Lambda is the 11th letter of the Greek alphabet, representing the sound /l/. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed. Letters in other alphabets that stemmed from lambda include the Cyrillic letter El; the ancient grammarians and dramatists give evidence to the pronunciation as in Classical Greek times. In Modern Greek the name of the letter, Λάμδα, is pronounced. In early Greek alphabets, the shape and orientation of lambda varied. Most variants consisted one longer than the other, connected at their ends; the angle might be in lower-left, or top. Other variants had a vertical line with a sloped stroke running to the right. With the general adoption of the Ionic alphabet, Greek settled on an angle at the top; the HTML 4 character entity references for the Greek capital and small letter lambda are "Λ. The Unicode code points for lambda are U+039B and U+03BB. Examples of the symbolic use of uppercase lambda include: The lambda particle is a type of subatomic particle in subatomic particle physics.
Lambda is the set of logical axioms in the axiomatic method of logical deduction in first-order logic. Lambda was used as a shield pattern by the Spartan army; this stood for Lacedaemon, the name of the polis of the Spartans, as opposed to the city itself. Lambda is the von Mangoldt function in mathematical number theory. In statistics, Wilks's lambda is used in multivariate analysis of variance to compare group means on a combination of dependent variables. In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the matrix. In computer science, lambda is the time window over which a process is observed for determining the working memory set for a digital computer's virtual memory management. In astrophysics, lambda represents the likelihood that a small body will encounter a planet or a dwarf planet leading to a deflection of a significant magnitude. An object with a large value of lambda is expected to have cleared its neighborhood, satisfying the current definition of a planet.
In crystal optics, lambda is used to represent the period of a lattice. In NATO military operations, a chevron is painted on the vehicles of this military alliance for identification. In chemistry there are Δ and Λ isomers, see: coordination complex In electrochemistry, lambda denotes the "equivalent conductance" of an electrolyte solution. In cosmology, lambda is the symbol for the cosmological constant, a term added to some dynamical equations to account for the acceleration of the universe. In optics, lambda denotes the grating pitch of a Bragg reflector. In block-handwritten Russian, this letter represents Л in both lowercase. In politics the lambda is the symbol of Identitarianism a white nationalist movement that originated in France before spreading out to the rest of Europe and on to North America and New Zealand; the Identitarian lambda represents the Battle of Thermopylae. Examples of the symbolic use of lowercase lambda include: In evolutionary algorithms, λ indicates the number of offspring that would be generated from μ current population in each generation.
The terms μ and λ are originated from Evolution strategy notation. Lambda indicates the wavelength of any wave in physics, electronics engineering, mathematics. Lambda indicates the radioactivity decay constant in nuclear radioactivity; this constant is simply related to the half-life of any radioactive material. In probability theory, lambda represents the density of occurrences within a time interval, as modeled by the Poisson distribution. In mathematical logic and computer science, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus. Lambda is a unit of volume, synonymous with one microliter; this use is deprecated. Lambda indicates an eigenvalue in the mathematics of linear algebra. In the physics of electric fields, lambda sometimes indicates the linear charge density of a uniform line of electric charge. Lambda denotes a Lagrange multiplier in multi-dimensional calculus. In solid-state electronics, lambda indicates the channel length modulation parameter of a MOSFET.
In ecology, lambda denotes the long-term intrinsic growth rate of a population. This value is calculated as the dominant eigenvalue of the age/size class matrix. In formal language theory and in computer science, lambda denotes the empty string. Lambda is a nonstandard symbol in the International Phonetic Alphabet. Lambda denotes the Lebesgue measure in mathematical set theory; the Goodman and Kruskal's lambda in statistics indicates the proportional reduction in error when one variable's values are used to predict the values of another variable. Lambda denotes the oxygen sensor in a vehicle that measures the air-to-fuel ratio in the exhaust gases of an internal-combustion engine. A Lambda 4S solid-fuel rocket was used to launch Japan's first orbital satellite in 1970. Lambda denotes the failure rate of devices and systems in reliability theory, it is measured in failure events per hour. Numerically, this lambda is the reciprocal of the mean time between failures. In criminology, lambda denotes an individual's frequency of offenses.
In cartography and navigation, lambda denotes the longitude of a location. In electrochemistry, lambda denotes the ionic cond
In written language, a logogram or logograph is a written character that represents a word or phrase. Chinese characters are logograms; the use of logograms in writing is called logography, a writing system, based on logograms is called a logographic system. In alphabets and syllabaries, individual written characters represent sounds only, rather than entire concepts; these characters are called phonograms in linguistics. Unlike logograms, phonograms do not have word or phrase meanings singularly until the phonograms are combined with additional phonograms thus creating words and phrases that have meaning. Writing language in this way, is called phonetic writing as well as orthographical writing. Logographic systems include the earliest writing systems. A purely logographic script would be impractical for most languages, none is known, apart from one devised for the artificial language Toki Pona, a purposely limited language with only 120 morphemes. All logographic scripts used for natural languages rely on the rebus principle to extend a limited set of logograms: A subset of characters is used for their phonetic values, either consonantal or syllabic.
The term logosyllabary is used to emphasize the phonetic nature of these scripts when the phonetic domain is the syllable. In both Ancient Egyptian hieroglyphs and in Chinese, there has been the additional development of fusing such phonetic elements with determinatives. Logographic writing systems include: Logoconsonantal scripts These are scripts in which the graphemes may be extended phonetically according to the consonants of the words they represent, ignoring the vowels. For example, Egyptian was used to write both sȝ'duck' and sȝ'son', though it is that these words were not pronounced the same apart from their consonants; the primary examples of logoconsonantal scripts are:Hieroglyphs and demotic: Ancient Egyptian Logosyllabic scripts These are scripts in which the graphemes represent morphemes polysyllabic morphemes, but when extended phonetically represent single syllables. They include:Anatolian hieroglyphs: Luwian Cuneiform: Sumerian, other Semitic languages, Hittite, Luwian and Urartian Maya glyphs: Chorti and other Classic Maya languages Han characters: Chinese, Japanese, Zhuang Derivatives of Han characters: Chữ nôm: Vietnam Dongba script written with Geba script: Naxi language Jurchen script: Jurchen Khitan large script: Khitan Sawndip: Zhuang languages Shui script: Shui language Tangut script: Tangut language Yi: various Yi languagesNone of these systems is purely logographic.
This can be illustrated with Chinese. Not all Chinese characters represent morphemes: some morphemes are composed of more than one character. For example, the Chinese word for spider, 蜘蛛 zhīzhū, was created by fusing the rebus 知朱 zhīzhū with the "bug" determinative 虫. Neither *蜘 zhī nor *蛛 zhū can be used separately; this is incorrect. In Archaic Chinese, one can find the reverse: a single character representing more than one morpheme. An example is Archaic Chinese 王 hjwangs, a combination of a morpheme hjwang meaning king and a suffix pronounced /s/. In modern Mandarin, bimorphemic syllables are always written with two characters, for example 花儿 huār'flower'. A peculiar system of logograms developed within the Pahlavi scripts used to write Middle Persian during much of the Sassanid period; these logograms, called hozwārishn, were dispensed with altogether after the Arab conquest of Persia and the adoption of a variant of the Arabic alphabet. Logograms are used in modern shorthand to represent common words.
In addition, the numerals and mathematical symbols are logograms – 1'one', 2'two', +'plus', ='equals', so on. In English, the ampersand & is used for'and' and for Latin et, % for'percent', # for'number', § for'section', $ for'dollar', € for'euro', £ for'pound', ° for'degree', @ for'at', so on. All historical logographic systems include a phonetic dimension, as it is impractical to have a separate basic character for every word or morpheme in a language. In some cases, such as cuneiform as it was used for Akkadian, the vast majority of glyphs are used for their sound values rather than logographically. Many logographic systems have a semantic/ideographic component, called "determinatives" in the case of Egyptian and "radicals" in the case of Chinese. Typical Egyptian usage was to augment a logogram, which may represent several words with different pronunciations, with a determinate to narrow down the meaning, a phonetic component to specify the pronunciation. In the case of Chinese, the vast majority of characters are a fixed combination of a radical that indicates its nominal category, plus a phonetic to give an idea of the pronunciation.
The Mayan system used logograms
Ll/ll is a digraph which occurs in several natural languages. In English, ll represents the same sound as single l: /l/; the doubling is used to indicate that the preceding vowel is short, or that the "l" sound is to be extended longer than a single "l" would provide. It is worth noting that different English language traditions transpose "l" and "ll": British English "travelled" and like words, for example, are spelled with a single "l" in U. S. English. In Welsh, ll stands for a voiceless alveolar lateral fricative sound; the IPA signifies this sound as. This sound is common in place names in Wales because it occurs in the word Llan, for example, where the ll appears twice, or Llanfairpwllgwyngyll, where the ll appears three times. In Welsh,'Ll' is a separate letter from L; this led to its ligature being included in the Latin Extended Additional Unicode block. The capital ligature appears similar to a joined "IL" and the minuscule ligature like "ll" joined across the top.. This ligatured character is not used in Modern Welsh.
In Spanish, ll was considered a digraph from 1754 to 2010 as the fourteenth letter of the Spanish alphabet because of its representation of a palatal lateral articulation consonant phoneme. This single letter was called "elle"; this letter was collated after L as a separate entry, from 1803 until April 1994, after a vote in the X Congress of the Association of Spanish Language Academies ruled for the adoption of the standard Latin alphabet collation rules. Since the digraph ll is now considered a sequence of two characters. A similar situation occurred with the Spanish-language digraph ch. Hypercorrection leads some to wrongly capitalize it as a single letter, as with the Dutch IJ. In handwriting, it is written with a distinct uppercase and lowercase form. An old ligature for Ll is known as the "broken L", which takes the form of a lowercase l with the top half shifted to the left, connected to the lower half with a thin horizontal stroke; this ligature is displayed Ꝇ and ꝇ respectively. Today, most Spanish speakers outside of Spain pronounce ll as the same sound as y, a phenomenon called yeísmo.
As a result, in most Spanish-speaking parts of the Americas as well as in many regions of Spain, Spanish speakers pronounce it /ʝ/, while some other Spanish speakers in the Americas pronounce it /ʒ/ or /ʃ/. In official Galician spelling the ll combination stands for the phoneme /ʎ/. In Catalan, ll represents the phoneme /ʎ/. For example, as in llengua "language" or "tongue", enllaç "linkage", "connection" or coltell "knife". In order to not confuse ll /ʎ/ with a geminated l /ll/, the ligature ŀl is used with the second meaning. For example, exceŀlent is the Catalan word from Latin excellente. In Catalan, l·l must occupy two spaces, so the interpunct is placed in the narrow space between the two L: ĿL and ŀl. However, it is more common to write l · l, occupying three spaces. L. L and l.l are incorrect and not accepted. See interpunct for more information. While Philippine languages like Tagalog and Ilokano write ly or li in the spelling of Spanish loanwords, ll still survives in proper nouns. However, the pronunciation of ll is rather than.
Hence the surnames Llamzon, Llamas and Villanueva are pronounced /, /. Furthermore, in Ilokano ll represents a geminate alveolar lateral approximant /lː/, like in Italian. In Albanian, L stands for the sound /l/, while Ll is pronounced as the velarized sound /ɫ/. In Icelandic, the "ll" represents either the sound combination or, depending on the context, it occurs in the words "fell", "fjall", "jökull", in the names of many geographical features, including Eyjafjallajökull. In the Gwoyeu Romatzyh romanization of Mandarin Chinese, final -ll indicates a falling tone on a syllable ending in /ɻ/, otherwise spelled -l. In Central Alaskan Yup'ik and the Greenlandic language, ll stands for /ɬː/, in Haida it is glottalized /ˀl/. Lh Lj Hungarian ly
Geʽez known as Ethiopic, is a script used as an abugida for several languages of Eritrea and Ethiopia. It originated as an abjad and was first used to write Geʽez, now the liturgical language of the Eritrean Orthodox Tewahedo Church, the Ethiopian Orthodox Tewahedo Church, Beta Israel, the Jewish community in Ethiopia. In Amharic and Tigrinya, the script is called fidäl, meaning "script" or "alphabet"; the Geʽez script has been adapted to write other Semitic, languages Amharic in Ethiopia, Tigrinya in both Eritrea and Ethiopia. It is used for Sebatbeit, Meʼen, most other languages of Ethiopia. In Eritrea it is used for Tigre, it has traditionally been used for Blin, a Cushitic language. Tigre, spoken in western and northern Eritrea, is considered to resemble Geʽez more than do the other derivative languages; some other languages in the Horn of Africa, such as Oromo, used to be written using Geʽez, but have migrated to Latin-based orthographies. For the representation of sounds, this article uses a system, common among linguists who work on Ethiopian Semitic languages.
This differs somewhat from the conventions of the International Phonetic Alphabet. See the articles on the individual languages for information on the pronunciation; the earliest inscriptions of Semitic languages in Eritrea and Ethiopia date to the 9th century BC in Epigraphic South Arabian, an abjad shared with contemporary kingdoms in South Arabia. After the 7th and 6th centuries BC, variants of the script arose, evolving in the direction of the Geʽez abugida; this evolution can be seen most in evidence from inscriptions in Tigray region in northern Ethiopia and the former province of Akkele Guzay in Eritrea. By the first centuries AD, what is called "Old Ethiopic" or the "Old Geʽez alphabet" arose, an abjad written left-to-right with letters identical to the first-order forms of the modern vocalized alphabet. There were minor differences such as the letter "g" facing to the right, instead of to the left as in vocalized Geʽez, a shorter left leg of "l", as in ESA, instead of equally-long legs in vocalized Geʽez.
Vocalization of Geʽez occurred in the 4th century, though the first vocalized texts known are inscriptions by Ezana, vocalized letters predate him by some years, as an individual vocalized letter exists in a coin of his predecessor Wazeba. Linguist Roger Schneider has pointed out anomalies in the known inscriptions of Ezana that imply that he was consciously employing an archaic style during his reign, indicating that vocalization could have occurred much earlier; as a result, some believe that the vocalization may have been adopted to preserve the pronunciation of Geʽez texts due to the moribund or extinct status of Geʽez, that, by that time, the common language of the people were later Ethio-Semitic languages. At least one of Wazeba's coins from the late 3rd or early 4th century contains a vocalized letter, some 30 or so years before Ezana. Kobishchanov and others have suggested possible influence from the Brahmic family of alphabets in vocalization, as they are abugidas, Aksum was an important part of major trade routes involving India and the Greco-Roman world throughout the common era of antiquity.
According to the beliefs of the Eritrean Orthodox Tewahedo Church and Ethiopian Orthodox Tewahedo Church, the original consonantal form of the Geʽez fidel was divinely revealed to Henos "as an instrument for codifying the laws", the present system of vocalisation is attributed to a team of Aksumite scholars led by Frumentius, the same missionary said to have converted the king Ezana to Christianity in the 4th century AD. It has been argued that the vowel marking pattern of the script reflects a South Asian system, such as would have been known by Frumentius. A separate tradition, recorded by Aleqa Taye, holds that the Geʽez consonantal alphabet was first adapted by Zegdur, a legendary king of the Ag'azyan Sabaean dynasty held to have ruled in Ethiopia c. 1300 BC. Geʽez has 26 consonantal letters. Compared to the inventory of 29 consonants in the South Arabian alphabet, continuants are missing of ġ, ẓ, South Arabian s3, as well as z and ṯ, these last two absences reflecting the collapse of interdental with alveolar fricatives.
On the other hand, emphatic P̣ait ጰ, a Geʽez innovation, is a modification of Ṣädai ጸ, while Pesa ፐ is based on Tawe ተ. Thus, there are 24 correspondences of Geʽez and the South Arabian alphabet: Many of the letter names are cognate with those of Phoenician, may thus be assumed for Proto-Sinaitic. Two alphabets were used to write the Geʽez language, an abjad and an abugida; the abjad, used until c. 330 AD, had 26 consonantal letters: h, l, ḥ, m, ś, r, s, ḳ, b, t, ḫ, n, ʾ, k, w, ʿ, z, y, d, g, ṭ, p̣, ṣ, ṣ́, f, p Vowels were not indicated. Modern Geʽez is written from left to right; the Geʽez abugida developed under the influence of Christian scripture by adding obligatory vocalic diacritics to the consonantal letters. The diacritics for the vowels, u, i, a, e, ə, o, were fused with the consonants in a recognizable but irregular way, so that the system is laid out as a syllabary; the original form of the consonant was used when the vowel was the so-called inherent vowel. The resulting forms are shown below in their traditional order.
For some vowels, there is an eighth form for the diphthong -wa or -oa
Old Italic script
Old Italic is one of several now-extinct alphabet systems used on the Italian Peninsula in ancient times for various Indo-European languages and non-Indo-European languages. The alphabets derive from the Euboean Greek Cumaean alphabet, used at Ischia and Cumae in the Bay of Naples in the eighth century BC. Various Indo-European languages belonging to the Italic branch used the alphabet. Faliscan, Umbrian, North Picene, South Picene all derive from an Etruscan form of the alphabet; the Germanic runic alphabet may have been derived from one of these alphabets by the 2nd century AD. The Etruscan alphabet originated as an adaptation of the Western Greek alphabet used by the Euboean Greeks in their first colonies in Italy, the island of Pithekoussai and the city of Cumae in Campania. In the alphabets of the West, X had the sound value, Ψ stood for; the earliest Etruscan abecedarium, the Marsiliana tablet which dates to c. 700 BC, lists 26 letters corresponding to contemporary forms of the Greek alphabet which retained digamma and qoppa but which had not yet developed omega.
Until about 600 BC, the archaic form of the Etruscan alphabet remained unchanged, the direction of writing was free. From the 6th century, the alphabet evolved, adjusting to the phonology of the Etruscan language, letters representing phonemes nonexistent in Etruscan were dropped. By 400 BC, it appears that all of Etruria was using the classical Etruscan alphabet of 20 letters written from left to right: An additional sign, in shape similar to the numeral 8, transcribed as F, was present in both Lydian and Etruscan, its origin is disputed. Its sound value was /f/ and it replaced the Etruscan digraph FH, used to express that sound; some letters were, on the other hand, falling out of use. Etruscan did not have any voiced stops, for which B, C, D were intended; the B and D therefore fell out of use, the C, simpler and easier to write than K, was adopted to write /k/ displacing K itself. Since Etruscan had no /o/ vowel sound, O disappeared and was replaced by U. In the course of its simplification, the redundant letters showed some tendency towards a semi-syllabary: C, K and Q were predominantly used in the contexts CE, KA, QU.
This classical alphabet remained in use until the 2nd century BC when it began to be influenced by the rise of the Latin alphabet. The Romans, who did have voiced stops in their language, revived B and D for /b/ and /d/, used C for both /k/ and /g/, until they invented a separate letter G to distinguish the two sounds. Soon after, the Etruscan language itself became extinct; the Osci adopted the archaic Etruscan alphabet during the 7th century BC, but a recognizably Oscan variant of the alphabet is attested only from the 5th century BC. Ú came to be used to represent Oscan /o/, while U was used for /u/ as well as historical long */oː/, which had undergone a sound shift in Oscan to become ~. The Nucerian alphabet is based on inscriptions found in southern Italy, it is attested only between the 6th and the 5th century BC. The most important sign is the /S/, shaped like a fir tree, a derivation from the Phoenician alphabet; the Alphabet of Lugano, based on inscriptions found in northern Italy and Canton Ticino, was used to record Lepontic inscriptions, among the oldest testimonies of any Celtic language, in use from the 7th to the 5th centuries BC.
The alphabet has 18 letters, derived from the archaic Etruscan alphabet: The alphabet does not distinguish voiced and unvoiced occlusives, i.e. P represents /b/ or /p/, T is for /t/ or /d/, K for /g/ or /k/. Z is for /ts/. U /u/ and V /w/ are distinguished. Θ is for /t/ and X for /g/. There are claims of a related script discovered in Glozel; the alphabet of Sanzeno, about 100 Raetic inscriptions. The alphabet of Magrè, east Raetian inscriptions. Alphabet of Este: Similar but not identical to that of Magrè, Venetic inscriptions. Inscribed abecedarium on rock drawings in Valcamonica. 21 of the 26 archaic Etruscan letters were adopted for Old Latin from the 7th century BC, either directly from the Cumae alphabet, or via archaic Etruscan forms, compared to the classical Etruscan alphabet retaining B, D, K, O, Q, X but dropping Θ, Ś, Φ, Ψ, F. The South Picene alphabet, known from the 6th century BC, is most like the southern Etruscan alphabet in that it uses Q for /k/ and K for /g/, it is: ⟨.⟩ is a reduced ⟨o⟩ and ⟨:⟩ is a reduced ⟨8⟩, used for /f/.
The Old Italic alphabets were unified and added to the Unicode Standard in March, 2001 with the release of version 3.1. The Unicode block for Old Italic is U+10300–U+1032F without specification of a particular alphabet. Writing direction varies based on the language and the time period. For simplicity most scholars use left-to-right and this is the Unicode default direction for the Old Italic block. For this reason, the glyphs in the code chart are shown with left-to-right orientation. Euboean alphabet Negau he
An alphabet is a standard set of letters that represent the phonemes of any spoken language it is used to write. This is in contrast to other types such as syllabaries and logographic systems; the first phonemic script, the Proto-Canaanite script known as the Phoenician alphabet, is considered to be the first alphabet, is the ancestor of most modern alphabets, including Arabic, Latin, Cyrillic and Brahmic. Peter T. Daniels, distinguishes an abugida or alphasyllabary, a set of graphemes that represent consonantal base letters which diacritics modify to represent vowels, an abjad, in which letters predominantly or represent consonants, an "alphabet", a set of graphemes that represent both vowels and consonants. In this narrow sense of the word the first "true" alphabet was the Greek alphabet, developed on the basis of the earlier Phoenician alphabet. Of the dozens of alphabets in use today, the most popular is the Latin alphabet, derived from the Greek, which many languages modify by adding letters formed using diacritical marks.
While most alphabets have letters composed of lines, there are exceptions such as the alphabets used in Braille. The Khmer alphabet is the longest, with 74 letters. Alphabets are associated with a standard ordering of letters; this makes them useful for purposes of collation by allowing words to be sorted in alphabetical order. It means that their letters can be used as an alternative method of "numbering" ordered items, in such contexts as numbered lists and number placements; the English word alphabet came into Middle English from the Late Latin word alphabetum, which in turn originated in the Greek ἀλφάβητος. The Greek word was made from the first two letters and beta; the names for the Greek letters came from the first two letters of the Phoenician alphabet. Sometimes, like in the alphabet song in English, the term "ABCs" is used instead of the word "alphabet". "Knowing one's ABCs", in general, can be used as a metaphor for knowing the basics about anything. The history of the alphabet started in ancient Egypt.
Egyptian writing had a set of some 24 hieroglyphs that are called uniliterals, to represent syllables that begin with a single consonant of their language, plus a vowel to be supplied by the native speaker. These glyphs were used as pronunciation guides for logograms, to write grammatical inflections, to transcribe loan words and foreign names. In the Middle Bronze Age, an "alphabetic" system known as the Proto-Sinaitic script appears in Egyptian turquoise mines in the Sinai peninsula dated to circa the 15th century BC left by Canaanite workers. In 1999, John and Deborah Darnell discovered an earlier version of this first alphabet at Wadi el-Hol dated to circa 1800 BC and showing evidence of having been adapted from specific forms of Egyptian hieroglyphs that could be dated to circa 2000 BC suggesting that the first alphabet had been developed about that time. Based on letter appearances and names, it is believed to be based on Egyptian hieroglyphs; this script had no characters representing vowels, although it was a syllabary, but unneeded symbols were discarded.
An alphabetic cuneiform script with 30 signs including three that indicate the following vowel was invented in Ugarit before the 15th century BC. This script was not used after the destruction of Ugarit; the Proto-Sinaitic script developed into the Phoenician alphabet, conventionally called "Proto-Canaanite" before ca. 1050 BC. The oldest text in Phoenician script is an inscription on the sarcophagus of King Ahiram; this script is the parent script of all western alphabets. By the tenth century, two other forms can be distinguished, namely Aramaic; the Aramaic gave rise to the Hebrew script. The South Arabian alphabet, a sister script to the Phoenician alphabet, is the script from which the Ge'ez alphabet is descended. Vowelless alphabets, which are not true alphabets, are called abjads exemplified in scripts including Arabic and Syriac; the omission of vowels was not always a satisfactory solution and some "weak" consonants are sometimes used to indicate the vowel quality of a syllable. These letters have a dual function since they are used as pure consonants.
The Proto-Sinaitic or Proto-Canaanite script and the Ugaritic script were the first scripts with a limited number of signs, in contrast to the other used writing systems at the time, Egyptian hieroglyphs, Linear B. The Phoenician script was the first phonemic script and it contained only about two dozen distinct letters, making it a script simple enough for common traders to learn. Another advantage of Phoenician was that it could be used to write down many different languages, since it recorded words phonemically; the script was spread by the Phoenicians across the Mediterranean. In Greece, the script was modified to add vowels, giving rise to the ancestor of all alphabets in the West; the vowels have independent letter forms separate from those of consonants. The Greeks chose letters representing sounds. Vowels are significant in the Greek language, the syllabical Linear B scri
Azimuthal quantum number
The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers which describe the unique quantum state of an electron, it is known as the orbital angular momentum quantum number, orbital quantum number or second quantum number, is symbolized as ℓ. Connected with the energy states of the atom's electrons are four quantum numbers: n, ℓ, mℓ, ms; these specify the complete, unique quantum state of a single electron in an atom, make up its wavefunction or orbital. The wavefunction of the Schrödinger equation reduces to three equations that when solved, lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated; the azimuthal quantum number arose in the solution of the polar part of the wave equation as shown below. To aid understanding of this concept of the azimuth, it may prove helpful to review spherical coordinate systems, and/or other alternative mathematical coordinate systems besides the Cartesian coordinate system.
The spherical coordinate system works best with spherical models, the cylindrical system with cylinders, the cartesian with general volumes, etc. An atomic electron's angular momentum, L, is related to its quantum number ℓ by the following equation: L 2 Ψ = ℏ 2 ℓ Ψ where ħ is the reduced Planck's constant, L2 is the orbital angular momentum operator and Ψ is the wavefunction of the electron; the quantum number ℓ is always a non-negative integer: 1, 2, 3, etc.. While many introductory textbooks on quantum mechanics will refer to L by itself, L has no real meaning except in its use as the angular momentum operator; when referring to angular momentum, it is better to use the quantum number ℓ. Atomic orbitals have distinctive shapes denoted by letters. In the illustration, the letters s, p, d describe the shape of the atomic orbital, their wavefunctions take the form of spherical harmonics, so are described by Legendre polynomials. The various orbitals relating to different values of ℓ are sometimes called sub-shells, are referred to by letters, as follows: Each of the different angular momentum states can take 2 electrons.
This is because the third quantum number mℓ runs from −ℓ to ℓ in integer units, so there are 2ℓ + 1 possible states. Each distinct n, ℓ, mℓ orbital can be occupied by two electrons with opposing spins, giving 2 electrons overall. Orbitals with higher ℓ than given in the table are permissible, but these values cover all atoms so far discovered. For a given value of the principal quantum number n, the possible values of ℓ range from 0 to n − 1. Speaking, the maximum number of electrons in the nth energy level is 2n2; the angular momentum quantum number, ℓ, governs the number of planar nodes going through the nucleus. A planar node can be described in an electromagnetic wave as the midpoint between crest and trough, which has zero magnitude. In an s orbital, no nodes go through the nucleus, therefore the corresponding azimuthal quantum number ℓ takes the value of 0. In a p orbital, one node traverses the nucleus and therefore ℓ has the value of 1. L has the value 2 ℏ. Depending on the value of n, there is the following series.
The wavelengths listed are for a hydrogen atom: n = 1, L = 0, Lyman series n = 2, L = 2 ℏ, Balmer series n = 3, L = 6 ℏ, Ritz-Paschen series n = 4, L = 2 3 ℏ, Brackett series n = 5, L = 2 5 ℏ, Pfund series. Given a quantized total angular momentum ȷ →, the sum of two individual quantized angular momenta ℓ 1 → and ℓ 2 →, ȷ → = ℓ 1 → + ℓ 2 → the quantum number j