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Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. 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THE FIDE LAWS OF CHESS. Introduction FIDE Laws of Chess cover over-the-board play. The Laws of Chess have two parts: 1. Basic Rules of Play and 2. Competitive Rules of Play. The English text is the authentic version of the Laws of Chess (which were adopted at the 93rd FIDE Congress at Chennai, India) coming into force on 1 January 2023. Preface. The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct decision by studying analogous situations which are regulated in the Laws. The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Too detailed a rule might deprive the arbiter of his/her freedom of judgement and thus prevent him/her from finding a solution to a problem dictated by fairness, logic and special factors. FIDE appeals to all chess players and federations to accept this view. A necessary condition for a game to be rated by FIDE is that it shall be played according to the FIDE Laws of Chess. It is recommended that competitive games not rated by FIDE be played according to the FIDE Laws of Chess. Member federations may ask FIDE to give a ruling on matters relating to the Laws of Chess. BASIC RULES OF PLAY. Article 1: The Nature and Objectives of the Game of Chess 1.1 1.2 1.3 1.4 The game of chess is played between two opponents who move their pieces on a square board called a ‘chessboard’. The player with the light-coloured pieces (White) makes the first move, then the players move alternately, with the player with the dark-coloured pieces (Black) making the next move. A player is said to ‘have the move’ when his/her opponent’s move has been ‘made’. The objective of each player is to place the opponent’s king ‘under attack’ in such a way that the opponent has no legal move. 1.4.1 The player who achieves this goal is said to have ‘checkmated’ the opponent’s king and to have won the game. Leaving one’s own king under attack, exposing one’s own king to attack and also ’capturing’ the opponent’s king is not allowed. 1.4.2 The opponent whose king has been checkmated has lost the game. 1.5 If the position is such that neither player can possibly checkmate the opponent’s king, the game is drawn (see Article 5.2.2). Article 2: The Initial Position of the Pieces on the Chessboard 2.1 2.2 The chessboard is composed of an 8 x 8 grid of 64 equal squares alternately light (the ‘white’ squares) and dark (the ‘black’ squares). The chessboard is placed between the players in such a way that the near corner square to the right of the player is white. At the beginning of the game White has 16 light-coloured pieces (the ‘white’ pieces); Black has 16 dark-coloured pieces (the ‘black’ pieces). These pieces are as follows: A white king usually indicated by the symbol K A white queen Two white rooks Two white bishops Two white knights Eight white pawns A black king A black queen Two black rooks Two black bishops Two black knights Eight black pawns usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol usually indicated by the symbol K usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol Staunton Pieces p Q K B N R 9 2.3 The initial position of the pieces on the chessboard is as follows: 2.4 The eight vertical columns of squares are called ‘files’. The eight horizontal rows of squares are called ‘ranks’. A straight line of squares of the same colour, running from one edge of the board to an adjacent edge, is called a ‘diagonal’. Article 3: The Moves of the Pieces 3.1 It is not permitted to move a piece to a square occupied by a piece of the same colour. 3.1.1 If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move. 3.1.2 A piece is said to attack an opponent’s piece if the piece could make a capture on that square according to Articles 3.2 to 3.8. 3.1.3 A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack. 3.2 The bishop may move to any square along a diagonal on which it stands. 3.3 The rook may move to any square along the file or the rank on which it stands. 3.4 The queen may move to any square along the file, the rank or a diagonal on which it stands. 3.5 3.6 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. The pawn: 3.7.1 The pawn may move forward to the square immediately in front of it on the same file, provided that this square is unoccupied, or 3.7.2 on its first move the pawn may move as in 3.7.1 or alternatively it may advance two squares along the same file, provided that both squares are unoccupied, or 3.7.3 the pawn may move to a square occupied by an opponent’s piece diagonally in front of it on an adjacent file, capturing that piece. 3.7.3.1 A pawn occupying a square on the same rank as and on an adjacent file to an opponent’s pawn which has just advanced two squares in one move from its original square may capture this opponent’s pawn as though the latter had been moved only one square. 3.7.3.2 This capture is only legal on the move following this advance and is called an ‘en passant’ capture. 3.7.3.3 When a player, having the move, plays a pawn to the rank furthest from its starting position, he/she must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival. This is called the square of ‘promotion’. 3.7.3.4 The player's choice is not restricted to pieces that have been captured previously. 3.7.3.5 This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate. 3.8 There are two different ways of moving the king: 3.8.1 by moving to an adjoining square. 3.8.2 by ‘castling’. This is a move of the king and either rook of the same colour along the player’s first rank, counting as a single move of the king and executed as follows: the king is transferred from its original square two squares towards the rook on its original square, then that rook is transferred to the square the king has just crossed. 3.8.2.1 The right to castle has been lost: 3.8.2.1.1 If the king has already moved, or 3.8.2.1.2 With a rook that has already moved. 3.8.2.2 Castling is prevented temporarily: 3.8.2.2.1 if the square on which the king stands, or the square which it must cross, or the square which it is to occupy, is attacked by one or more of the opponent's pieces, or 3.8.2.2.2 if there is any piece between the king and the rook with which castling is to be effected. 3.9 The king in check: 3.9.1 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces, even if such pieces are constrained from moving to the square occupied by the king because they would then leave or place their own king in check. 3.9.2 No piece can be moved that will either expose the king of the same colour to check or leave that king in check. 3.10 Legal and illegal moves; illegal positions: 3.10.1 A move is legal when all the relevant requirements of Articles 3.1 – 3.9 have been fulfilled. 3.10.2 A move is illegal when it fails to meet the relevant requirements of Articles 3.1 –3.9. 3.10.3 A position is illegal when it cannot have been reached by any series of legal moves. Article 4: The Act of Moving the Pieces 4.1 4.2 Each move must be played with one hand only. Adjusting the pieces or other physical contact with a piece: 4.2.1 Only the player having the move may adjust one or more pieces on their squares, provided that he/she first expresses his/her intention (for example by saying “j’adoube” or “I adjust”). 4.2.2 Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent. 4.3 Except as provided in Article 4.2.1, if the player having the move touches on the chessboard, with the intention of moving or capturing: 4.3.1 one or more of his/her own pieces, he/she must move the first piece touched that can be moved. 4.3.2 one or more of his/her opponent’s pieces, he/she must capture the first piece touched that can be captured. 4.3.3 one or more pieces of each colour, he/she must capture the first touched opponent’s piece with his/her first touched piece or, if this is illegal, move or capture the first piece touched that can be moved or captured. If it is unclear whether the player’s own piece or his/her opponent’s was touched first, the player’s own piece shall be considered to have been touched before his/her opponent’s. 4.4 If a player having the move: 4.4.1 touches his/her king and a rook he/she must castle on that side if it is legal to do so 4.4.2 deliberately touches a rook and then his/her king he/she is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.1. 4.4.3 intending to castle, touches the king and then a rook, but castling with this rook is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.4.4 promotes a pawn, the choice of the piece is finalised when the piece has touched the square of promotion. 4.5 4.6 If none of the pieces touched in accordance with Article 4.3 or Article 4.4 can be moved or captured, the player may make any legal move. The act of promotion may be performed in various ways: 4.6.1 the pawn does not have to be placed on the square of arrival. 4.6.2 removing the pawn and putting the new piece on the square of promotion may occur in any order. 4.6.3 If an opponent’s piece stands on the square of promotion, it must be captured. 4.7 When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made in the case of: 4.7.1 A capture, when the captured piece has been removed from the chessboard and the player, having placed his/her own piece on its new square, has released this capturing piece from his/her hand. 4.7.2 Castling, when the player's hand has released the rook on the square previously crossed by the king. When the player has released the king from his/her hand, the move is not yet made, but the player no longer has the right to make any move other than castling on that side, if this is legal. If castling on this side is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.7.3 Promotion, when the player's hand has released the new piece on the square of promotion and the pawn has been removed from the board. 4.8 4.9 A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 once the player touches a piece with the intention of moving or capturing it. 4.8. A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 .4.9. If a player is unable to move the pieces, an assistant, who shall be acceptable to the arbiter, may be provided by the player to perform this operation. Article 5: The Completion of the Game 5.1.1 The game is won by the player who has checkmated his/her opponent’s king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.1.2 The game is lost by the player who declares he/she resigns (this immediately ends the game), unless the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. In this case the result of the game is a draw. 5.2.1 The game is drawn when the player to move has no legal move and his/her king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game, provided that the move producing the stalemate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.3 The game is drawn upon agreement between the two players during the game, provided both players have made at least one move. This immediately ends the game. COMPETITIVE RULES OF PLAY Article 6: The Chessclock 6.1 ‘Chessclock’ means a clock with two time displays, connected to each other in such a way that only one of them can run at a time. ‘Clock’ in the Laws of Chess means one of the two time displays. Each time display has a ‘flag’. ‘Flag-fall’ means the expiration of the allotted time for a player. 6.2 Handling the chessclock: 6.2.1 During the game each player, having made his/her move on the chessboard, shall pause his/her own clock and start his/her opponent’s clock (that is to say, he/she shall press his/her clock). This “completes” the move. A move is also completed if: 6.2.1.1 6.2.1.2 the move ends the game (see Articles 5.1.1, 5.2.1, 5.2.2, 9.2.1, 9.6.1 and 9.6.2), or the player has made his/her next move, when his/her previous move was not completed. 6.2.2 A player must be allowed to pause his/her clock after making his/her move, even after the opponent has made his/her next move. The time between making the move on the chessboard and pressing the clock is regarded as part of the time allotted to the player. 6.2.3 A player must press his/her clock with the same hand with which he/she made his/her move. It is forbidden for a player to keep his/her finger on the clock or to ‘hover’ over it. 6.2.4 The players must handle the chessclock properly. It is forbidden to press it forcibly, to pick it up, to press the clock before moving or to knock it over. Improper clock handling shall be penalised in accordance with Article 12.9. 6.2.5 6.2.6 Only the player whose clock is running is allowed to adjust the pieces. If a player is unable to use the clock, an assistant, who must be acceptable to the arbiter, may be provided by the player to perform this operation. His/Her clock shall be adjusted by the arbiter in an equitable way. This adjustment of the clock shall not apply to the clock of a player with a disability. 6.3 Allotted time: 6.3.1 When using a chessclock, each player must complete a minimum number of moves or all moves in an allotted period of time including any additional amount of time added with each move. All these must be specified in advance. 6.3.2 The time saved by a player during one period is added to his/her time available for the next period, where applicable. In the time-delay mode both players receive an allotted ‘main thinking time’. Each player also receives a ‘fixed extra time’ with every move. The countdown of the main thinking time only commences after the fixed extra time has expired. Provided the player presses his/her clock before the expiration of the fixed extra time, the main thinking time does not change, irrespective of the proportion of the fixed extra time used. 6.4 Immediately after a flag falls, the requirements of Article 6.3.1 must be checked. 6.5 Before the start of the game the arbiter shall decide where the chessclock is placed. 6.6 At the time determined for the start of the game White’s clock is started.6.7. Default time: 6.7.1 The regulations of an event shall specify a default time in advance. If the default time is not specified, then it is zero. Any player who arrives at the chessboard after the default time shall lose the game unless the arbiter decides otherwise. 6.7.2 If the regulations of an event specify that the default time is not zero and if neither player is present initially, White shall lose all the time that elapses until he/she arrives, unless the regulations of an event specify, or the arbiter decides otherwise. 6.8 A flag is considered to have fallen when the arbiter observes the fact or when either player has made a valid claim to that effect. 6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. 6.10 Chessclock setting: 6.10.1 Every indication given by the chessclock is considered to be conclusive in the absence of any evident defect. A chessclock with an evident defect shall be replaced by the arbiter, who shall use his/her best judgement when determining the times to be shown on the replacement chessclock. 6.10.2 If during a game it is found that the setting of either or both clocks is incorrect, either player or the arbiter shall pause the chessclock immediately. The arbiter shall install the correct setting and adjust the times and move-counter, if necessary he/she shall use his/her best judgement when determining the clock settings. 6.11.1 If the game needs to be interrupted, the arbiter shall pause the chessclock. 6.11.2 A player may pause the chessclock only in order to seek the arbiter’s assistance, for example when promotion has taken place and the piece required is not available. 6.11.3 The arbiter shall decide when the game restarts. 6.11.4 If a player pauses the chessclock in order to seek the arbiter’s assistance, the arbiter shall determine whether the player had any valid reason for doing so. If the player has no valid reason for pausing the chessclock, the player shall be penalised in accordance with Article 12.9. 6.12.1 Screens, monitors, or demonstration boards showing the current position on the chessboard, the moves and the number of moves made/completed, and clocks which also show the number of moves, are allowed in the playing hall. 6.12.2 The player may not make a claim relying only on information shown in this manner.

MYTH The British helped the Jews displace the native Arab population of Palestine. FACT Herbert Samuel, a British Jew who served as the first High Commissioner of Palestine, placed restrictions on Jewish immigration “in the ‘interests of the present population’ and the ‘absorptive capacity’ of the country.”1 The influx of Jewish settlers was said to force the Arab fellahin (native peasants) from their land. This was when less than a million people lived in an area that now supports more than nine million. The British limited the absorptive capacity of Palestine when, in 1921, Colonial Secretary Winston Churchill severed nearly four-fifths of Palestine—some thirty-five thousand square miles—to create a new Arab entity, Transjordan. As a consolation prize for the Hejaz and Arabia (which are both now Saudi Arabia) going to the Saud family, Churchill rewarded Sharif Hussein’s son Abdullah for his contribution to the war against Turkey by installing him as Transjordan’s emir. The British went further and placed restrictions on Jewish land purchases in what remained of Palestine. By 1949, the British had allotted 87,500 acres of the 187,500 acres of cultivable land to Arabs and only 4,250 acres to Jews. This contradicted Article 6 of the Mandate which stated that “the Administration of Palestine…shall encourage, in cooperation with the Jewish Agency…close settlement by Jews on the land, including State lands and waste lands not acquired for public purposes.”2 Ultimately, the British admitted that the argument about the country’s absorptive capacity was specious. The Peel Commission said, “The heavy immigration in the years 1933–36 would seem to show that the Jews have been able to enlarge the absorptive capacity of the country for Jews.”3 MYTH The British allowed Jews to flood Palestine while Arab immigration was tightly controlled. FACT The British response to Jewish immigration set a precedent of appeasing the Arabs, which was followed for the duration of the Mandate. The British restricted Jewish immigration while allowing Arabs to enter the country freely. Apparently, London did not feel that a flood of Arab immigrants would affect the country’s “absorptive capacity.” During World War I, the Jewish population in Palestine declined because of the war, famine, disease, and expulsion by the Turks. In 1915, approximately 83,000 Jews lived in Palestine among 590,000 Muslim and Christian Arabs. According to the 1922 census, the Jewish population was 83,000, while the Arabs numbered 643,000.4 Thus, the Arab population grew exponentially while that of the Jews stagnated. In the mid-1920s, Jewish immigration to Palestine increased primarily because of anti-Jewish economic legislation in Poland and Washington’s imposition of restrictive quotas.5 The record number of immigrants in 1935 (see table) was a response to the growing persecution of Jews in Nazi Germany. The British administration considered this number too large, however, so the Jewish Agency was informed that less than one-third of the quota it asked for would be approved in 1936.6 The British gave in further to Arab demands by announcing in the 1939 White Paper that an independent Arab state would be created within ten years and that Jewish immigration was to be limited to 75,000 for the next five years, after which it was to cease altogether. It also forbade land sales to Jews in 95% of the territory of Palestine. The Arabs, nevertheless, rejected the proposal. Jewish Immigration to Palestine7 1919 1,806 1931 4,075 1920 8,223 1932 12,533 1921 8,294 1933 37,337 1922 8,685 1934 45,267 1923 8,175 1935 66,472 1924 13,892 1936 29,595 1925 34,386 1937 10,629 1926 13,855 1938 14,675 1927 3,034 1939 31,195 1928 2,178 1940 10,643 1929 5,249 1941 4,592 1930 4,944 By contrast, throughout the Mandatory period, Arab immigration was unrestricted. In 1930, the Hope Simpson Commission, sent from London to investigate the 1929 Arab riots, said the British practice of ignoring the uncontrolled illegal Arab immigration from Egypt, Transjordan, and Syria had the effect of displacing the prospective Jewish immigrants.8 The British governor of the Sinai from 1922 to 1936 observed, “This illegal immigration was not only going on from the Sinai, but also from Transjordan and Syria, and it is very difficult to make a case out for the misery of the Arabs if at the same time their compatriots from adjoining states could not be kept from going in to share that misery.”9 The Peel Commission reported in 1937 that the “shortfall of land is…due less to the amount of land acquired by Jews than to the increase in the Arab population.”10 MYTH The British changed their policy to allow Holocaust survivors to settle in Palestine. FACT The gates of Palestine remained closed for the duration of the war, stranding hundreds of thousands of Jews in Europe, many of whom became victims of Hitler’s “Final Solution.” After the war, the British refused to allow the survivors of the Nazi nightmare to find sanctuary in Palestine. On June 6, 1946, President Truman urged the British government to relieve the suffering of the Jews confined to displaced persons camps in Europe by immediately accepting 100,000 Jewish immigrants. Britain’s foreign minister Ernest Bevin replied sarcastically that the United States wanted displaced Jews to immigrate to Palestine “because they did not want too many of them in New York.”11 Some Jews reached Palestine, many smuggled in on dilapidated ships organized by the Haganah. Between August 1945 and the establishment of the State of Israel in May 1948, sixty-five “illegal” immigrant ships, carrying 69,878 people, arrived from European shores. In August 1946, however, the British began to intern those they caught in camps on Cyprus. Approximately 50,000 people were detained in the camps, and 28,000 remained imprisoned when Israel declared independence.12 MYTH As the Jewish population grew, the plight of the Palestinian Arabs worsened. FACT In July 1921, Hasan Shukri, the mayor of Haifa and president of the Muslim National Associations, sent a telegram to the British government in reaction to a delegation of Palestinians that went to London to try to stop the implementation of the Balfour Declaration. Shukri wrote: We are certain that without Jewish immigration and financial assistance there will be no future development of our country as may be judged from the fact that the towns inhabited in part by Jews such as Jerusalem, Jaffa, Haifa, and Tiberias are making steady progress while Nablus, Acre, and Nazareth where no Jews reside are steadily declining.13 The Jewish population increased by 470,000 between World War I and World War II, while the non-Jewish population rose by 588,000.14 The permanent Arab population increased by 120% between 1922 and 1947.15 This rapid growth of the Arab population was a result of several factors. One was immigration from neighboring states—constituting 37% of the total immigration to pre-state Israel—by Arabs who wanted to take advantage of the higher standard of living the Jews had made possible.16 The Arab population also grew because of the improved living conditions created by the Jews as they drained malarial swamps and brought improved sanitation and health care to the region. Thus, for example, the Muslim infant mortality rate fell from 201 per thousand in 1925 to 94 per thousand in 1945, and life expectancy rose from 37 years in 1926 to 49 in 1943.17 The Arab population increased the most in cities where large Jewish populations had created new economic opportunities. From 1922–1947, the non-Jewish population increased by 290% in Haifa, 131% in Jerusalem, and 158% in Jaffa. The growth in Arab towns was more modest: 42% in Nablus, 78% in Jenin, and 37% in Bethlehem.18 MYTH Jews stole Arab land. FACT Despite the growth in their population, the Arabs continued to assert they were being displaced. From the beginning of World War I, however, part of Palestine’s land was owned by absentee landlords who lived in Cairo, Damascus, and Beirut. About 80% of the Palestinian Arabs were debt-ridden peasants, semi-nomads, and Bedouins.19 Jews went out of their way to avoid purchasing land in areas where Arabs might be displaced. They sought land that was largely uncultivated, swampy, cheap, and—most important—without tenants. In 1920, Labor Zionist leader David Ben-Gurion expressed his concern about the Arab fellahin, whom he viewed as “the most important asset of the native population.” He insisted that “under no circumstances must we touch land belonging to fellahs or worked by them.” Instead, he advocated helping liberate them from their oppressors. “Only if a fellah leaves his place of settlement,” Ben-Gurion added, “should we offer to buy his land, at an appropriate price.”20 Jews only began to purchase cultivated land after buying all the uncultivated territory. Many Arabs were willing to sell because of the migration to coastal towns and because they needed money to invest in the citrus industry.21 When John Hope Simpson arrived in Palestine in May 1930, he observed, “They [the Jews] paid high prices for the land and, in addition, they paid to certain of the occupants of those lands a considerable amount of money which they were not legally bound to pay.”22 In 1931, Lewis French conducted a survey of landlessness for the British government and offered new plots to any Arabs who had been “dispossessed.” British officials received more than 3,000 applications, of which 80% were ruled invalid by the government’s legal adviser because the applicants were not landless Arabs. This left only about 600 landless Arabs, 100 of whom accepted the government land offer.23 In April 1936, a new outbreak of Arab attacks on Jews was instigated by local Palestinian leaders who were later joined by Arab volunteers led by a Syrian guerrilla named Fawzi al-Qawuqji, the commander of the Arab Liberation Army. By November, when the British finally sent a new commission headed by Lord Peel to investigate, 89 Jews had been killed and more than 300 wounded.24 The Peel Commission’s report found that Arab complaints about Jewish land acquisition were baseless. It pointed out that “much of the land now carrying orange groves was sand dunes or swamp and uncultivated when it was purchased…There was at the time of the earlier sales little evidence that the owners possessed either the resources or training needed to develop the land.”25 Moreover, the Commission found the shortage was “due less to the amount of land acquired by Jews than to the increase in the Arab population.” The report concluded that the presence of Jews in Palestine, along with the work of the British administration, had resulted in higher wages, an improved standard of living, and ample employment opportunities.26 It is made quite clear to all, both by the map drawn up by the Simpson Commission and by another compiled by the Peel Commission, that the Arabs are as prodigal in selling their land as they are in useless wailing and weeping (emphasis in the original). —Transjordan’s king Abdullah27 Even at the height of the Arab revolt in 1938 (which began in April 1936 with the murder of two Jews by Arabs and the subsequent murder of two Arab workers by members of the Jewish underground28), the British high commissioner to Palestine believed the Arab landowners were complaining about sales to Jews to drive up prices for lands they wished to sell. Many Arab landowners had been so terrorized by Arab rebels they decided to leave Palestine and sell their property to the Jews.29 The Jews paid exorbitant prices to wealthy landowners for small tracts of arid land. “In 1944, Jews paid between $1,000 and $1,100 per acre in Palestine, mostly for arid or semiarid land; in the same year, rich black soil in Iowa was selling for about $110 per acre.”30 By 1947, Jewish holdings in Palestine amounted to about 463,000 acres. Approximately 45,000 were acquired from the mandatory government, 30,000 were bought from various churches, and 387,500 were purchased from Arabs. Analyses of land purchases from 1880 to 1948 show that 73% of Jewish plots were purchased from large landowners, not poor fellahin.31 Many leaders of the Arab nationalist movement, including members of the Muslim Supreme Council, and the mayors of Gaza, Jerusalem, and s sold land to the Jews. As’ad el-Shuqeiri, a Muslim religious scholar and father of Palestine Liberation Organization chairman Ahmed Shuqeiri, took Jewish money for his land. Even King Abdullah leased land to the Jews.32 MYTH The British helped the Palestinians to live peacefully with the Jews. FACT In 1921, Haj Amin el-Husseini first began to organize fedayeen (“one who sacrifices himself”) to terrorize Jews. El-Husseini hoped to duplicate the success of Kemal Atatürk in Turkey by driving the Jews out of Palestine just as Kemal had driven the invading Greeks from his country.33 Arab radicals gained influence because the British administration was unwilling to take effective action against them until they began a revolt against British rule. Colonel Richard Meinertzhagen, former head of British military intelligence in Cairo, and later chief political officer for Palestine and Syria, wrote in his diary that British officials “incline towards the exclusion of Zionism in Palestine.” The British encouraged the Palestinians to attack the Jews. According to Meinertzhagen, Col. Bertie Harry Waters-Taylor (financial adviser to the military administration in Palestine 1919–23) met with el-Husseini in 1920, a few days before Easter, and told him that “he had a great opportunity at Easter to show the world…that Zionism was unpopular not only with the Palestine administration but in Whitehall.” He added that “if disturbances of sufficient violence occurred in Jerusalem at Easter, both General [Louis] Bols [chief administrator in Palestine, 1919–20] and General [Edmund] Allenby [commander of the Egyptian force, 1917–19, then high commissioner of Egypt] would advocate the abandonment of the Jewish Home. Waters-Taylor explained that freedom could only be attained through violence.”34 El-Husseini took the colonel’s advice and instigated a riot. The British withdrew their troops and the Jewish police from Jerusalem, allowing the Arab mob to attack Jews and loot their shops. Because of el-Husseini’s overt role in instigating the pogrom, the British decided to arrest him. He escaped, however, and was sentenced to ten years in absentia. A year later, some British Arabists convinced High Commissioner Herbert Samuel to pardon el-Husseini and to appoint him Mufti (a cleric in charge of Jerusalem’s Islamic holy places). By contrast, Vladimir Jabotinsky and several followers, who had formed a Jewish defense organization during the unrest, were sentenced to 15 years. They were released a few months later.35 Samuel met with el-Husseini on April 11, 1921, and was assured “that the influences of his family and himself would be devoted to tranquility.” Three weeks later, riots in Jaffa and elsewhere left forty-three Jews dead.36 El-Husseini consolidated his power and took control of all Muslim religious funds in Palestine. He used his authority to gain control over the mosques, the schools, and the courts. No Arab could reach an influential position without being loyal to the Mufti. His power was so absolute that “no Muslim in Palestine could be born or die without being beholden to Haj Amin.”37 The Mufti’s henchmen also ensured he would have no opposition by systematically killing Palestinians who discussed cooperation with the Jews from rival clans. As the spokesman for Palestinian Arabs, el-Husseini did not ask that Britain grant them independence. On the contrary, in a letter to Churchill in 1921, he demanded that Palestine be reunited with Syria and Transjordan.38 The Arabs found rioting an effective political tool because of the lax British response toward violence against Jews. In handling each riot, the British prevented Jews from protecting themselves but made little effort to prevent the Arabs from attacking them. After each outbreak, a British commission of inquiry would try to establish the cause of the violence. The conclusion was always the same: The Arabs feared being displaced by the Jews. To stop the rioting, the commissions would recommend that restrictions be placed on Jewish immigration. Thus, the Arabs learned they could always stop the influx of Jews by staging riots. This cycle began after a series of riots in May 1921. After failing to protect the Jewish community from Arab mobs, the British appointed the Haycraft Commission to investigate the cause of the violence. Although the panel concluded the Arabs had been the aggressors, it rationalized the cause of the attack: “The fundamental cause of the riots was a feeling among the Arabs of discontent with, and hostility to, the Jews, due to political and economic causes, and connected with Jewish immigration, and with their conception of Zionist policy.”39 One consequence of the violence was the institution of a temporary ban on Jewish immigration. The Arab fear of being “displaced” or “dominated” was an excuse for their attacks on Jewish settlers. Note, too, that these riots were not inspired by nationalistic fervor—nationalists would have rebelled against their British overlords—they were motivated by economics, the radical Islamic views of the Mufti, and misunderstanding. In 1929, Arab provocateurs convinced the masses that the Jews had designs on the Temple Mount (a tactic still used today to incite violence). A Jewish religious observance at the Western Wall, which forms a part of the Temple Mount, served as a pretext for rioting by Arabs against Jews, which spilled out of Jerusalem into other villages and towns, including Safed and Hebron. Again, the British administration made no effort to prevent the violence, and, after it began, the British did nothing to protect the Jewish population. After six days of mayhem, the British finally brought troops in to quell the disturbance. By this time, most of Hebron’s Jews had fled or been killed. In all, 133 Jews were killed and 399 wounded in the pogroms.40 After the riots, the British ordered an investigation, resulting in the Passfield White Paper. It said the “immigration, land purchase and settlement policies of the Zionist Organization were already or were likely to become, prejudicial to Arab interests. It understood the mandatory government’s obligation to the non-Jewish community to mean that Palestine’s resources must be primarily reserved for the growing Arab economy.”41 This meant it was necessary to restrict Jewish immigration and land purchases. MYTH The Mufti was not a Nazi collaborator. FACT In 1941, Haj Amin al-Husseini, the Mufti of Jerusalem, fled to Germany and met with Adolf Hitler, Heinrich Himmler, Joachim Von Ribbentrop, and other Nazi leaders. He wanted to persuade them to extend the Nazis’ anti-Jewish program to the Arab world. The Mufti sent Hitler fifteen drafts of declarations he wanted Germany and Italy to make concerning the Middle East. One called on the two countries to declare the illegality of the Jewish home in Palestine. He also asked the Axis powers to “accord to Palestine and to other Arab countries the right to solve the problem of the Jewish elements in Palestine and other Arab countries in accordance with the interest of the Arabs, and by the same method that the question is now being settled in the Axis countries.”42 In November 1941, the Mufti met with Hitler, who told him the Jews were his foremost enemy. The Nazi dictator rebuffed the Mufti’s requests for a declaration in support of the Arabs, however, telling him the time was not right. The Mufti offered Hitler his “thanks for the sympathy which he had always shown for the Arab and especially Palestinian cause, and to which he had given clear expression in his public speeches.” He added, “The Arabs were Germany’s natural friends because they had the same enemies as had Germany, namely…the Jews.” Hitler told the Mufti he opposed the creation of a Jewish state and that Germany’s objective was destroying the Jewish element in the Arab sphere.43 In 1945, Yugoslavia sought to indict the Mufti as a war criminal for his role in recruiting twenty thousand Muslim volunteers for the SS, who participated in the killing of Jews in Croatia and Hungary. He escaped French detention in 1946, however, and continued his fight against the Jews from Cairo and later Beirut where he died in 1974. MYTH The bombing of the King David Hotel was part of a deliberate terror campaign against civilians. FACT British troops seized the Jewish Agency compound on June 29, 1946, and confiscated large quantities of documents. At about the same time, more than 2,500 Jews from all over Palestine were arrested. A week later, news of a massacre of 40 Jews in a pogrom in Poland reminded the Jews of Palestine how Britain’s restrictive immigration policy had condemned thousands to death. In response to the British provocations, and a desire to demonstrate that the Jews’ spirit could not be broken, the United Resistance Movement planned to bomb the King David Hotel, which housed the British military command and the Criminal Investigation Division in addition to hotel guests. The Haganah pulled out of the plot and left it up to the Irgun. Irgun leader Menachem Begin stressed his desire to avoid civilian casualties and the plan was to warn the British so they would evacuate the building before it was blown up. Three telephone calls were placed on July 22, 1946, one to the hotel, another to the French Consulate, and a third to the Palestine Post warning that explosives in the King David Hotel would soon be detonated. The call to the hotel was received and ignored. Begin quotes one British official who supposedly refused to evacuate the building, saying, “We don’t take orders from the Jews.”44 As a result, when the bombs exploded, the casualty toll was high: 91 killed and 45 injured. Among the casualties were 15 Jews. Few people in the main part of the hotel were injured.45 For decades, the British denied they had been warned. In 1979, however, a member of the British Parliament provided the testimony of a British officer who heard other officers in the King David Hotel bar joking about a Zionist threat to the headquarters. The officer who overheard the conversation immediately left the hotel and survived.46 In contrast to Arab attacks against Jews, which Arab leaders hailed as heroic actions, the Jewish National Council denounced the bombing of the King David.47 1 Aharon Cohen, Israel and the Arab World, (NY: Funk and Wagnalls, 1970), p. 172

Topic: A.10-A.12 Number and Algebraic Methods

Multiplying any number by 12

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

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