sometimes called "nurse bees", clean the hive and feed the larvae. When their royal jelly-producing glands begin to atrophy, they begin building comb cells. They progress to other within-colony tasks as they become older, such as receiving nectar and pollen from foragers, and guarding the hive. Later still, a worker takes her first orientation flights and finally leaves the hive and typically spends the remainder of her life as a forager.
Worker bees cooperate to find food and use a pattern of "dancing" (known as the bee dance or waggle dance) to communicate information regarding resources with each other; this dance varies from species to species, but all living species of Apis exhibit some form of the behavior. If the resources are very close to the hive, they may also exhibit a less specific dance commonly known as the "round dance".
Honey bees also perform tremble dances, which recruit receiver bees to collect nectar from returning foragers.
Virgin queens go on mating flights away from their home colony to a drone congregation area, and mate with multiple drones before returning. The drones die in the act of mating. Queen honey bees do not mate with drones from their home colony.
Colonies are established not by solitary queens, as in most bees, but by groups known as "swarms", which consist of a mated queen and a large contingent of worker bees. This group moves en masse to a nest site which was scouted by worker bees beforehand and whose location is communicated with a special type of dance. Once the swarm arrives, they immediately construct a new wax comb and begin to raise new worker brood. This type of nest founding is not seen in any other living bee genus, though several groups of vespid wasps also found new nests by swarming (sometimes including multiple queens). Also, stingless bees will start new nests with large numbers of worker bees, but the nest is constructed before a queen is escorted to the site, and this worker force is not a true "swarm".

text: Life cycle[edit]

text:
A coloured dot applied by a beekeeper identifies the queen

Honey bee eggs shown in opened wax cells

Eggs and larvae

Drone pupae

Emergence of a black bee (A. m. mellifera)

text: Winter survival[edit]

text: In cold climates, honey bees stop flying when the temperature drops below about 10 °C (50 °F) and crowd into the central area of the hive to form a "winter cluster". The worker bees huddle around the queen bee at the center of the cluster, shivering to keep the center between 27 °C (81 °F) at the start of winter (during the broodless period) and 34 °C (93 °F) once the queen resumes laying. The worker bees rotate through the cluster from the outside to the inside so that no bee gets too cold. The outside edges of the cluster stay at about 8–9 °C (46–48 °F). The colder the weather is outside, the more compact the cluster becomes. During winter, they consume their stored honey to produce body heat. The amount of honey consumed during the winter is a function of winter length and severity, but ranges in temperate climates from 15 to 50 kilograms (33 to 110 lb).[18] In addition, certain bees, including the Western honey bee as well as Apis cerana, are known to engage in effective methods of nest thermoregulation during periods of varying temperature in both summer and winter. During the summer, however, this is achieved through fanning and water evaporation from water collected in various fields.[19]

text: Pollination[edit]

text: Species of Apis are generalist floral visitors, and pollinate a large variety of plants, but by no means all plants. Of all the honey bee species, only A. mellifera has been used extensively for commercial pollination of crops and other plants. The value of these pollination services is commonly measured in the billions of dollars. Bees collect 66 pounds (30 kg) of pollen per year per hive.[20]

text: Nutrition[edit]

text: Honey bees obtain all of their nutritional requirements from a diverse combination of pollen and nectar. Pollen is the only natural protein source for honey bees. Adult worker honey bees consume 3.4-4.3 mg of pollen per day to meet a dry matter requirement of 66-74% protein.[21] The rearing of one larva requires 125-187.5 mg pollen or 25-37.5 mg protein for proper development.[21] Dietary proteins are broken down into amino acids, ten of which are considered essential to honey bees: methionine, tryptophan, arginine, lysine, histidine, phenylalanine, isoleucine, threonine, leucine, and valine. Of these amino acids, honey bees require highest concentrations of leucine, isoleucine, and valine, however elevated concentrations of arginine and lysine are required for brood rearing.[22] In addition to these amino acids, some B vitamins including biotin, folic acid, nicotinamide, riboflavin, thiamine, pantothenate, and most importantly, pyridoxine are required to rear larvae. Pyridoxine is the most prevalent B vitamin found in royal jelly and concentrations vary throughout the foraging season with lowest concentrations found in May and highest concentrations found in July and August. Honey bees lacking dietary pyridoxine were unable to rear brood.[22]

text: Pollen is also a lipid source for honey bees ranging from 0.8% to 18.9%.[21] Lipids are metabolized during the brood stage for precursors required for future biosynthesis. Fat-soluble vitamins A, D, E, and K are not considered essential but have shown to significantly improve the number of brood reared.[21] Honey bees ingest phytosterols from pollen to produce 24-methylenecholesterol and other sterols as they cannot directly synthesize cholesterol from phytosterols. Nurse bees have the ability to selectively transfer sterols to larvae through brood food.[21]

text: Nectar is collected by foraging worker bees as a source of water and carbohydrates in the form of sucrose. The dominant monosaccharides in honey bee diets are fructose and glucose but the most common circulating sugar in hemolymph is trehalose which is a disaccharide consisting of two glucose molecules.[23] Adult worker honey bees require 4 mg of utilizable sugars per day and larvae require about 59.4 mg of carbohydrates for proper development.[21]

text: Honey bees require water to maintain osmotic homeostasis, prepare liquid brood food, and to cool the hive through evaporation. A colony’s water needs can generally be met by nectar foraging as it has high water content. Occasionally on hot days or when nectar is limited, foragers will collect water from streams or ponds to meet the needs of the hive.[24]

text: Parasites[edit]

text: Galleria mellonella[edit]

text: Larval stages of G. mellonella parasitize both wild and cultivated honeybees.  Eggs are laid within the hive, and the larva that hatch tunnel through and destroy the honeycombs that contain honeybee larva and their honey stores. The tunnels they create are lined with silk, which entangles and starves emerging bees. Destruction of honeycombs also result in honey leaking and being wasted. Finally, both G. mellonella adults and larvae can be vectors for pathogens that can infect honeybees, including the Israeli acute paralysis virus (IAPV) and the black queen cell virus (BQCV).[25]

text: Management[edit]

text: Temperature treatments are possible, but also distorts wax of the honeycombs. Chemical fumigants, particularly CO2,are also used. [25]

text: Beekeeping[edit]

text: Two species of honey bee, A. mellifera and A. cerana indica, are often maintained, fed, and transported by beekeepers. Modern hives also enable beekeepers to transport bees, moving from field to field as the crop needs pollinating and allowing the beekeeper to charge for the pollination services they provide, revising the historical role of the self-employed beekeeper, and favoring large-scale commercial operations.

text: Colony collapse disorder[edit]

text: Since 2007, abnormally high die-offs (30–70% of hives) of European honey bee colonies have occurred in North America. This has been dubbed "colony collapse disorder" (CCD) and was at first unexplained.[26] It seems to be caused by a combination of factors rather than a single pathogen or poison, possibly including neonicotinoid pesticides[27] or Israeli acute paralysis virus.[28]

text: Bee products[edit]

text: Honey[edit]

text: Honey is the complex substance made when bees ingest nectar, process it, and store the substance into honey combs.[29] All living species of Apis have had their honey gathered by indigenous peoples for consumption. A. mellifera and A. cerana are the only species that have had their honey harvested for commercial purposes.

text: Beeswax[edit]

text: Worker bees of a certain age secrete beeswax from a series of glands on their abdomens.[30] They use the wax to form the walls and caps of the comb. As with honey, beeswax is gathered by humans for various purposes.

text: Pollen[edit]

text: Bees collect pollen in their pollen baskets and carry it back to the hive.[31] In the hive, pollen is used as a protein source necessary during brood-rearing. In certain environments, excess pollen can be collected from the hives of A. mellifera and A. cerana. It is often eaten as a health supplement. It also has been used with moderate success as a source of pollen for hand pollination.

text: Bee bread[edit]

text: Worker bees combine pollen, honey and glandular secretions and allow it to ferment in the comb to make bee bread. The fermentation process releases additional nutrients from the pollen and can produce antibiotics and fatty acids which inhibit spoilage. Bee bread is eaten by nurse bees (younger workers) who then produce the protein-rich royal jelly needed by the queen and developing larvae in their hypopharyngeal glands.

text: Propolis[edit]

text: Propolis is a resinous mixture collected by honey bees from tree buds, sap flows or other botanical sources, which is used as a sealant for unwanted open spaces in the hive.[32] Although propolis is alleged to have health benefits (tincture of Propolis is marketed as a cold and flu remedy), it may cause severe allergic reactions in some individuals.[33] Propolis is also used in wood finishes, and gives a Stradivarius violin its unique red color.[34]

text: Royal jelly[edit]

text: Royal jelly is a honey-bee secretion used to nourish the larvae.[35] It is marketed for its alleged but unsupported claims of health benefits.[36][37] On the other hand, it may cause severe allergic reactions in some individuals.[38]

text: Sexes and castes[edit]

text: Honey bees have three castes: drones, workers, and queens.[39][40] Drones are male, while workers and queens are female.[40]

text: Drones[edit]

text: Males, or drones, are typically haploid, having only one set of chromosomes and primarily exist for the purpose of reproduction.[40] They are produced by the queen if she chooses not to fertilize an egg or by an unfertilized laying worker. Diploid drones may be produced if an egg is fertilized but is homozygous for the sex-determination allele. Drones take 24 days to develop and may be produced from summer through to autumn, numbering as many as 500 per hive.[40] They are expelled from the hive during the winter months when the hive's primary focus is warmth and food conservation.[40] Drones have large eyes used to locate queens during mating flights. They do not defend the hive or kill intruders, and do not have a stinger.[41]

text: Workers[edit]

text: Workers have two sets of chromosomes.[42] They are produced from an egg that the queen has selectively fertilized from stored sperm. Workers typically develop in 21 days. A typical colony may contain as many as 60,000 worker bees.[40] Workers exhibit a wider range of behaviors than either queens or drones. Their duties change upon the age of the bee in the following order (beginning with cleaning out their own cell after eating through their capped brood cell): feed brood, receive nectar, clean hive, guard duty, and foraging.[40][41] Some workers engage in other specialized behaviors, such as "undertaking" (removing corpses of their nestmates from inside the hive).[41]

text: Workers have morphological specializations, including the pollen basket (corbicula),[43] abdominal glands that produce beeswax, brood-feeding glands, and barbs on the sting. Under certain conditions (for example, if the colony becomes queenless), a worker may develop ovaries.

text: Queens[edit]

text: Queen honey bees are created when worker bees feed a single female larvae an exclusive diet of a food called "royal jelly".[40][41] Queens are produced in oversized cells and develop in only 16 days; they differ in physiology, morphology, and behavior from worker bees. In addition to the greater size of the queen, she has a functional set of ovaries, and a spermatheca, which stores and maintains sperm after she has mated. Apis queens practice polyandry, with one female mating with multiple males. The highest documented mating frequency for an Apis queen is in Apis nigrocincta, where queens mate with an extremely high number of males with observed numbers of different matings ranging from 42 to 69 drones per queen.[44] The sting of queens is not barbed like a worker's sting, and queens lack the glands that produce beeswax. Once mated, queens may lay up to 2,000 eggs per day.[41] They produce a variety of pheromones that regulate behavior of workers, and helps swarms track the queen's location during the swarming.[41]

text: Defense[edit]

text: All honey bees live in colonies where the workers sting intruders as a form of defense, and alarmed bees release a pheromone that stimulates the attack response in other bees. The different species of honey bees are distinguished from all other bee species (and virtually all other Hymenoptera) by the possession of small barbs on the sting, but these barbs are found only in the worker bees. The sting and associated venom sac of honey bees are also modified so as to pull free of the body once lodged (autotomy), and the sting apparatus has its own musculature and ganglion, which allows it to keep delivering venom once detached. The gland which produces the alarm pheromone is also associated with the sting apparatus. The embedded stinger continues to emit additional alarm pheromone after it has torn loose; other defensive workers are thereby attracted to the sting site. The worker dies after the sting becomes lodged and is subsequently torn loose from the bee's abdomen. The honey bee's venom, known as apitoxin, carries several active components, the most abundant of which is melittin, and the most destructive is phospholipase A2.

text: This complex apparatus, including the barbs on the sting, is thought to have evolved specifically in response to predation by vertebrates, as the barbs do not usually function (and the sting apparatus does not detach) unless the sting is embedded in fleshy tissue. While the sting can also penetrate the membranes between joints in the exoskeleton of other insects (and is used in fights between queens), in the case of Apis cerana japonica, defense against larger insects such as predatory wasps (e.g. Asian giant hornet) is usually performed by surrounding the intruder with a mass of defending worker bees, which vibrate their muscles vigorously to raise the temperature of the intruder to a lethal level ("balling").[45] Previously, heat alone was thought to be responsible for killing intruding wasps, but recent experiments have demonstrated the increased temperature in combination with increased carbon dioxide levels within the ball produce the lethal effect.[46][47] This phenomenon is also used to kill a queen perceived as intruding or defective, an action known to beekeepers as 'balling the queen', named for the ball of bees formed.

text: Defense can vary based on the habitat of the bee. In the case of those honey bee species with open combs (e.g., A. dorsata), would-be predators are given a warning signal that takes the form of a "Mexican wave" that spreads as a ripple across a layer of bees densely packed on the surface of the comb when a threat is perceived, and consists of bees momentarily arching their bodies and flicking their wings.[48] In cavity dwelling species such as Apis cerana, Apis mellifera, and Apis nigrocincta, entrances to these cavities are guarded and checked for intruders in incoming traffic. Another act of defense against nest invaders, particularly wasps, is "body shaking," a violent and pendulum like swaying of the abdomen, performed by worker bees.[49]

text: Competition[edit]

text: With an increased number of honey bees in a specific area due to beekeeping, domesticated bees and native wild bees often have to compete for the limited habitat and food sources available.[50] European bees may become defensive in response to the seasonal arrival of competition from other colonies, particularly Africanized bees which may be on the offence and defense year round due to their tropical origin.[51] In the United Kingdom, honey bees are known to compete with Bombus hortorum, a bumblebee species, because they forage at the same sites. To resolve the issue and maximize both their total consumption during foraging, bumblebees forage early in the morning, while honey bees forage during the afternoon.[52]

text: Communication[edit]

text: Honey bees are known to communicate through many different chemicals and odors, as is common in insects. They also rely on a sophisticated dance language that conveys information about the distance and direction to a specific location (typically a nutritional source, e.g., flowers or water). The dance language is also used during the process of reproductive fission, or swarming, when scouts communicate the location and quality of nesting sites.[53]

text: The details of the signalling being used vary from species to species; for example, the two smallest species, Apis andreniformis and A. florea, dance on the upper surface of the comb, which is horizontal (not vertical, as in other species), and worker bees orient the dance in the actual compass direction of the resource to which they are recruiting.

text: Apis mellifera carnica honey bees use their antennae asymmetrically for social interactions with a strong lateral preference to use their right antennae.[54][55]

text: There has been speculation as to honeybee consciousness.[56]

text: Symbolism[edit]

text: The bee was revived as a symbol of government by Emperor Napoleon I of France.[57] Both the Hindu Atharva Veda[58] and the ancient Greeks associated lips anointed with honey with the gift of eloquence and even of prescience. The priestess at Delphi was the "Delphic Bee". The Quran has a chapter titled "The Bee". A community of honey bees has often been employed by political theorists as a model of human society, from Aristotle and Plato to Virgil[59] and Seneca; in Erasmus and Shakespeare; in Marx and Tolstoy.[60] Honey bees, signifying immortality and resurrection, were royal emblems of the Merovingians. The bee also is the heraldic emblem of the Barberini.[citation needed] The state of Utah is called the "Beehive State", the state emblem is the beehive, the state insect is the honey bee, and a beehive and the word "industry" appear on both the state flag and seal.[61][62][63][64]

text: Gallery[edit]

text:
Foragers loaded with pollen on the hive landing board

Eastern honey bee (A. cerana) in Hong Kong

Giant honey bee (A. dorsata)

Honey bee visiting flowers

A colony of giant honey bees on their comb

Play media

Pollinating flowers

Genus Apis


document_title: Bohr model

question_text: who discovered the quantum mechanical model of the atom

root

text: Bohr model

text: Origin[edit]

text: In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a diffuse cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus.[2] Given this experimental data, Rutherford naturally considered a planetary-model atom, the Rutherford model of 1911 – electrons orbiting a solar nucleus – however, said planetary-model atom has a technical difficulty. The laws of classical mechanics (i.e. the Larmor formula), predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds.[3] This atom model is disastrous, because it predicts that all atoms are unstable.[4]

tag: p

text: Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster. This would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharges have shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies.

text: To overcome this difficulty, Niels Bohr proposed, in 1913, what is now called the Bohr model of the atom. He suggested that electrons could only have certain classical motions:

text:
Electrons in atoms orbit the nucleus.
The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits"[5]) at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics. The Bohr model of an atom was based upon Planck's quantum theory of radiation.
Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency ν determined by the energy difference of the levels according to the Planck relation:

Δ

E

=

E

2

−

E

1

=
h
ν

,

{\displaystyle \Delta {E}=E_{2}-E_{1}=h\nu \ ,}

where h is Planck's constant. The frequency of the radiation emitted at an orbit of period T is as it would be in classical mechanics; it is the reciprocal of the classical orbit period:

ν
=

1
T

.

{\displaystyle \nu ={1 \over T}~~.}

:

tag: ol

text: where n = 1, 2, 3, ... is called the principal quantum number, and ħ = h/2π. The lowest value of n is 1; this gives a smallest possible orbital radius of 0.0529 nm known as the Bohr radius. Once an electron is in this lowest orbit, it can get no closer to the proton. Starting from the angular momentum quantum rule, Bohr[2] was able to calculate the energies of the allowed orbits of the hydrogen atom and other hydrogen-like atoms and ions.

text: Other points are:

text:
Like Einstein's theory of the Photoelectric effect, Bohr's formula assumes that during a quantum jump a discrete amount of energy is radiated. However, unlike Einstein, Bohr stuck to the classical Maxwell theory of the electromagnetic field. Quantization of the electromagnetic field was explained by the discreteness of the atomic energy levels; Bohr did not believe in the existence of photons.
According to the Maxwell theory the frequency ν of classical radiation is equal to the rotation frequency νrot of the electron in its orbit, with harmonics at integer multiples of this frequency. This result is obtained from the Bohr model for jumps between energy levels En and En−k when k is much smaller than n. These jumps reproduce the frequency of the k-th harmonic of orbit n. For sufficiently large values of n (so-called Rydberg states), the two orbits involved in the emission process have nearly the same rotation frequency, so that the classical orbital frequency is not ambiguous. But for small n (or large k), the radiation frequency has no unambiguous classical interpretation. This marks the birth of the correspondence principle, requiring quantum theory to agree with the classical theory only in the limit of large quantum numbers.
The Bohr-Kramers-Slater theory (BKS theory) is a failed attempt to extend the Bohr model, which violates the conservation of energy and momentum in quantum jumps, with the conservation laws only holding on average.

text: Bohr's condition, that the angular momentum is an integer multiple of ħ was later reinterpreted in 1924 by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit:

text: Bohr described angular momentum of the electron orbit as 1/2h while de Broglie's wavelength of λ = h/p described h divided by the electron momentum. In 1913, however, Bohr justified his rule by appealing to the correspondence principle, without providing any sort of wave interpretation. In 1913, the wave behavior of matter particles such as the electron (i.e., matter waves) was not suspected.

text: In 1925, a new kind of mechanics was proposed, quantum mechanics, in which Bohr's model of electrons traveling in quantized orbits was extended into a more accurate model of electron motion. The new theory was proposed by Werner Heisenberg. Another form of the same theory, wave mechanics, was discovered by the Austrian physicist Erwin Schrödinger independently, and by different reasoning. Schrödinger employed de Broglie's matter waves, but sought wave solutions of a three-dimensional wave equation describing electrons that were constrained to move about the nucleus of a hydrogen-like atom, by being trapped by the potential of the positive nuclear charge.

text: Electron energy levels[edit]

text: The Bohr model gives almost exact results only for a system where two charged points orbit each other at speeds much less than that of light. This not only involves one-electron systems such as the hydrogen atom, singly ionized helium, and doubly ionized lithium, but it includes positronium and Rydberg states of any atom where one electron is far away from everything else. It can be used for K-line X-ray transition calculations if other assumptions are added (see Moseley's law below). In high energy physics, it can be used to calculate the masses of heavy quark mesons.

text: Calculation of the orbits requires two assumptions.

text: Classical mechanics

tag: ul

text: A quantum rule

text:
How The Equation Was Derived:

If an electron in an atom is moving on an orbit with period T, classically the electromagnetic radiation will repeat itself every orbital period. If the coupling to the electromagnetic field is weak, so that the orbit doesn't decay very much in one cycle, the radiation will be emitted in a pattern which repeats every period, so that the Fourier transform will have frequencies which are only multiples of 1/T. This is the classical radiation law: the frequencies emitted are integer multiples of 1/T.
In quantum mechanics, this emission must be in quanta of light, of frequencies consisting of integer multiples of 1/T, so that classical mechanics is an approximate description at large quantum numbers. This means that the energy level corresponding to a classical orbit of period 1/T must have nearby energy levels which differ in energy by h/T, and they should be equally spaced near that level,

Δ

E

n

=

h

T
(

E

n

)

.

{\displaystyle \Delta E_{n}={h \over T(E_{n})}.}

Bohr worried whether the energy spacing 1/T should be best calculated with the period of the energy state

E

n

{\displaystyle E_{n}}

, or

E

n
+
1

{\displaystyle E_{n+1}}

, or some average—in hindsight, this model is only the leading semiclassical approximation.
Bohr considered circular orbits. Classically, these orbits must decay to smaller circles when photons are emitted. The level spacing between circular orbits can be calculated with the correspondence formula. For a Hydrogen atom, the classical orbits have a period T determined by Kepler's third law to scale as r3/2. The energy scales as 1/r, so the level spacing formula amounts to

Δ
E
∝

1

r

3
2

∝

E

3
2

.

{\displaystyle \Delta E\propto {1 \over r^{3 \over 2}}\propto E^{3 \over 2}.}

It is possible to determine the energy levels by recursively stepping down orbit by orbit, but there is a shortcut.
The angular momentum L of the circular orbit scales as √r. The energy in terms of the angular momentum is then

E
∝

1
r

∝

1

L

2

{\displaystyle E\propto {1 \over r}\propto {1 \over L^{2}}}

.

Assuming, with Bohr, that quantized values of L are equally spaced, the spacing between neighboring energies is

Δ
E
∝

1

(
L
+
ℏ

)

2

−

1

L

2

≈
−

2
ℏ

L

3

∝
−

E

3
2

.

{\displaystyle \Delta E\propto {1 \over (L+\hbar )^{2}}-{1 \over L^{2}}\approx -{2\hbar  \over L^{3}}\propto -E^{3 \over 2}.}

This is as desired for equally spaced angular momenta. If one kept track of the constants, the spacing would be ħ, so the angular momentum should be an integer multiple of ħ,

L
=

n
h

2
π

=
n
ℏ

.

{\displaystyle L={nh \over 2\pi }=n\hbar ~.}

This is how Bohr arrived at his model.

tag: table

text: An electron in the lowest energy level of hydrogen (n = 1) therefore has about 13.6 eV less energy than a motionless electron infinitely far from the nucleus. The next energy level (n = 2) is −3.4 eV. The third (n = 3) is −1.51 eV, and so on. For larger values of n, these are also the binding energies of a highly excited atom with one electron in a large circular orbit around the rest of the atom. The hydrogen formula also coincides with the Wallis product.[6]

text: The combination of natural constants in the energy formula is called the Rydberg energy (RE):

text: This expression is clarified by interpreting it in combinations that form more natural units:

text: Since this derivation is with the assumption that the nucleus is orbited by one electron, we can generalize this result by letting the nucleus have a charge q = Z e where Z is the atomic number. This will now give us energy levels for hydrogenic atoms, which can serve as a rough order-of-magnitude approximation of the actual energy levels. So for nuclei with Z protons, the energy levels are (to a rough approximation):

text: The actual energy levels cannot be solved analytically for more than one electron (see n-body problem) because the electrons are not only affected by the nucleus but also interact with each other via the Coulomb Force.

text: When Z = 1/α (Z ≈ 137), the motion becomes highly relativistic, and Z2 cancels the α2 in R; the orbit energy begins to be comparable to rest energy. Sufficiently large nuclei, if they were stable, would reduce their charge by creating a bound electron from the vacuum, ejecting the positron to infinity. This is the theoretical phenomenon of electromagnetic charge screening which predicts a maximum nuclear charge. Emission of such positrons has been observed in the collisions of heavy ions to create temporary super-heavy nuclei.[citation needed]

text: The Bohr formula properly uses the reduced mass of electron and proton in all situations, instead of the mass of the electron,

text: However, these numbers are very nearly the same, due to the much larger mass of the proton, about 1836.1 times the mass of the electron, so that the reduced mass in the system is the mass of the electron multiplied by the constant 1836.1/(1+1836.1) = 0.99946. This fact was historically important in convincing Rutherford of the importance of Bohr's model, for it explained the fact that the frequencies of lines in the spectra for singly ionized helium do not differ from those of hydrogen by a factor of exactly 4, but rather by 4 times the ratio of the reduced mass for the hydrogen vs. the helium systems, which was much closer to the experimental ratio than exactly 4.

text: For positronium, the formula uses the reduced mass also, but in this case, it is exactly the electron mass divided by 2. For any value of the radius, the electron and the positron are each moving at half the speed around their common center of mass, and each has only one fourth the kinetic energy. The total kinetic energy is half what it would be for a single electron moving around a heavy nucleus.

text: Rydberg formula[edit]

text: The Rydberg formula, which was known empirically before Bohr's formula, is seen in Bohr's theory as describing the energies of transitions or quantum jumps between orbital energy levels. Bohr's formula gives the numerical value of the already-known and measured Rydberg's constant, but in terms of more fundamental constants of nature, including the electron's charge and Planck's constant.

text: When the electron gets moved from its original energy level to a higher one, it then jumps back each level until it comes to the original position, which results in a photon being emitted. Using the derived formula for the different energy levels of hydrogen one may determine the wavelengths of light that a hydrogen atom can emit.

text: The energy of a photon emitted by a hydrogen atom is given by the difference of two hydrogen energy levels:

text: where nf is the final energy level, and ni is the initial energy level.

text: Since the energy of a photon is

text: the wavelength of the photon given off is given by

text: This is known as the Rydberg formula, and the Rydberg constant R is RE/hc, or RE/2π in natural units. This formula was known in the nineteenth century to scientists studying spectroscopy, but there was no theoretical explanation for this form or a theoretical prediction for the value of R, until Bohr. In fact, Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the Lyman (nf =1), Balmer (nf =2), and Paschen (nf =3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted.

text: To apply to atoms with more than one electron, the Rydberg formula can be modified by replacing Z with Z−b or n with n−b where b is constant representing a screening effect due to the inner-shell and other electrons (see Electron shell and the later discussion of the "Shell Model of the Atom" below). This was established empirically before Bohr presented his model.

text: Shell model of heavier atoms[edit]

text: Bohr extended the model of hydrogen to give an approximate model for heavier atoms. This gave a physical picture that reproduced many known atomic properties for the first time.

text: Heavier atoms have more protons in the nucleus, and more electrons to cancel the charge. Bohr's idea was that each discrete orbit could only hold a certain number of electrons. After that orbit is full, the next level would have to be used. This gives the atom a shell structure, in which each shell corresponds to a Bohr orbit.

text: This model is even more approximate than the model of hydrogen, because it treats the electrons in each shell as non-interacting. But the repulsions of electrons are taken into account somewhat by the phenomenon of screening. The electrons in outer orbits do not only orbit the nucleus, but they also move around the inner electrons, so the effective charge Z that they feel is reduced by the number of the electrons in the inner orbit.

text: For example, the lithium atom has two electrons in the lowest 1s orbit, and these orbit at Z=2. Each one sees the nuclear charge of Z=3 minus the screening effect of the other, which crudely reduces the nuclear charge by 1 unit. This means that the innermost electrons orbit at approximately 1/4 the Bohr radius. The outermost electron in lithium orbits at roughly Z=1, since the two inner electrons reduce the nuclear charge by 2. This outer electron should be at nearly one Bohr radius from the nucleus. Because the electrons strongly repel each other, the effective charge description is very approximate; the effective charge Z doesn't usually come out to be an integer. But Moseley's law experimentally probes the innermost pair of electrons, and shows that they do see a nuclear charge of approximately Z−1, while the outermost electron in an atom or ion with only one electron in the outermost shell orbits a core with effective charge Z−k where k is the total number of electrons in the inner shells.

text: The shell model was able to qualitatively explain many of the mysterious properties of atoms which became codified in the late 19th century in the periodic table of the elements. One property was the size of atoms, which could be determined approximately by measuring the viscosity of gases and density of pure crystalline solids. Atoms tend to get smaller toward the right in the periodic table, and become much larger at the next line of the table. Atoms to the right of the table tend to gain electrons, while atoms to the left tend to lose them. Every element on the last column of the table is chemically inert (noble gas).

text: In the shell model, this phenomenon is explained by shell-filling. Successive atoms become smaller because they are filling orbits of the same size, until the orbit is full, at which point the next atom in the table has a loosely bound outer electron, causing it to expand. The first Bohr orbit is filled when it has two electrons, which explains why helium is inert. The second orbit allows eight electrons, and when it is full the atom is neon, again inert. The third orbital contains eight again, except that in the more correct Sommerfeld treatment (reproduced in modern quantum mechanics) there are extra "d" electrons. The third orbit may hold an extra 10 d electrons, but these positions are not filled until a few more orbitals from the next level are filled (filling the n=3 d orbitals produces the 10 transition elements). The irregular filling pattern is an effect of interactions between electrons, which are not taken into account in either the Bohr or Sommerfeld models and which are difficult to calculate even in the modern treatment.

text: Moseley's law and calculation of K-alpha X-ray emission lines[edit]

text: Niels Bohr said in 1962, "You see actually the Rutherford work was not taken seriously. We cannot understand today,but it was not taken seriously at all. There was no mention of it any place. The great change came from Moseley."

text: In 1913 Henry Moseley found an empirical relationship between the strongest X-ray line emitted by atoms under electron bombardment (then known as the K-alpha line), and their atomic number Z. Moseley's empiric formula was found to be derivable from Rydberg and Bohr's formula (Moseley actually mentions only Ernest Rutherford and Antonius Van den Broek in terms of models). The two additional assumptions that [1] this X-ray line came from a transition between energy levels with quantum numbers 1 and 2, and [2], that the atomic number Z when used in the formula for atoms heavier than hydrogen, should be diminished by 1, to (Z−1)2.

text: Moseley wrote to Bohr, puzzled about his results, but Bohr was not able to help. At that time, he thought that the postulated innermost "K" shell of electrons should have at least four electrons, not the two which would have neatly explained the result. So Moseley published his results without a theoretical explanation.

text: Later, people realized that the effect was caused by charge screening, with an inner shell containing only 2 electrons. In the experiment, one of the innermost electrons in the atom is knocked out, leaving a vacancy in the lowest Bohr orbit, which contains a single remaining electron. This vacancy is then filled by an electron from the next orbit, which has n=2. But the n=2 electrons see an effective charge of Z−1, which is the value appropriate for the charge of the nucleus, when a single electron remains in the lowest Bohr orbit to screen the nuclear charge +Z, and lower it by −1 (due to the electron's negative charge screening the nuclear positive charge). The energy gained by an electron dropping from the second shell to the first gives Moseley's law for K-alpha lines,

text: or

text: Here, Rv = RE/h is the Rydberg constant, in terms of frequency equal to 3.28 x 1015 Hz. For values of Z between 11 and 31 this latter relationship had been empirically derived by Moseley, in a simple (linear) plot of the square root of X-ray frequency against atomic number (however, for silver, Z = 47, the experimentally obtained screening term should be replaced by 0.4). Notwithstanding its restricted validity,[7] Moseley's law not only established the objective meaning of atomic number (see Henry Moseley for detail) but, as Bohr noted, it also did more than the Rydberg derivation to establish the validity of the Rutherford/Van den Broek/Bohr nuclear model of the atom, with atomic number (place on the periodic table) standing for whole units of nuclear charge.

text: The K-alpha line of Moseley's time is now known to be a pair of close lines, written as (Kα1 and Kα2) in Siegbahn notation.

text: Shortcomings[edit]

text: The Bohr model gives an incorrect value L=ħ for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment.[8] Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to rotate "around" the nucleus at all, but merely to go tightly around it in an ellipse with zero area (this may be pictured as "back and forth", without striking or interacting with the nucleus). This is only reproduced in a more sophisticated semiclassical treatment like Sommerfeld's. Still, even the most sophisticated semiclassical model fails to explain the fact that the lowest energy state is spherically symmetric – it doesn't point in any particular direction.

text: Nevertheless, in the modern fully quantum treatment in phase space, the proper deformation (careful full extension) of the semi-classical result adjusts the angular momentum value to the correct effective one. As a consequence, the physical ground state expression is obtained through a shift of the vanishing quantum angular momentum expression, which corresponds to spherical symmetry.

text: In modern quantum mechanics, the electron in hydrogen is a spherical cloud of probability that grows denser near the nucleus. The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a "coincidence". (However, many such coincidental agreements are found between the semiclassical vs. full quantum mechanical treatment of the atom; these include identical energy levels in the hydrogen atom and the derivation of a fine structure constant, which arises from the relativistic Bohr–Sommerfeld model (see below) and which happens to be equal to an entirely different concept, in full modern quantum mechanics).

text: The Bohr model also has difficulty with, or else fails to explain:

text:
Much of the spectra of larger atoms. At best, it can make predictions about the K-alpha and some L-alpha X-ray emission spectra for larger atoms, if two additional ad hoc assumptions are made (see Moseley's law above). Emission spectra for atoms with a single outer-shell electron (atoms in the lithium group) can also be approximately predicted. Also, if the empiric electron–nuclear screening factors for many atoms are known, many other spectral lines can be deduced from the information, in similar atoms of differing elements, via the Ritz–Rydberg combination principles (see Rydberg formula). All these techniques essentially make use of Bohr's Newtonian energy-potential picture of the atom.
the relative intensities of spectral lines; although in some simple cases, Bohr's formula or modifications of it, was able to provide reasonable estimates (for example, calculations by Kramers for the Stark effect).
The existence of fine structure and hyperfine structure in spectral lines, which are known to be due to a variety of relativistic and subtle effects, as well as complications from electron spin.
The Zeeman effect – changes in spectral lines due to external magnetic fields; these are also due to more complicated quantum principles interacting with electron spin and orbital magnetic fields.
The model also violates the uncertainty principle in that it considers electrons to have known orbits and locations, two things which can not be measured simultaneously.
Doublets and Triplets: Appear in the spectra of some atoms: Very close pairs of lines. Bohr’s model cannot say why some energy levels should be very close together.
Multi-electron Atoms: don’t have energy levels predicted by the model. It doesn’t work for (neutral) helium.
A rotating charge, such as the electron classically orbiting around the nucleus, would constantly lose energy in form of electromagnetic radiation (via various mechanisms: dipole radiation, Bremsstrahlung,...). But such radiation is not observed.

text: Refinements[edit]

text: Several enhancements to the Bohr model were proposed, most notably the Sommerfeld model or Bohr–Sommerfeld model, which suggested that electrons travel in elliptical orbits around a nucleus instead of the Bohr model's circular orbits.[1] This model supplemented the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Sommerfeld–Wilson quantization condition[9][10]

text: where pr is the radial momentum canonically conjugate to the coordinate q which is the radial position and T is one full orbital period. The integral is the action of action-angle coordinates. This condition, suggested by the correspondence principle, is the only one possible, since the quantum numbers are adiabatic invariants.

text: The Bohr–Sommerfeld model was fundamentally inconsistent and led to many paradoxes. The magnetic quantum number measured the tilt of the orbital plane relative to the xy-plane, and it could only take a few discrete values. This contradicted the obvious fact that an atom could be turned this way and that relative to the coordinates without restriction. The Sommerfeld quantization can be performed in different canonical coordinates and sometimes gives different answers. The incorporation of radiation corrections was difficult, because it required finding action-angle coordinates for a combined radiation/atom system, which is difficult when the radiation is allowed to escape. The whole theory did not extend to non-integrable motions, which meant that many systems could not be treated even in principle. In the end, the model was replaced by the modern quantum mechanical treatment of the hydrogen atom, which was first given by Wolfgang Pauli in 1925, using Heisenberg's matrix mechanics. The current picture of the hydrogen atom is based on the atomic orbitals of wave mechanics which Erwin Schrödinger developed in 1926.

text: However, this is not to say that the Bohr-Sommerfeld model was without its successes. Calculations based on the Bohr–Sommerfeld model were able to accurately explain a number of more complex atomic spectral effects. For example, up to first-order perturbations, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the Stark effect. At higher-order perturbations, however, the Bohr model and quantum mechanics differ, and measurements of the Stark effect under high field strengths helped confirm the correctness of quantum mechanics over the Bohr model. The prevailing theory behind this difference lies in the shapes of the orbitals of the electrons, which vary according to the energy state of the electron.

text: The Bohr–Sommerfeld quantization conditions lead to questions in modern mathematics. Consistent semiclassical quantization condition requires a certain type of structure on the phase space, which places topological limitations on the types of symplectic manifolds which can be quantized. In particular, the symplectic form should be the curvature form of a connection of a Hermitian line bundle, which is called a prequantization.