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

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Chemistry and Physics

IPC.7

IPC.7.E

The Pauli Exclusion Principle

Atomorbitale sind die Bereiche, in denen die Elektronen eines Atoms am wahrscheinlichsten zu finden sind. Aber wie viele Elektronen kann jedes Orbital aufnehmen? Das Paulische Ausschließungsprinzip beantwortet diese Frage, da es besagt, dass keine zwei Elektronen in einem Atom die gleiche Menge an vier Quantenzahlen haben können.Jedes Orbital entspricht einem festen Prinzip;Drehimpuls, oder azimutal;und magnetische Quantenzahlwerte. Zum Beispiel, hat ein Elektron im 1s-Orbital immer eine Hauptquantenzahl von eins sowie eine azimutale und magnetische Quantenzahlen von null. Dementsprechend müssen Elektronen eine unterschiedliche Spinquantenzahl, oder Spins, haben, um das gleiche Atomorbital zu besetzen.Erinnern Sie sich, dass die Spinquantenzahl nur zwei mögliche Werte hat:1/2 und 1/2. Daher können nur zwei Elektronen das gleiche Orbital besetzen. Also jede s Unterschale, die ein Orbital hat, kann nur zwei Elektronen aufnehmen, und jede p-Unterschale, die drei Orbitale hat, kann nur sechs Elektronen aufnehmen.Jede der Unterschalen d und f hat eine maximale Kapazität von zehn bzw. vierzehn Elektronen. Die Verteilung der Elektronen auf die Atomorbitale eines Atoms wird durch seine Elektronenkonfiguration in Text-oder Diagrammform dargestellt.Betrachten Sie ein Wasserstoffatom im Grundzustand, wobei ein Elektron das Orbital mit der niedrigsten Energie besetzt:1s. Die geschriebene Elektronenkonfiguration bezeichnet jede besetzte Unterschale mit der Zahl der entsprechenden Schale, der Buchstabe der Unterschale, und einer hochgestellten Zahl, die die Zahl der Elektronen in der Unterschale darstellt. Das Aufbauprinzip der Elektronenkonfiguration beschreibt jedes Orbital innerhalb einer besetzten Unterschale als Kasten oder Linie und jedes Elektron als Pfeil.Ein Pfeil der nach oben zeigt, hat einen 1/2 Spin oder Spin-up, und ein Abwärtspfeil bedeutet einen 1/2 Spin, oder Spin-down. Das Aufbauprinzip von Wasserstoff hat also, hat einen Pfeil nach oben. Die Elektronenkonfiguration von Helium ist 1s^2.Die beiden Elektronen haben drei identische Quantenzahlen, da sie zur selben Schale und Unterschale gehören. Ihre Spinquantenzahlen sind unterschiedlich, in Übereinstimmung mit dem Pauli-Prinzip. Elektronen mit entgegengesetztem Spin werden gepaart"genannt, wenn sie sich auf derselben Umlaufbahn befinden.Für Lithium, das eine Ordnungszahl von drei hat, sind die beiden Elektronen im 1s-Orbital gepaart und das Elektron im 2s-Orbital ist ungepaart. Konventionell, ungepaarte Elektronen werden als Spin-up dargestellt.

das pauli verbot

Die Anordnung der Elektronen in den Orbitalen eines Atoms wird als Elektronenkonfiguration bezeichnet. Wir beschreiben eine Elektronenkonfiguration mit einer Zeichenfolge, die drei Informationen enthält: <ol> <li>Die Nummer der Hauptquantenschale, n,</li> <li>Der Buchstabe, der den Orbitaltyp (die Unterschale, l) bezeichnet, und</li> <li>Eine hochgestellte Zahl, die die Anzahl der Elektronen in dieser bestimmten Unterschale angibt.</li> </ol> Beispielsweise gibt die Notation 2p4 vier Elektronen in einer p-Unterschale (l = 1) mit einer Hauptquantenzahl (n) von 2 an. Die Notation 3d 8 gibt acht Elektronen in der d-Unterschale (l = 2) der Hauptquantenzahl an n = 3. Während sich die drei Quantenzahlen gut zur Beschreibung von Elektronenorbitalen eignen, zeigten einige Experimente, dass sie nicht ausreichten, um alle beobachteten Ergebnisse zu erklären. In den 1920er Jahren wurde gezeigt, dass es sich bei der Untersuchung von Wasserstofflinienspektren mit extrem hoher Auflösung bei einigen Linien tatsächlich nicht um einzelne Peaks, sondern um Paare eng beieinander liegender Linien handelt. Dies ist die sogenannte Feinstruktur des Spektrums und impliziert, dass es zusätzlich kleine Unterschiede in der Energie der Elektronen gibt, selbst wenn sie sich im selben Orbital befinden. Diese Beobachtungen veranlassten Samuel Goudsmit und George Uhlenbeck zu der Annahme, dass Elektronen eine vierte Quantenzahl haben. Sie nannten dies die Spinquantenzahl oder ms. In einem angelegten Magnetfeld kann ein Elektron zwei mögliche Orientierungen mit unterschiedlichen Energien einnehmen: eine mit Spin nach oben, ausgerichtet auf das Magnetfeld, und eine mit Spin nach unten gegen dieses ausgerichtet. Die vierte Quantenzahl, die Spinquantenzahl (ms), beschreibt diese beiden unterschiedlichen Spinzustände eines Elektrons. Eine Spinquantenzahl hat zwei mögliche Werte: −1/2 (Spin-Down) und +1/2 (Spin-Up). Der Elektronenspin beschreibt eine intrinsische „Rotation“ oder „Spin“ eines Elektrons. Jedes Elektron wirkt wie ein winziger Magnet oder ein winziges rotierendes Objekt mit einem Drehimpuls oder wie eine Spule durch die elektrischer Strom fließt, auch wenn diese Rotation oder dieser Strom nicht in räumlichen Koordinaten beobachtet werden können. Die Größe des Gesamtelektronenspins kann nur einen Wert haben und ein Elektron kann sich nur in einem von zwei quantisierten Zuständen „drehen“. Einer wird als α-Zustand bezeichnet, wobei die z-Komponente des Spins in der positiven Richtung der z-Achse liegt. Dies entspricht der Spinquantenzahl ms = +1/2. Der andere wird β-Zustand genannt, wobei die z-Komponente des Spins negativ ist und ms = −1/2. Jedes Elektron, unabhängig davon, in welchem Atomorbital es sich befindet, kann nur einen dieser beiden Werte der Spinquantenzahl haben. Die Energien von Elektronen mit unterschiedlichen Spins sind unterschiedlich, wenn ein äußeres Magnetfeld angelegt wird. Ein Elektron in einem Atom wird vollständig durch vier Quantenzahlen beschrieben: n, l, ml und ms. Die ersten drei Quantenzahlen definieren das Orbital und sind voneinander abhängig, während die vierte Quantenzahl unabhängig von anderen Quantenzahlen ist, da sie eine intrinsische Elektroneneigenschaft nämlich den Spin beschreibt. Der österreichische Physiker Wolfgang Pauli (Nobelpreis für Physik: 1945) formulierte ein allgemeines Prinzip, das uns die letzten Informationen liefert, die wir zum Verständnis des allgemeinen Verhaltens von Elektronen in Atomen benötigen. Das Pauli-Verbot oder Pauli-Ausschließungsprinzip lässt sich wie folgt formulieren: Keine zwei Elektronen im selben Atom können genau die gleichen vier Quantenzahlen haben. Dies bedeutet, dass zwei Elektronen nur dann dasselbe Orbital (denselben Satz der Quantenzahlen n, l und ml) teilen können, wenn ihre Spinquantenzahlen unterschiedliche Werte haben. Da die Spinquantenzahl (ms) nur zwei Werte +1/2 und -1/2 annehmen kann, können nicht mehr als zwei Elektronen dasselbe Orbital besetzen (und wenn sich zwei Elektronen im selben Orbital befinden, müssen sie entgegengesetzte Spins haben). Daher kann jedes Atomorbital nur mit null, einem oder zwei Elektronen besetzt sein. Im Orbitaldiagramm der Elektronenkonfiguration wird jedes Orbital innerhalb einer besetzten Unterschale als Kästchen oder Linie und jedes Elektron als Pfeil dargestellt. Das Orbitaldiagramm von Wasserstoff, welcher eine Elektronenkonfiguration von 1s1 hat, ist: <img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;"> Ein Aufwärtspfeil zeigt einen +1/2 Spin oder Spin-Up und ein Abwärtspfeil einen -1/2 Spin oder Spin-Down an. Das Orbitaldiagramm von Wasserstoff hat daher einen Aufwärtspfeil. Die Elektronenkonfiguration von Helium ist 1s2. Die beiden Elektronen haben drei identische Quantenzahlen, da sie zur gleichen Schale und Unterschale gehören. Ihre Spinquantenzahlen sind entsprechend dem Pauli-Ausschlussprinzip unterschiedlich. Elektronen mit entgegengesetztem Spin werden als gepaart bezeichnet, wenn sie dasselbe Orbital besetzen. <img alt="Figure2" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;"> Dieser Text ist übernommen aus Openstax, Chemistry 2e, Abschnitt 6.3: Entwicklung der Quantentheorie.

Das Pauli Verbot

Die Anordnung der Elektronen in den Orbitalen eines Atoms wird als Elektronenkonfiguration bezeichnet. Wir beschreiben eine Elektronenkonfiguration mit einem Symbol, das ...

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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.

Electron Spin and Orbital Pairing

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Electron Spin and Orbital Pairing

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