Name: electron spin and orbital pairing
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 6 s
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The Pauli Exclusion Principle

Atoomorbitalen zijn de gebieden waar de elektronen van een atoom het meest waarschijnlijk worden gevonden. Maar hoeveel elektronen kan elke orbitaal bevatten? Het uitsluitingsprincipe van Pauli beantwoordt deze vraag, omdat het betekent dat geen twee elektronen in een atoom dezelfde set van vier kwantumgetallen kunnen hebben.Elke orbitaal komt overeen met een vast hoofd;impulsmoment, of azimutaal;en magnetische kwantumgetal-waarden. Een elektron in de 1s-orbitaal heeft bijvoorbeeld altijd een hoofdkwantumgetal van één en azimutale en magnetische kwantumgetallen nul. Dienovereenkomstig moeten elektronen verschillende spinkwantumgetalwaarden, of spins, hebben om in dezelfde atoomorbitaal te verblijven.Bedenk dat het spinkwantumgetal slechts twee mogelijke waarden heeft:1/2 en 1/2. Daarom kunnen slechts twee elektronen dezelfde orbitaal bezetten. Daarom kan elke s-subschil, die één orbitaal heeft, slechts twee elektronen bevatten, en elke p-subshell, die drie orbitalen heeft, kan zes elektronen bevatten.Elk van de d-en f-subschillen heeft een maximale capaciteit van respectievelijk tien en veertien elektronen. De verdeling van elektronen over de atomaire orbitalen van een atoom wordt weergegeven door de elektronenconfiguratie in tekst-of diagramvorm. Beschouw een waterstofatoom in de grondtoestand, waar één elektron de orbitaal met de laagste energie bezet:1s.De geschreven elektronenconfiguratie geeft elke bezette subschil aan met het getal van de overeenkomstige schil, de letter van de subschil en een superscriptgetal dat het aantal elektronen in de subschil specificeert. De orbitale diagramstijl van de elektronenconfiguratie geeft elke orbitaal binnen een bezette subschil aan als een doos of lijn en elk elektron als een pijl. Een opwaartse pijl geeft een 1/2 spin of spin-up aan, en een neerwaartse pijl geeft een 1/2 spin of spin-down aan.Het orbitale diagram van waterstof heeft daarom één opwaartse pijl. De elektronenconfiguratie van helium is 1s^2. De twee elektronen hebben drie identieke kwantumgetallen, omdat ze tot dezelfde schil en subschil behoren.Hun spinkwantumgetallen zijn verschillend, in overeenstemming met het Pauli-uitsluitingsprincipe. Elektronen met tegengestelde spins worden paren"genoemd als ze dezelfde orbitaal bezetten. Voor lithium, dat een atoomgetal van drie heeft, zijn de twee elektronen in de 1s-orbitaal gepaard en is het elektron in de 2s-orbitaal ongepaard.Gewoonlijk worden ongepaarde elektronen weergegeven als spin-up.

het pauli-uitsluitingsprincipe

De rangschikking van elektronen in de orbitalen van een atoom wordt de elektronenconfiguratie genoemd. We beschrijven een elektronenconfiguratie met een symbool dat drie stukjes informatie bevat: 
 <ol> 
 	<li>Het nummer van de belangrijkste kwantumschil, n,</li> 
 	<li>De letter die het orbitale type aangeeft (de subshell, l), en</li> 
 	<li>Een superscriptgetal dat het aantal elektronen in die specifieke subshell aangeeft.</li> 
 </ol> 
 De notatie 2p4 geeft bijvoorbeeld vier elektronen aan in een p-subschil (l = 1) met een hoofdkwantumgetal (n) van 2. De notatie 3d 8 geeft acht elektronen aan in de d-subschil (l = 2) van de hoofdschil waarvoor n = 3. 

 Hoewel de drie kwantumgetallen goed werken voor het beschrijven van elektronenorbitalen, toonden sommige experimenten aan dat ze niet voldoende waren om alle waargenomen resultaten te verklaren. In de jaren twintig werd aangetoond dat wanneer waterstoflijnspectra met extreem hoge resolutie worden onderzocht, sommige lijnen eigenlijk geen enkele pieken zijn, maar eerder paren dicht bij elkaar gelegen lijnen. Dit is de zogenaamde fijne structuur van het spectrum, en dit houdt in dat er extra kleine verschillen zijn in de energieën van elektronen, zelfs als ze zich in dezelfde orbitaal bevinden. Deze waarnemingen brachten Samuel Goudsmit en George Uhlenbeck ertoe te veronderstellen dat elektronen een vierde kwantumgetal hebben. Ze noemden dit het spinkwantumgetal of ms. 

 In een aangelegd magnetisch veld heeft een elektron twee mogelijke oriëntaties met verschillende energieën, één met spin-up, uitgelijnd met het magnetische veld, en één met spin-down, uitgelijnd ertegenover. 

 Het vierde kwantumgetal, spinkwantumgetal (ms), beschrijft deze twee verschillende spintoestanden van een elektron. Een spinkwantumgetal heeft twee mogelijke waarden: −1/2 (spin-down) en +1/2 (spin-up). 

 Elektronenspin beschrijft een intrinsieke elektron-"rotatie" of "spinning". Elk elektron fungeert als een kleine magneet of een klein roterend object met impulsmoment, of als een lus met een elektrische stroom, ook al kan deze rotatie of stroom niet worden waargenomen in termen van ruimtelijke coördinaten. 

 De omvang van de totale elektronenspin kan slechts één waarde hebben, en een elektron kan slechts in een van de twee gekwantiseerde toestanden ‘draaien’. De ene wordt de α-toestand genoemd, waarbij de z-component van de spin zich in de positieve richting van de z-as bevindt. Dit komt overeen met het spinkwantumgetal ms = +1/2. De andere wordt de β-toestand genoemd, waarbij de z-component van de spin negatief is en ms = −1/2. 

 Elk elektron, ongeacht de atomaire orbitaal waarin het zich bevindt, kan slechts één van deze twee waarden van het spinkwantumgetal hebben. De energieën van elektronen met verschillende spins zijn verschillend als een extern magnetisch veld wordt aangelegd. 

 Een elektron in een atoom wordt volledig beschreven door vier kwantumgetallen: n, l, ml en ms. De eerste drie kwantumgetallen definiëren de orbitaal en zijn onderling afhankelijk, terwijl het vierde kwantumgetal onafhankelijk is van andere kwantumgetallen omdat het een intrinsieke elektroneneigenschap beschrijft die spin wordt genoemd. Een Oostenrijkse natuurkundige Wolfgang Pauli (Nobelprijs voor de natuurkunde: 1945) formuleerde een algemeen principe dat het laatste stukje informatie geeft dat we nodig hebben om het algemene gedrag van elektronen in atomen te begrijpen. Het Pauli-uitsluitingsprincipe kan als volgt worden geformuleerd: Geen twee elektronen in hetzelfde atoom kunnen exact dezelfde set van alle vier de kwantumgetallen hebben. Wat dit betekent is dat twee elektronen dezelfde orbitaal (dezelfde reeks kwantumgetallen n, l en ml) alleen kunnen delen als hun spin-kwantumgetallen verschillende waarden hebben. Omdat het spinkwantumgetal (ms) slechts twee waarden +1/2 en -1/2 kan hebben, kunnen niet meer dan twee elektronen dezelfde orbitaal bezetten (en als twee elektronen zich in dezelfde orbitaal bevinden, moeten ze tegengestelde spins hebben). Daarom kan elke atomaire orbitaal slechts door nul, één of twee elektronen worden bevolkt. 

 De orbitale diagramstijl van de elektronenconfiguratie vertegenwoordigt elke orbitaal binnen een bezette subshell als een doos of lijn en elk elektron als een pijl. Het orbitale diagram van waterstof, met een elektronenconfiguratie van 1s1, is: 

 <img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;"> 

 Een pijl naar boven geeft een plus-halve spin of spin-up aan, en een neerwaartse pijl betekent een min-halve spin of spin-down. Het orbitale diagram van waterstof heeft daarom één pijl naar boven. 

 De elektronenconfiguratie van helium is 1s2. De twee elektronen hebben drie identieke kwantumgetallen, omdat ze tot dezelfde schil en subschil behoren. Hun spinkwantumgetallen zijn verschillend, in overeenstemming met het uitsluitingsprincipe van Pauli. Elektronen met tegengestelde spins worden gepaard genoemd als ze dezelfde orbitaal bezetten. 

 <img alt="Figure2" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;"> Deze tekst is overgenomen uit Openstax, Chemistry 2e, Sectie 6.3: Ontwikkeling van de kwantumtheorie.

Het Pauli-uitsluitingsprincipe

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

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electron spin and orbital pairing

Electron spin and orbital pairing explain why only two electrons can fit in one atomic orbital. Electron configuration describes how electrons are arranged in an atom’s orbitals. It is written with three parts: the principal quantum number, n, the orbital type, or subshell, and a superscript that shows how many electrons are in that subshell. For example, 2p4 means four electrons in a p subshell with n = 2, and 3d8 means eight electrons in a d subshell with n = 3.

The three quantum numbers describe orbitals well, but they do not explain every experimental result. In the 1920s, very high-resolution hydrogen spectra showed fine structure, where some lines split into two close peaks instead of one. This suggested that electrons in the same orbital can still have small energy differences. Samuel Goudsmit and George Uhlenbeck proposed a fourth quantum number to explain this behavior. They called it the spin quantum number, ms.

An electron can have two spin states in an external magnetic field. One state is spin up, which aligns with the magnetic field, and the other is spin down, which points against it. The spin quantum number has only two values, +1/2 and -1/2. These are also called the alpha and beta states. Electron spin is an intrinsic property, so each electron behaves like a tiny magnet, even though this motion cannot be observed in normal space.

A complete electron description uses four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and depend on one another. The spin quantum number is independent because it describes the electron’s spin. Austrian physicist Wolfgang Pauli used this idea to state the Pauli exclusion principle. It says that no two electrons in the same atom can have the same set of all four quantum numbers.

This principle means that two electrons may share the same orbital only if their spin quantum numbers are different. Because ms has only two possible values, no more than two electrons can occupy one orbital. An atomic orbital can therefore hold zero, one, or two electrons. In orbital diagrams, each orbital is shown as a box or line and each electron as an arrow. A hydrogen atom with configuration 1s1 has one upward arrow, which means one spin-up electron.

Helium has the configuration 1s2. Its two electrons share the same shell and subshell, so they have three identical quantum numbers. They differ in spin, which follows the Pauli exclusion principle. Electrons with opposite spins in the same orbital are called paired.

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Electron Spin and Orbital Pairing

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