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Michael Corleone
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Michael Corleone
The Godfather Saga character
Michael Corleone, as portrayed by Al Pacino in The Godfather.
First appearance
The Godfather
Last appearance
'The Godfather's Revenge
Created by
Mario Puzo
Portrayed by
Al Pacino
Information
Nickname(s)
Mike,
Mikey,
Mickey,
The Don,
Don Corleone,
Don Michael
Aliases
The Godfather
Gender
Male
Occupation
U.S. Marine Captain
Mafia boss
Affiliation
Corleone family
Title
Don Corleone
Family
Vito Corleone (father)
Carmela Corleone (mother)
Santino "Sonny" Corleone (brother)
Frederico "Fredo" Corleone (brother)
Constanzia "Connie" Corleone (sister)
Tom Hagen (adopted brother)

Spouse(s)
Apollonia Vitelli-Corleone (deceased; 1947-48)
Kay Adams (divorced; 1951-60)
Children
Anthony Corleone
Mary Corleone
Relatives
Francesca Corleone (niece)
Kathryn Corleone (niece)
Frank Corleone (nephew)
Santino Corleone, Jr. (nephew)
Vincent Corleone (nephew)
Victor Rizzi (nephew)
Michael Rizzi (nephew)
Sandra Corleone (sister-in-law)
Carlo Rizzi (brother-in-law)
Deanna Dunn (sister-in-law)
Religion
Roman Catholic
Nationality
American
rank
Captain
serviceyears & battles
1941-1945 (World War II)
Michael Corleone is the main protagonist of Mario Puzo's novel The Godfather. In the three Godfather films, directed by Francis Ford Coppola, Michael was portrayed by Al Pacino, for which he was twice-nominated for Academy Awards.
In June 2003, Michael Corleone was recognized as the 11th most iconic villain in film history by the American Film Institute, although some critics consider him to be a tragic hero.[1][2]
Contents
1 Family
2 The Godfather
3 The Godfather Part II
4 The Godfather Part III
5 The Sicilian
6 Sequel novels
7 Family members
8 References
9 Bibliography
Family[edit]
Born in 1920 to Mafia don Vito Corleone and his wife Carmela, Michael has two older brothers, Santino "Sonny" Corleone and Frederico "Fredo" Corleone, and a younger sister, Constanzia "Connie" Corleone. The family consigliere, Tom Hagen, is their informal adoptive brother.
The Godfather[edit]
Unlike his two older brothers, Michael wants nothing to do with the Corleone “family business”, wanting instead to lead a more normal, Americanized life. Vito does not want Michael to join the Corleone criminal empire either, preferring that his favorite son go into politics. As a young man, Michael enrolls in Dartmouth College, but dropped out in 1941 to enlist in the U.S. Marine Corps when the United States enters World War II. During the war, he fights in the Pacific, and is wounded in battle. He receives a battlefield commission to the rank of captain and is awarded the Navy Cross for bravery. His war heroism is featured in Life magazine.
During the summer of 1945, Michael has been discharged from the Marine Corps. Vito had secretly arranged for his discharge. He returns home to attend his sister Connie's wedding, accompanied by Kay Adams, his college sweetheart. Michael stays for a few weeks before re-entering college without consulting his family.
Just before Christmas 1945, Vito is severely wounded in an assassination attempt by drug kingpin Virgil Sollozzo, throwing Michael into the middle of the Mafia world he had for so long avoided. Arriving at the hospital to find his father unprotected, Michael calls Sonny and prevents Sollozzo's second attempt on Vito's life, then reaffirms his loyalty at his father's bedside. Captain Mark McCluskey, a corrupt NYPD officer on Sollozzo's payroll, breaks Michael's jaw. In retaliation for trying to kill Vito, Sonny orders the murder of Bruno Tattaglia, son and underboss of Sollozzo's ally Philip Tattaglia. Sollozzo proposes that Michael be sent to broker a truce, but Sonny, believing that it's a trap, refuses and demands that the other Mafia families hand over Sollozzo to the Corleone family or else face war. Michael suggests they agree to Sollozzo's meeting but insist that it be in a public place, where he will kill both Sollozzo and McCluskey. Hagen warns Sonny that killing McCluskey would violate a long-standing Mafia rule not to kill police officers, and that the backlash from rival Mafia families and law enforcement would be severe. Michael successfully argues that McCluskey is fair game because he is a corrupt cop mixed up in the drug trade and serving as Sollozzo's bodyguard. Sonny agrees and approves the hit.
Michael meets with Sollozzo and McCluskey at an Italian restaurant in the Bronx, retrieves a handgun that Corleone caporegime Peter Clemenza had planted beforehand in the toilet and kills Sollozzo and McCluskey. This ignites the New York underworld's first Mafia war in a decade.
Michael flees to Sicily, where he spends two years under the protection of Vito's friend and longtime ally, Don Tommasino. Michael meets and falls in love with a young local woman named Apollonia Vitelli. They marry, and when Michael is notified that Sonny has been murdered they prepare to move to Siracusa. Apollonia is killed by a car bomb intended for Michael, planted by Fabrizio, Michael's bodyguard who is secretly working for the Corleones' rivals.
Michael returns to the United States in early 1951[3] and assumes Sonny's role as Vito's heir apparent. After Don Corleone's suspicions are confirmed that Don Emilio Barzini, his main rival in New York, had been the power behind Sollozzo and Tattaglia all along, Michael and his father begin a secret, long-range plot to wipe out the other New York Dons. They deliberately allow their rivals to whittle away at Corleone interests in order to lull them into inaction. Meanwhile, Michael convinces his father the time is right to remove the family from the Mafia. More than a year after his return, Michael reunites with Kay and they marry. He promises her the Corleone family will be completely legitimate in five years. Within two years, they have two children, Anthony and Mary. In the novel, Kay gives birth to two sons.
Vito semi-retires in 1954, and Michael becomes operating head of the family. He attempts to buy out casino owner Moe Greene's stake in the Las Vegas casino that the Corleones bankrolled, intending to move the family to Nevada and legitimize all Corleone enterprises, but Greene refuses to sell. Before his death in 1955, Vito warns Michael that Barzini will likely attempt to assassinate Michael under the pretense of establishing peace between the families, and tells Michael that whoever approaches him about the meeting is the traitor within the family. When caporegime Salvatore Tessio unknowingly exposes his complicity with Barzini by arranging the meeting, Michael sets the plan in motion to murder the other New York Mafia heads: Barzini, Philip Tattaglia, Carmine Cuneo, and Victor Stracci, as well as Greene. The plot unfolds on the same day Michael stands as godfather to Connie's newborn son. Later the same day, he has Tessio and Carlo Rizzi, Connie's abusive husband who conspired in Sonny's murder, executed. In one stroke, Michael re-establishes the Corleone family as the nation's most powerful crime family, and makes a reputation for himself as being even more cunning and ruthless than his father.
Connie accuses Michael of murdering Carlo. Michael dismisses her accusations as hysteria, and when questioned by Kay denies any involvement. In the novel, Connie recants her accusations a few weeks later, assuring Kay she was mistaken. Kay, initially believing Michael, later observes him receiving his capos. Clemenza addresses Michael as "Don Corleone" and kisses his hand in the same manner that he did with Michael's father. Kay realizes Connie's accusations were true, and that Michael has become his father's successor in every way. In the novel, Kay leaves Michael, but Hagen persuades her to return.
The Godfather Part II[edit]
The Godfather Part II is set in 1958 and 1959. The Corleone family has relocated to Nevada, while Frank Pentangeli runs the family's operations in New York, Clemenza having died a few years before. Although Michael is the most powerful Mafia leader in the nation, he still actively works to remove the Corleone family from crime. His efforts have been largely unsuccessful, however, as his many enemies and growing obsession with revenge keep him tethered to the criminal underworld. Michael plans to finally legitimize the family by negotiating with Hyman Roth, his father's former business partner, over controlling casino operations in Cuba.
Hours after Anthony's First Communion party, unseen gunmen shoot at the Corleone house, nearly killing Michael and Kay. Michael suspects Roth ordered the hit, and believes a mole within the Corleone family aided him. To uncover Roth's involvement, Michael maintains their business relationship, and orders Pentangeli to settle a dispute with Roth's business partners, the Rosato Brothers. When Pentangeli meets with them, they try to kill him, but he survives.
Michael, Roth, and Fredo travel to Cuba to forge a partnership with Fulgencio Batista allowing them to operate casinos in Cuba without interference in exchange for generous payments to the Cuban government. Michael sends his bodyguard to eliminate Roth on New Year's Eve, but Cuban soldiers kill the bodyguard during the attempt. That same night, Fredo unintentionally reveals that he was the mole within the family; Michael confronts Fredo and gives him the Sicilian "kiss of death". During the New Year's Eve festivities, victorious rebel forces enter Havana, forcing Batista into exile and ruining Michael's plans. Fredo, fearing Michael, runs off; Roth escapes to Miami.
Meanwhile, Pentangeli, believing Michael had ordered a hit on him, prepares to testify against him in the Senate's investigation of organized crime. However, Michael has Pentangeli's brother Vincenzo brought from Sicily. Just prior to the hearing, Vincenzo and Frank exchange glances. Understanding the threat, Pentangeli recants his earlier sworn statements, throwing the hearings into chaos and effectively destroying the government's case against Michael.
Fredo confesses to Michael that Roth's right-hand man, Johnny Ola, had promised to reward him for information about Michael. Fredo also reveals that he resented being "passed over" to head the family in favor of Michael, and that he withheld key information about the Senate investigation. Michael disowns Fredo, and tells his capo Al Neri that nothing is to happen to his brother while their mother is alive — the implication being Neri has been given a contract to assassinate Fredo after their mother's death.
Meanwhile, Kay decides to leave Michael and take their children with her, believing Michael will always live in a world of crime and violence. Michael asks her to reconsider, but Kay reveals she aborted their unborn son because she refused to bring another child into the Corleones' crime world. Enraged, Michael strikes Kay and banishes her, preventing her from seeing their children.
Following their mother's death, and at sister Connie's behest, Michael seemingly forgives Fredo, but it is actually a ploy to draw Fredo in closer in order to have him killed. Soon after, Neri murders Fredo on Michael's orders. At the same time, Michael sends Hagen to persuade Pentangeli to commit suicide to spare his family, and has caporegime Rocco Lampone kill a heavily guarded Roth at Idlewild Airport upon his return to the U.S.
The film ends as Michael recalls a surprise birthday party for his father on December 7, 1941. In a flashback scene, Michael informs the family that he has dropped out of college to enlist in the Marines. Only Fredo supports Michael's decision. When Vito arrives off-screen, everyone goes to greet him except Michael, who sits alone. The film closes with Michael sitting alone in the Corleones' Lake Tahoe compound.
The Godfather Part III[edit]
The Godfather Part III is set in 1979 and 1980. Michael has moved back to New York and taken great strides to remove the family from crime. He turns over his New York criminal interests to longtime enforcer Joey Zasa. Ridden with guilt over his ruthless rise to power, he uses his wealth in an attempt to rehabilitate his reputation through numerous philanthropic acts, administered by a foundation named after his father. A decade earlier, he gave custody of his two children to Kay, who has since remarried. He sells his gambling interests to the other Mafia families and reorganizes his vast business holdings as the "Corleone Group".
The Holy See has named him a Commander of the Order of Saint Sebastian for his charitable works. At the ceremony, Michael and Kay have an uneasy reunion after nine years. Kay supports their son Anthony's decision to reject the "family business" and become an opera singer, and tells Michael that both she and Anthony know the truth about Fredo's death. Michael had initially wanted Anthony to finish law school, but consents to Anthony going his own way.
Michael's new connection to the Church provides an opportunity to take over the large property company, Immobiliare. He is already its largest shareholder, and offers to buy the Vatican's 25 percent share, which will give him controlling interest. He also takes in Sonny's illegitimate son Vincent Mancini, a soldier in Zasa's crew, as his protegé. Michael recognizes that Vincent has inherited Sonny's fiery temper, however, and fears Vincent will suffer his father's fate. Michael also disapproves of the romance developing between him and Michael's daughter, Mary. Michael fears that Vincent's growing involvement in the Mafia will endanger Mary, just as it did Michael's first wife, Apollonia.[4]
On the night Michael announces he is dissolving his gambling empire, Zasa wipes out most of The Commission in a helicopter attack in Atlantic City. Michael escapes with help from Vincent and Neri. Michael realizes that his old friend, Don Altobello, is the brains behind the attempt on his life. Traumatized by the attack, Michael suffers a diabetic stroke, briefly incapacitating him. (Francis Ford Coppola reveals in his audio commentary that Michael is seen drinking a lot of water in the first two films—subtle hints that he is a diabetic.[4]) While Michael recovers, his sister, Connie, gives Vincent her consent to assassinate Zasa. Michael is enraged upon discovering this, and demands that no similar orders be issued while he is alive.
Michael returns to Sicily for Anthony's operatic debut at the Teatro Massimo. Suspecting that Altobello may make another attempt on his life, he has Vincent infiltrate Altobello's regime under the pretense of defecting. Michael and Kay tour Sicily together, during which Michael asks for Kay's forgiveness. Kay admits she will always love him.
Meanwhile, the Immobiliare deal has stalled, supposedly because Pope Paul VI must personally approve it. Michael learns that the Immobiliare deal is an elaborate swindle concocted by Immobiliare chairman Licio Lucchesi, who schemed with Vatican Bank head Archbishop Gilday and accountant Frederick Keinszig to embezzle a fortune from the Vatican Bank, using Michael's "investment" to cover their tracks. Hoping to salvage the deal, Michael seeks Don Tommasino's assistance. He directs Michael to Cardinal Lamberto (the future Pope John Paul I). With Lamberto's prodding, Michael makes his first confession in 30 years, tearfully breaking down as he admits to ordering Fredo's murder. Lamberto tells Michael he deserves to suffer for his terrible sins, but that there is hope for redemption.
John Paul I dies soon after being elected pope, poisoned by Gilday. Michael learns that Altobello (in league with the conspirators) has hired an assassin named Mosca to kill him. Mosca murders Tommasino, and Michael vows before his old friend's casket to sin no more. Vincent reports that Lucchesi, working with Altobello, is behind the assassination attempts on Michael.
Weary of the bloody, lonely life of a Don, Michael retires, making Vincent his successor, but not before giving him permission to retaliate. In return, Vincent agrees to end his romance with Mary. That night, Michael, reconciled with Kay and Anthony, watches his son's performance in the opera Cavalleria Rusticana. Meanwhile, Vincent orchestrates the murders of Lucchesi, Gilday and Keinszig, and Connie murders Altobello with a poisoned cannoli.
After the performance, Mosca shoots Michael, and the bullet passes through his body and hits Mary, killing her. Her death breaks Michael's spirit, and he screams in agony over her body. He returns to Bagheria, Sicily, where he dies in 1997, alone in the courtyard where he married Apollonia.
The Sicilian[edit]
Michael is a secondary character in Puzo's novel The Sicilian, which takes place during his first exile in Sicily. He learns from Clemenza about the legendary exploits of the novel's main character, Salvatore Giuliano, and is eager to meet him, but Giuliano is murdered before the meeting can take place.
Sequel novels[edit]
Michael appears in Mark Winegardner's sequel novels The Godfather Returns and The Godfather's Revenge. In Godfather Returns, set roughly during the time of Godfather Part II, Michael battles with a new rival, Nick Geraci, while attempting to legitimize the family.[5] In The Godfather's Revenge, set a few years after the second film, he moves to protect his criminal empire against Geraci and the machinations of a powerful political dynasty, while dealing with his guilt over having Fredo murdered. In the latter novel, he has a relationship with actress Marguerite "Rita" Duvall in the early 1960s, but he ends it upon realizing that he is still in love with Kay.[6]
Family members[edit]
Vito Corleone – Michael's father and The Godfather, played by Marlon Brando in The Godfather, and by Robert De Niro in flashback scenes in Part II
Carmela Corleone – Mother, played by Morgana King in The Godfather Part I and Part II, and by Francesca De Sapio in flashback scenes in Part II
Tom Hagen – Adopted brother and consigliere, played by Robert Duvall
Santino "Sonny" Corleone – Eldest brother, underboss to Vito, played by James Caan in The Godfather Part 1, and by Roman Coppola in flashback scenes from Part II
Constanzia "Connie" Corleone – Sister, played by Talia Shire
Frederico "Fredo" Corleone – Elder brother, underboss to Michael; played by John Cazale
Apollonia Vitelli-Corleone – First wife, played by Simonetta Stefanelli
Kay Adams-Corleone – Second wife, played by Diane Keaton
Anthony Corleone – Son, played by Anthony Gounaris in The Godfather, by James Gounaris in Part II, and by Franc D'Ambrosio in Part III
Mary Corleone – Daughter, played by an uncredited actress in Part II, and by Sofia Coppola in Part III
Vincent Corleone – Nephew and succeeding Don, played by Andy García
References[edit]
Jump up ^ AFI's 100 Years... 100 Heroes and Villains Archived October 23, 2007, at the Wayback Machine.
Jump up ^ Leong, Anthony (2002). "The Godfather Movie Review". Mediacircus.net. Retrieved April 19, 2013.
Jump up ^ Coppola, Francis Ford (Director), Puzo, Mario (screenwriter) (March 29, 1971). The Godfather, early script (Motion picture). United States: Internet Movie Script Database.
^ Jump up to: a b Coppola, Francis Ford (Director) (2005). The Godfather Part III DVD commentary (DVD). Los Angeles, California: Paramount Studios.
Jump up ^ Winegardner, Mark (2005). The Godfather Returns: The Saga of the Family Corleone. New York City: Ballantine Books. ISBN 978-0345478986.
Jump up ^ Winegardner, Mark (2006). The Godfather's Revenge. New York City: Ballantine Books. ISBN 978-0399153846.
Bibliography[edit]
Puzo, Mario (1969). The Godfather. New York City: G. P. Putnam's Sons. ISBN 978-0451205766.
Coccimiglio, Carmela (2006). "I'm with You Now. I'm with You...": Michael Corleone as Gangster Figure in Mario Puzo's and Francis Ford Coppola's The Godfather Texts. Ontario, Canada: Lakehead University. ISBN 978-0-494-31189-9.
Messenger, Chris (1 February 2012). The Godfather and American Culture: How the Corleones Became "Our Gang". Albany, New York: SUNY Press. p. 31. ISBN 978-0-7914-8870-6.
Coppola, Francis Ford (2004). Francis Ford Coppola: Interviews. Jackson, Mississippi: University Press of Mississippi. p. 27. ISBN 978-1-57806-666-7.
Bondanella, Peter E. (2004). Hollywood Italians: Dagos, Palookas, Romeos, Wise Guys, and Sopranos. London, England: A&C Black. p. 244. ISBN 978-0-8264-1544-8.
Tamburri, Anthony Julian; Giordano, Paolo; Gardaphe, Fred L. (2000). From the Margin: Writings in Italian Americana. West Lafeyette, Indiana: Purdue University Press. p. 406. ISBN 978-1-55753-152-0.
Preceded by
Vito Corleone Head of the Corleone crime family
The Godfather
c 1955–1958 Succeeded by
Tom Hagen (Interim)
Preceded by
Tom Hagen (Interim) Head of the Corleone crime family
The Godfather
c 1959–1980 Succeeded by
Vincent Corleone
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The selected stars for navigation are often used for sextant observations
Fifty-eight selected navigational stars are given a special status in the field of celestial navigation. Of the approximately 6,000 stars visible to the naked eye under optimal conditions, the selected stars are among the brightest and span thirty-eight constellations of the celestial sphere from the declination of 70° south to 89° north. Many of the selected stars were named in antiquity by the Babylonians, Greeks, Romans, and Arabs.
The star Polaris, often called the "North Star", is treated specially due to its proximity to the north celestial pole. When navigating in the Northern Hemisphere, special techniques can be used with Polaris to determine latitude or gyrocompass error. The other 57 selected stars have daily positions given in nautical almanacs, aiding the navigator in efficiently performing observations on them. A second group of 115 "tabulated stars" can also be used for celestial navigation, but are often less familiar to the navigator and require extra calculations.
For purposes of identification, the positions of navigational stars — expressed as declination and sidereal hour angle — are often rounded to the nearest degree. In addition to tables, star charts provide an aid to the navigator in identifying the navigational stars, showing constellations, relative positions, and brightness.
Contents
[hide]
1 Background
2 Table
3 Star charts
3.1 Equatorial stars
3.2 Northern stars
3.3 Southern stars
4 Footnotes
5 References
Background[edit]
Selected navigation stars (except Polaris) listed on a U.S. Nautical Almanac page for May 1995
Under optimal conditions, approximately 6,000 stars are visible to the naked eye of an observer on Earth.[1] Of these, 58 are known in the field of navigational astronomy as "selected stars", including 19 stars of the first magnitude, 38 stars of the second magnitude, and Polaris.[1] The selection of the stars is made by Her Majesty's Nautical Almanac Office and the US Naval Observatory, in the production of the yearly Nautical Almanac which the two organizations have published jointly since 1958.[2] Criteria in the choice of stars includes their distribution across the celestial sphere, brightness, and ease of identification.[3] Information for another 115 stars, known as "tabulated stars", is also available to the navigator.[1] This list provides information on the name, approximate position in the celestial sphere, and apparent magnitude of the 58 selected stars in tabular form and by star charts.
These stars are typically used in two ways by the navigator. The first is to obtain a line of position by use of a sextant observation and the techniques of celestial navigation.[4] Multiple lines of position can be intersected to obtain a position known as a celestial fix. The second typical use of the navigational stars is to determine gyrocompass error by computing the azimuth of a star and comparing it to an azimuth measured using the ship's gyrocompass.[5] Numerous other applications also exist.
Navigators typically refer to stars using one of two naming systems for stars: common names and Bayer's designations.[1] All of the selected stars have had a common name since 1953, and many were named in antiquity by the Arabs, Greeks, Romans, and Babylonians.[1] Bayer's naming convention has been in use since 1603, and consists of a Greek letter combined with the possessive form of the star's constellation.[1] Both names are shown for each star in the tables and charts below.
Each star's approximate position on the celestial sphere is given using the equatorial coordinate system. The celestial sphere is an imaginary globe of infinite size with the Earth at its center.[6] Positions on the celestial sphere are often expressed using two coordinates: declination and sidereal hour angle, which are similar to latitude and longitude on the surface of the Earth. To define declination, the Earth's equator is projected out to the celestial sphere to construct the celestial equator, and declination is measured in degrees north or south of this celestial equator.[6] Sidereal hour angle is a measurement between 0 and 360 degrees, indicating how far west a body is from an arbitrarily chosen point on the celestial sphere called the First Point of Aries.
The final characteristic provided in the tables and star charts is the star's brightness, expressed in terms of apparent magnitude. Magnitude is a logarithmic scale of brightness, designed so that a body of one magnitude is approximately 2.512 times brighter than a body of the next magnitude.[Note 1][7] Thus, a body of magnitude 1 is 2.5125, or 100 times brighter than a body of magnitude 6.[7] The dimmest stars that can be seen through a 200-inch terrestrial telescope are of the 20th magnitude, and very bright objects like the Sun and a full Moon have magnitudes of −26.7 and −12.6 respectively.[7]
Table[edit]
Key to the table
Column title
Description
No. The number used to identify stars in navigation publications and star charts.[Note 2]
Common name The name of the star commonly used navigation publications and star charts.
Bayer designation Another name of the star which combines a Greek letter with the possessive form of its constellation's Latin name.
Etymology of
common name Etymology of the common name.[8]
SHA Sidereal hour angle (SHA), the angular distance west of the vernal equinox.
Dec. Declination, the angular distance north or south of the celestial equator.
App.
magnitude Apparent magnitude, an indicator of the star's brightness.
The table of navigational stars provides several types of information. In the first column is the identifying index number, followed by the common name, the Bayer designation, and the etymology of the common name. Then the star's approximate position, suitable for identification purposes, is given in terms of declination and sidereal hour angle, followed by the star's magnitude. The final column presents citations to the sources of the data, The American Practical Navigator and the star's entry at the SIMBAD database, a project of the Strasbourg Astronomical Data Center or CDS.
No.[Note 2]
Common
name
Bayer
designation
Etymology of common name
SHA
Declination
App.
magnitude
References
-100 a a a -100 -100 -100 -100
1 Alpheratz Andromedae αα Andromedae the horse's navel 358 29N 29° 2.06 [8][9]
2 Ankaa Phoenicis αα Phoenicis coined name, "phoenix bird" in Arabic 354 -42S 42° 2.37 [8][10]
3 Schedar Cassiopeiae αα Cassiopeiae the breast (of Cassiopeia) 350 56N 56° 2.25 [8][11]
4 Diphda Ceti ββ Ceti the second frog (Fomalhaut was once the first) 349 -18S 18° 2.04 [8][12]
5 Achernar Eridani αα Eridani end of the river (Eridanus) 336 -57S 57° 0.50 [8][13]
6 Hamal Arietis αα Arietis full-grown lamb 328 23N 23° 2.00 [8][14]
7 Acamar Eridani θθ Eridani another form of Achernar 316 -40S 40° 3.2 [8][15]
8 Menkar Ceti α α Ceti nose (of the whale) 315 4N 04° 2.5 [8][16]
9 Mirfak Persei α α Persei elbow of the Pleiades 309 50N 50° 1.82 [8][17]
10 Aldebaran Tauri αα Tauri follower (of the Pleiades) 291 16N 16° 0.85 var[Note 3] [8][18]
11 Rigel Orionis β β Orionis foot (left foot of Orion) 282 -8S 08° 0.12 [8][19]
12 Capella Aurigae α α Aurigae little she-goat 281 46N 46° 0.71 [8][20]
13 Bellatrix Orionis γγ Orionis female warrior 279 6N 06° 1.64 [8][21]
14 Elnath Tauri ββ Tauri one butting with the horns 279 29N 29° 1.68 [8][22]
15 Alnilam Orionis εε Orionis string of pearls 276 -1S 01° 1.70 [8][23]
16 Betelgeuse Orionis αα Orionis the arm pit (of Orion) 271 7N 07° 0.58 var[Note 3] [8][24]
17 Canopus Carinae αα Carinae city of ancient Egypt 264 -53S 53° −0.72 [8][25]
18 Sirius Canis Majoris αα Canis Majoris the scorching one (popularly, the dog star) 259 -17S 17° −1.47 [8][26]
19 Adhara Canis Majoris εε Canis Majoris the virgin(s) 256 -29S 29° 1.51 [8][27]
20 Procyon Canis Minoris αα Canis Minoris before the dog (rising before the dog star, Sirius) 245 5N 05° 0.34 [8][28]
21 Pollux Geminorum β β Geminorum Zeus' other twin son (Castor, α Gem, is the first twin) 244 28N 28° 1.15 [8][29]
22 Avior Carinae εε1 Carinae coined name 234 -59S 59° 2.4 [8][30]
23 Suhail Velorum λλ Velorum shortened form of Al Suhail, one Arabic name for Canopus 223 -43S 43° 2.23 [8][31]
24 Miaplacidus Carinae ββ Carinae quiet or still waters 222 -70S 70° 1.70 [8][32]
25 Alphard Hydrae α α Hydrae solitary star of the serpent 218 -9S 09° 2.00 [8][33]
26 Regulus Leonis α α Leonis the prince 208 12N 12° 1.35 [8][34]
27 Dubhe Ursae Majoris αα1 Ursae Majoris the bear's back 194 62N 62° 1.87 [8][35]
28 Denebola Leonis β β Leonis tail of the lion 183 15N 15° 2.14 [8][36]
29 Gienah Corvi γ γ Corvi right wing of the raven 176 -17S 17° 2.80 [8][37]
30 Acrux Crucis αα1 Crucis coined from Bayer name 174 -63S 63° 1.40 [8][38]
31 Gacrux Crucis γγ Crucis coined from Bayer name 172 -57S 57° 1.63 [8][39]
32 Alioth Ursae Majoris ε ε Ursae Majoris another form of Capella 167 56N 56° 1.76 [8][40]
33 Spica Virginis α α Virginis the ear of corn 159 -11S 11° 1.04 [8][41]
34 Alkaid Ursae Majoris η η Ursae Majoris leader of the daughters of the bier 153 49N 49° 1.85 [8][42]
35 Hadar Centauri β β Centauri leg of the centaur 149 -60S 60° 0.60 [8][43]
36 Menkent Centauri θ θ Centauri shoulder of the centaur 149 -36S 36° 2.06 [8][44]
38 Rigil Kentaurus Centauri αα1 Centauri foot of the centaur 140 -61S 61° −0.01 [8][45]
37 Arcturus Bootis αα Bootis the bear's guard 146 19N 19° −0.04 var[Note 3] [8][46]
39 Zubenelgenubi Librae α α Librae southern claw (of the scorpion) 138 -16S 16° 3.28 [8][47]
40 Kochab Ursae Minoris β β Ursae Minoris shortened form of "north star" (named when it was that,[Note 4] ca. 1500 BC – AD 300). 137 74N 74° 2.08 [8][48]
41 Alphecca Corona Borealis α α Corona Borealis feeble one (in the crown) 127 27N 27° 2.24 [8][49]
42 Antares Scorpii αα Scorpii rival of Mars (in color) 113 -26S 26° 1.09 [8][50]
43 Atria Trianguli Australis αα Trianguli Australis coined from Bayer name 108 -69S 69° 1.92 [8][51]
44 Sabik Ophiuchi η η Ophiuchi second winner or conqueror 103 -16S 16° 2.43 [8][52]
45 Shaula Scorpii λ λ Scorpii cocked-up part of the scorpion's tail 097 -37S 37° 1.62 [8][53]
46 Rasalhague Ophiuchi α α Ophiuchi head of the serpent charmer 096 13N 13° 2.10 [8][54]
47 Eltanin Draconis γ γ Draconis head of the dragon 091 51 N 51° 2.23 [8][55]
48 Kaus Australis Sagittarii ε ε Sagittarii southern part of the bow (of Sagittarius) 084 -34S 34° 1.80 [8][56]
49 Vega Lyrae α α Lyrae the falling eagle or vulture 081 39N 39° 0.03 [8][57]
50 Nunki Sagittarii σ σ Sagittarii constellation of the holy city (Eridu) 076 -26S 26° 2.06 [8][58]
51 Altair Aquilae α α Aquilae flying eagle or vulture 063 9N 09° 0.77 [8][59]
52 Peacock Pavonis α α Pavonis Coined from the English name of the constellation 054 -57S 57° 1.91 [8][60]
53 Deneb Cygni αα Cygni tail of the hen 050 45N 45° 1.25 [8][61]
54 Enif Pegasi εε Pegasi nose of the horse 034 10N 10° 2.40 [8][62]
55 Al Na'ir Gruis αα Gruis bright one (of the southern fish's tail) 028 -47S 47° 1.74 [8][63]
56 Fomalhaut Piscis Austrini α α Piscis Austrini mouth of the southern fish 016 -30S 30° 1.16 [8][64]
57 Markab Pegasi α α Pegasi saddle (of Pegasus) 014 15N 15° 2.49 [8][65]
99* [Note 2] Polaris[8] Ursae Minoris αα Ursae Minoris the pole (star) 319 89N 89° 2.01 var[Note 3] [8][66]
Star charts[edit]
Key to the Star charts
Item
Description
UPPERCASE TEXT Constellation names are indicated in uppercase text.
Selected star of magnitude 1.5 and brighter. Labeled with common name, star number, and Greek letter to indicate Bayer designation.
Selected star of magnitude 1.6 and fainter. Labeled with common name, star number, and Greek letter to indicate Bayer designation.
Tabulated star of magnitude 2.5 and brighter. Labeled with Greek letter to indicate Bayer designation.
Tabulated star of magnitude 2.6 and fainter. Labeled with Greek letter to indicate Bayer designation.
Untabulated star. Not labeled.
Dotted line Constellation outline.
Navigators often use star charts to identify a star by its position relative to other stars. References like the Nautical Almanac and The American Practical Navigator provide four star charts, covering different portions of the celestial sphere. Two of these charts are azimuthal equidistant projections of the north and south poles. The other two cover the equatorial region of the celestial sphere, from the declination of 30° south to 30° north. The two equatorial charts are mercator projections, one for the eastern hemisphere of the celestial sphere and one for the western hemisphere. Note that unlike familiar maps, east is shown to the left and west is shown to the right. With this orientation, the navigator can hold the star chart overhead, and the arrangement of the stars on the chart will resemble the stars in the sky.[1]
In the star charts, constellations are labelled with capital letters and indicated by dotted lines collecting their stars. The 58 selected stars for navigation are shown in blue and labelled with their common name, star number, and a Greek letter to indicate their Bayer designation. The additional 115 tabulated stars that can also be used for navigation are shown in red and labelled with a Greek letter to indicate their Bayer designation. Some additional stars not suitable for navigation are also included on the charts to indicate constellations, they are presented as unlabelled small red dots.
Equatorial stars[edit]
Equatorial stars of the eastern hemisphere
The equatorial region of the celestial sphere's eastern hemisphere includes 16 navigational stars from Alpheratz in the constellation Andromeda to Denebola in Leo. It also includes stars from the constellations Cetus, Aries, Taurus, Orion, Canis Major and Minor, Gemini, and Hydra. Of particular note among these stars are "the dog star" Sirius, the brightest star in the sky, and four stars of the easily identified constellation Orion.
Equatorial stars of the western hemisphere
The equatorial region of the celestial sphere's western hemisphere includes 13 navigational stars from Gienah in the constellation Corvus to Markab in Pegasus. It also includes stars from the constellations Virgo, Bootes, Libra, Corona Borealis, Scorpio, Ophiuchus, Sagittarius, and Aquila. The variable star Arcturus is the brightest star in this group.
Northern stars[edit]
The 11 northern stars are those with a declination between 30° north and 90° north. They are listed in order of decreasing sidereal hour angle, or from the vernal equinox westward across the sky. Starting with Schedar in the constellation Cassiopeia, the list includes stars from the constellations Auriga, the Great and Little Bears, Draco, Lyra and Cygnus. The two brightest northern stars are Vega and Capella.
In the star chart to the right, declination is shown by the radial coordinate, starting at 90° north in the center and decreasing to 30° north at the outer edge. Sidereal hour angle is shown as the angular coordinate, starting at 0° at the left of the chart, and increasing counter-clockwise.
Southern stars[edit]
The 18 southern stars are those with a declination between 30° south and 90° south. They are listed in order of decreasing sidereal hour angle, or from the vernal equinox westward across the sky. Starting with Ankaa in the constellation Phoenix, the list includes stars from the constellations Eridanus, Carina, Crux, Centaurus, Libra, Triangulum Australe, Scorpio, Sagittarius, Pavo, and Grus. Canopus, Rigil Kentaurus, Achernar, and Hadar are the brightest stars in the southern sky.
In the star chart to the right, declination is shown by the radial coordinate, starting at 90° south in the center and decreasing to 30° south at the outer edge. Sidereal hour angle is shown as the angular coordinate, starting at 0° at the right of the chart, and increasing clockwise.
Footnotes[edit]
Notes
Jump up ^ The value is actually the fifth root of 100, an irrational number known as Pogson's Ratio. See Australian Science Teachers' Association (2006). Teaching science, Volumes 52–53. Australian Science Teachers' Association. p. 44. Retrieved 2010-09-06.
^ Jump up to: a b c This list uses the assigned numbers from the nautical almanac, which includes only 57 stars. Polaris, which is included in the list given in The American Practical Navigator, is listed here without a number.
^ Jump up to: a b c d The suffix var after the numeric value denotes a variable star whose magnitude changes over time.
Jump up ^ For more information, see the article changing pole stars.
Citations
^ Jump up to: a b c d e f g Bowditch, 2002, p. 249.
Jump up ^ "History of the Nautical Almanac". US Naval Observatory. Retrieved 2011-01-23.
Jump up ^ Wright and Whitney, 1992, p. 273.
Jump up ^ Bowditch, 2002, pp. 301–303.
Jump up ^ Bowditch, 2002, pp. 271–274.
^ Jump up to: a b Bowditch, 2002, p. 234.
^ Jump up to: a b c Bowditch, 2002, p. 219.
^ Jump up to: a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw ax ay az ba bb bc bd be bf bg bh Bowditch, 2002, p. 248.
Jump up ^ "Alpheratz". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alpha Phe". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Schedar". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Beta Ceti". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Achernar". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Hamal". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Acamar". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Menkar". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Mirfak". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Aldebaran". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Rigel". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Capella A". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Bellatrix". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "bet Tau". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alnilam". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Betelgeuse". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Canopus". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Sirius". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Adara". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Procyon". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Pollux". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Eps Car". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "lam Vel". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Beta Car". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alphard". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Regulus". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Dubhe". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Denebola". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Gienah Corvi". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Acrux A". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Gacrux". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alioth". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Spica". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alkaid". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Agena". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Menkent". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alpha Centauri". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Arcturus". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alpha Librae". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Kochab". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alphecca". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Antares". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Atria". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Sabik". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Shaula". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Rasalhague". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Etamin". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Kaus Australis". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Vega". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Nunki". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Altair". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Peacock". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Deneb". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Enif". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Alpha Gruis". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Fomalhaut". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Markab". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
Jump up ^ "Polaris". SIMBAD. Centre de données astronomiques de Strasbourg. Retrieved 2010-06-21.
References[edit]
Bowditch, LL.D., Nathaniel (2002) [1802]. "15: Navigational Astronomy". The American Practical Navigator: An Epitome of Navigation (PDF). Bethesda, MD: National Imagery and Mapping Agency. ISBN 0-939837-54-4. Retrieved 2016-09-20.
Strasbourg Astronomical Data Center (CDS) (2010). "SIMBAD". Set of Identifications, Measurements, and Bibliography for Astronomical Data. Strasbourg: University of Strasbourg. Retrieved 2010-09-05.
United States Army Research Office (2009). 2010 Nautical Almanac. Arcata, CA: Paradise Cay Publications. pp. 28, leaf. ISBN 0-939837-85-4.
Wright, Frances; Whitney, Charles Allen (1992). Learn to navigate by the tutorial system developed at Harvard. Cambridge, Md: Cornell Maritime Press. ISBN 0-87033-426-3.
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Azimuthal quantum number
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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 (the others being the principal quantum number, following spectroscopic notation, the magnetic quantum number, and the spin quantum number). It is also known as the orbital angular momentum quantum number, orbital quantum number or second quantum number, and is symbolized as ℓ.
Contents
1 Derivation
2 Addition of quantized angular momenta
2.1 Total angular momentum of an electron in the atom
2.1.1 Relation between new and old quantum numbers
3 List of angular momentum quantum numbers
4 History
5 See also
6 References
7 External links
Derivation[edit]
The atomic orbital wavefunctions of a hydrogen atom. The principal quantum number (n) is at the right of each row and the azimuthal quantum number (ℓ) is denoted by letter at top of each column.
Connected with the energy states of the atom's electrons are four quantum numbers: n, ℓ, mℓ, and ms. These specify the complete, unique quantum state of a single electron in an atom, and 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 also prove helpful to review spherical coordinate systems, and/or other alternative mathematical coordinate systems besides the Cartesian coordinate system. Generally, the spherical coordinate system works best with spherical models, the cylindrical system with cylinders, the cartesian with general volumes, etc.
Illustration of quantum mechanical orbital angular momentum.
An atomic electron's angular momentum, L, is related to its quantum number ℓ by the following equation:
L 2 Ψ = ℏ 2 ℓ ( ℓ + 1 ) Ψ {\displaystyle \mathbf {L} ^{2}\Psi =\hbar ^{2}{\ell (\ell +1)}\Psi }
where ħ is the reduced Planck's constant, L2 is the orbital angular momentum operator and Ψ {\displaystyle \Psi } is the wavefunction of the electron. The quantum number ℓ is always a non-negative integer: 0, 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 simply use the quantum number ℓ.
Atomic orbitals have distinctive shapes denoted by letters. In the illustration, the letters s, p, and d describe the shape of the atomic orbital.
Their wavefunctions take the form of spherical harmonics, and so are described by Legendre polynomials. The various orbitals relating to different values of ℓ are sometimes called sub-shells, and (mainly for historical reasons) are referred to by letters, as follows:
Quantum Subshells for the Azimuthal Quantum Number
Azimuthal
number (ℓ)
Historical
Letter
Maximum
Electrons
Historical
Name
Shape
0 s 2 sharp spherical
1 p 6 principal three dumbbell-shaped polar-aligned orbitals; one lobe on each pole of the x, y, and z (+ and − axes); two electrons each lobe.
2 d 10 diffuse nine dumbbells and one doughnut (or “unique shape #1” see this picture of spherical harmonics, third row center)
3 f 14 fundamental “unique shape #2” (see this picture of spherical harmonics, bottom row center)
4 g 18
5 h 22
6 i 26
The letters after the f sub-shell just follow letter f in alphabetical order except the letter j and those already used.
Each of the different angular momentum states can take 2(2ℓ + 1) electrons. This is because the third quantum number mℓ (which can be thought of loosely as the quantized projection of the angular momentum vector on the z-axis) runs from −ℓ to ℓ in integer units, and so there are 2ℓ + 1 possible states. Each distinct n, ℓ, mℓ orbital can be occupied by two electrons with opposing spins (given by the quantum number ms = ±½), giving 2(2ℓ + 1) electrons overall. Orbitals with higher ℓ than given in the table are perfectly 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; therefore, the n = 1 shell only possesses an s subshell and can only take 2 electrons, the n = 2 shell possesses an s and a p subshell and can take 8 electrons overall, the n = 3 shell possesses s, p, and d subshells and has a maximum of 18 electrons, and so on. Generally 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 {\displaystyle L} has the value 2 ℏ {\displaystyle {\sqrt {2}}\hbar } .
Depending on the value of n, there is an angular momentum quantum number ℓ and the following series. The wavelengths listed are for a hydrogen atom:
n = 1 , L = 0 {\displaystyle n=1,L=0} , Lyman series (ultraviolet)
n = 2 , L = 2 ℏ {\displaystyle n=2,L={\sqrt {2}}\hbar } , Balmer series (visible)
n = 3 , L = 6 ℏ {\displaystyle n=3,L={\sqrt {6}}\hbar } , Ritz-Paschen series (near infrared)
n = 4 , L = 2 3 ℏ {\displaystyle n=4,L=2{\sqrt {3}}\hbar } , Brackett series (short-wavelength infrared)
n = 5 , L = 2 5 ℏ {\displaystyle n=5,L=2{\sqrt {5}}\hbar } , Pfund series (mid-wavelength infrared).
Addition of quantized angular momenta[edit]
Further information: Angular momentum coupling
Given a quantized total angular momentum ȷ → {\displaystyle {\vec {\jmath }}} which is the sum of two individual quantized angular momenta ℓ 1 → {\displaystyle {\vec {\ell _{1}}}} and ℓ 2 → {\displaystyle {\vec {\ell _{2}}}} ,
ȷ → = ℓ 1 → + ℓ 2 → {\displaystyle {\vec {\jmath }}={\vec {\ell _{1}}}+{\vec {\ell _{2}}}}
the quantum number j {\displaystyle j} associated with its magnitude can range from | ℓ 1 − ℓ 2 | {\displaystyle |\ell _{1}-\ell _{2}|} to ℓ 1 + ℓ 2 {\displaystyle \ell _{1}+\ell _{2}} in integer steps where ℓ 1 {\displaystyle \ell _{1}} and ℓ 2 {\displaystyle \ell _{2}} are quantum numbers corresponding to the magnitudes of the individual angular momenta.
Total angular momentum of an electron in the atom[edit]
"Vector cones" of total angular momentum J (purple), orbital L (blue), and spin S (green). The cones arise due to quantum uncertainty between measuring angular momentum components (see vector model of the atom.
Due to the spin-orbit interaction in the atom, the orbital angular momentum no longer commutes with the Hamiltonian, nor does the spin. These therefore change over time. However the total angular momentum J does commute with the Hamiltonian and so is constant. J is defined through
J → = L → + S → {\displaystyle {\vec {J}}={\vec {L}}+{\vec {S}}}
L being the orbital angular momentum and S the spin. The total angular momentum satisfies the same commutation relations as orbital angular momentum, namely
[ J i , J j ] = i ℏ ϵ i j k J k {\displaystyle [J_{i},J_{j}]=i\hbar \epsilon _{ijk}J_{k}}
from which follows
[ J i , J 2 ] = 0 {\displaystyle \left[J_{i},J^{2}\right]=0}
where Ji stand for Jx, Jy, and Jz.
The quantum numbers describing the system, which are constant over time, are now j and mj, defined through the action of J on the wavefunction Ψ {\displaystyle \Psi }
J 2 Ψ = ℏ 2 j ( j + 1 ) Ψ {\displaystyle \mathbf {J} ^{2}\Psi =\hbar ^{2}{j(j+1)}\Psi }
J z Ψ = ℏ m j Ψ {\displaystyle \mathbf {J} _{z}\Psi =\hbar {m_{j}}\Psi }
So that j is related to the norm of the total angular momentum and mj to its projection along a specified axis.
As with any angular momentum in quantum mechanics, the projection of J along other axes cannot be co-defined with Jz, because they do not commute.
Relation between new and old quantum numbers[edit]
Further information: Quantum number § Quantum numbers with spin-orbit interaction
j and mj, together with the parity of the quantum state, replace the three quantum numbers ℓ, mℓ and ms (the projection of the spin along the specified axis). The former quantum numbers can be related to the latter.
Furthermore, the eigenvectors of j, s, mj and parity, which are also eigenvectors of the Hamiltonian, are linear combinations of the eigenvectors of ℓ, s, mℓ and ms.
List of angular momentum quantum numbers[edit]
Intrinsic (or spin) angular momentum quantum number, or simply spin quantum number
orbital angular momentum quantum number (the subject of this article)
magnetic quantum number, related to the orbital momentum quantum number
total angular momentum quantum number
History[edit]
The azimuthal quantum number was carried over from the Bohr model of the atom, and was posited by Arnold Sommerfeld.[1] The Bohr model was derived from spectroscopic analysis of the atom in combination with the Rutherford atomic model. The lowest quantum level was found to have an angular momentum of zero. Orbits with zero angular momentum were considered as oscillating charges in one dimension and so described as "pendulum" orbits.[2] In three-dimensions the orbits become spherical without any nodes crossing the nucleus, similar (in the lowest-energy state) to a skipping rope that oscillates in one large circle.
See also[edit]
Angular momentum operator
Basic quantum mechanics
Particle in a spherically symmetric potential
Quantum number
Magnetic quantum number
Principal quantum number
Spin quantum number
Total angular momentum quantum number
Angular momentum coupling
Clebsch–Gordan coefficients
References[edit]
Jump up ^ Eisberg, Robert (1974). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. New York: John Wiley & Sons Inc. pp. 114–117. ISBN 978-0-471-23464-7.
Jump up ^ R.B. Lindsay (1927). "Note on "pendulum" orbits in atomic models". Proc. Natl. Acad. Sci. 13: 413–419. Bibcode:1927PNAS...13..413L. doi:10.1073/pnas.13.6.413. PMC 1085028  . PMID 16587189.
External links[edit]
Development of the Bohr atom
Detailed explanation of the Orbital Quantum Number l
The azimuthal equation explained
hide
v
t
e
Electron configuration
Introduction to quantum mechanics
Quantum mechanics
Quantum numbers
Principal quantum number (n)
Azimuthal quantum number (ℓ)
Magnetic quantum number (m)
Spin quantum number (s)
Periodic table
Periodic table (electron configurations)
Others
Pauli exclusion principle
Hund's rule
Octet rule
Aufbau principle
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values: Αζιμουθιακός κβαντικός αριθμός – Greek

values:
interlanguage-link interwiki-el
display: none;

values: عدد کوانتومی اوربیتالی – Persian

values:
interlanguage-link interwiki-fa
display: none;

values: 방위 양자수 – Korean

values:
interlanguage-link interwiki-ko
display: none;

values:
interlanguage-link interwiki-hr
display: none;

values:
interlanguage-link interwiki-it
display: none;

values: מספר קוונטי זוויתי – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values: Орбитален квантен број – Macedonian

values:
interlanguage-link interwiki-mk
display: none;

values:
interlanguage-link interwiki-pl
display: none;

values:
interlanguage-link interwiki-ro
display: none;

values: Орбитальное квантовое число – Russian

values:
interlanguage-link interwiki-sl
display: none;

values:
interlanguage-link interwiki-sr
display: none;

values: Azimutalni kvantni broj – Serbo-Croatian

values:
interlanguage-link interwiki-sh
display: none;

values:
interlanguage-link interwiki-fi
display: none;

values:
interlanguage-link interwiki-sv
display: none;

values: Орбиталь квант саны – Tatar

values:
interlanguage-link interwiki-tt
display: none;

values: เลขควอนตัมโมเมนตัมเชิงมุม – Thai

values:
interlanguage-link interwiki-th
display: none;

values:
interlanguage-link interwiki-tr
display: none;

values: Орбітальне квантове число – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values:
interlanguage-link interwiki-vi
display: none;

values: All languages (initial selection from common choices by you and others)

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Azimuthal_quantum_number rootpage-Azimuthal_quantum_number skin-vector action-view