Name: electron spin and orbital pairing
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 6 s
Channel: JoVE

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The Pauli Exclusion Principle

Orbitale atomowe to obszary, w których najprawdopodobniej zostaną znalezione elektrony atomu. Ale ile elektronów może pomieścić każdy orbital?
Na to pytanie odpowiada zasada wykluczenia Pauliego, która oznacza, że żadne dwa elektrony w atomie nie mogą mieć tego samego zestawu czterech liczb kwantowych.
Każdy orbital odpowiada ustalonej główce, momentowi pędu lub azymutalnemu i magnetycznym wartościom liczb kwantowych. Na przykład elektron na orbicie 1s zawsze ma główną liczbę kwantową równą jeden oraz azymutalne i magnetyczne liczby kwantowe równe zero.
W związku z tym elektrony muszą mieć różne wartości liczb kwantowych spinów lub spinów, aby znajdować się na tym samym orbicie atomowym. Przypomnijmy, że liczba kwantowa spinu ma tylko dwie możliwe wartości: +1/2 i −1/2. Dlatego tylko dwa elektrony mogą zajmować ten sam orbital .
Stąd każda podpowłoka s, która ma jeden orbital, może pomieścić tylko dwa elektrony, a każda podpowłoka p, która ma trzy orbitale, może pomieścić sześć elektronów. Każda z podpowłok d i f ma maksymalną pojemność odpowiednio dziesięciu i czternastu elektronów.
Rozkład elektronów na orbitalach atomowych atomu jest reprezentowany przez jego konfigurację elektronową w formie tekstu lub diagramu.
Rozważmy atom wodoru w stanie podstawowym, w którym jeden elektron zajmuje orbital o najniższej energii: 1s. Zapisana konfiguracja elektronowa oznacza każdą zajętą podpowłokę numerem odpowiedniej powłoki, literą podpowłoki i liczbą indeksu górnego określającą liczbę elektronów w podpowłoce.
Styl diagramu orbitalnego konfiguracji elektronowej oznacza każdy orbital w zajętej podpowłoce jako pudełko lub linię, a każdy elektron jako strzałkę. Strzałka w górę oznacza obrót +1/2 lub obrót w górę, a strzałka w dół oznacza obrót -1/2 lub obrót w dół. Diagram orbitalny wodoru ma zatem jedną strzałkę skierowaną w górę.
Konfiguracja elektronowa helu wynosi 1s2. Dwa elektrony mają trzy identyczne liczby kwantowe, ponieważ należą do tej samej powłoki i podpowłoki. Ich spinowe liczby kwantowe są różne, zgodnie z zasadą wykluczenia Pauliego.
Elektrony o przeciwnych spinach nazywane są "sparowanymi", jeśli zajmują ten sam orbital.
W przypadku litu, który ma liczbę atomową trzy, dwa elektrony na orbicie 1s są sparowane, a elektron na orbicie 2s jest niesparowany. Konwencjonalnie, niesparowane elektrony są reprezentowane jako spin-up.

zasada wykluczenia pauliego

Ułożenie elektronów na orbitach atomu nazywa się jego konfiguracją elektronową. Konfigurację elektronową opisujemy symbolem zawierającym trzy informacje:

<ol style="display: flex; flex-direction: column; gap: 10px;">
 <li>Numer głównej powłoki kwantowej, n,</li>
 <li>Litera określająca typ orbity (podpowłoka l) oraz</li>
 <li>Liczba w indeksie górnym, która określa liczbę elektronów w danej podpowłoce.</li>
</ol>

Na przykład zapis 2p4 wskazuje cztery elektrony na podpowłoce p (l = 1) z główną liczbą kwantową (n) wynoszącą 2. Notacja 3d 8 wskazuje osiem elektronów na podpowłoce d ( l = 2) powłoki głównej, dla których n = 3.

Chociaż te trzy liczby kwantowe dobrze sprawdzają się przy opisywaniu orbitali elektronów, niektóre eksperymenty wykazały, że nie są one wystarczające do wyjaśnienia wszystkich zaobserwowanych wyników. W latach dwudziestych XX wieku wykazano, że gdy widma linii wodoru są badane w niezwykle dużej rozdzielczości, niektóre linie w rzeczywistości nie są pojedynczymi pikami, ale raczej parami blisko rozmieszczonych linii. Jest to tak zwana drobna struktura widma, która implikuje, że istnieją dodatkowe niewielkie różnice w energiach elektronów, nawet jeśli znajdują się one na tej samej orbicie. Dzięki tym obserwacjom Samuel Goudsmit i George Uhlenbeck mogli stwiedzić, że elektrony mają czwartą liczbę kwantową. Nazwali ją spinową liczbą kwantową lub ms.

W przyłożonym polu magnetycznym elektron ma dwie możliwe orientacje o różnych energiach, jedną ze spinem w górę, zgodną z polem magnetycznym, i drugą ze spinem w dół, przeciwną mu.

Czwarta liczba kwantowa, spinowa liczba kwantowa (ms), opisuje te dwa różne stany spinowe elektronu. Liczba kwantowa spinu ma dwie możliwe wartości: −1/2 (spin w dół) i +1/2 (spin w górę).

Spin elektronu opisuje wewnętrzny obrót lub wirowanie elektronu. Każdy elektron działa jak mały magnes, maleńki obracający się obiekt o momencie pędu lub jak pętla z prądem elektrycznym. Mimo to tego obrotu lub prądu nie można zaobserwować w kategoriach współrzędnych przestrzennych.

Wielkość całkowitego spinu elektronu może mieć tylko jedną wartość, a elektron może „wirować” tylko w jednym z dwóch stanów skwantowanych. Jeden z nich nazywany jest stanem α, w którym składowa z spinu jest skierowana w kierunku dodatnim osi z. Odpowiada to spinowej liczbie kwantowej ms = +1/2. Drugi nazywa się stanem β, w którym składowa z spinu jest ujemna, a ms = −1/2.

Każdy elektron, niezależnie od orbitalu atomowego, na którym się znajduje, może mieć tylko jedną z dwóch wartości spinowej liczby kwantowej. Energie elektronów o różnych spinach są różne, jeśli przyłożone zostanie zewnętrzne pole magnetyczne.

Elektron w atomie jest całkowicie opisany czterema liczbami kwantowymi: n, l, ml i ms. Pierwsze trzy liczby kwantowe definiują orbital i są współzależne, podczas gdy czwarta liczba kwantowa jest niezależna od innych liczb kwantowych, ponieważ opisuje wewnętrzną właściwość elektronu zwaną spinem. Austriacki fizyk Wolfgang Pauli (Nagroda Nobla w dziedzinie fizyki w 1945 roku) sformułował ogólną zasadę, która dostarcza ostatniej informacji potrzebnej do zrozumienia ogólnego zachowania elektronów w atomach. Zasadę wykluczenia Pauliego można sformułować w następujący sposób: Żadne dwa elektrony w tym samym atomie nie mogą mieć dokładnie tego samego zestawu wszystkich czterech liczb kwantowych. Oznacza to, że dwa elektrony mogą dzielić ten sam orbital (ten sam zestaw liczb kwantowych n, l i ml) tylko wtedy, gdy ich spinowe liczby kwantowe mają różne wartości. Ponieważ spinowa liczba kwantowa (ms) może mieć tylko dwie wartości +1/2 i -1/2, na tym samym orbicie mogą znajdować się nie więcej niż dwa elektrony (a jeśli dwa elektrony znajdują się na tym samym orbicie, muszą mieć przeciwne spiny ). Dlatego każdy orbital atomowy może być obsadzony tylko przez zero, jeden lub dwa elektrony.

Styl diagramu orbitalnego konfiguracji elektronów przedstawia każdy orbital w zajętej podpowłoce jako pole lub linię, a każdy elektron jako strzałkę. Schemat orbitalny wodoru, którego konfiguracja elektronowa wynosi 1s1, wygląda następująco:

<img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;">

Strzałka w górę oznacza obrót o ponad połowę, czyli w górę, a strzałka w dół oznacza obrót o połowę, czyli w dół. Dlatego diagram orbitalny wodoru ma jedną strzałkę skierowaną w górę.

Konfiguracja elektronowa helu wynosi 1s2. Obydwa elektrony mają trzy identyczne liczby kwantowe, ponieważ należą do tej samej powłoki i podpowłoki. Ich spinowe liczby kwantowe są różne, zgodnie z zasadą wykluczenia Pauliego. Elektrony o przeciwnych spinach nazywane są sparowanymi, jeśli zajmują ten sam orbital.

<img alt="Figure2" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;">

Ten tekst jest adaptacją Openstax, Chemistry 2e, Sekcja 6.3: Rozwój teorii kwantowej.

Zasada wykluczenia Pauliego

Ułożenie elektronów na orbitalach atomu nazywa się jego konfiguracją elektronową. Konfigurację elektronową opisujemy symbolem, który ...

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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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