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

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IPC.7

IPC.7.E

The Pauli Exclusion Principle

Gli orbitali atomici sono le regioni in cui è più probabile che si trovino gli elettroni di un atomo. Ma quanti elettroni può contenere ogni orbitale? Il principio di esclusione di Pauli risponde a questa domanda, poichè iindica che non esistono due elettroni in un atomo aventi lo stesso insieme di quattro numeri quantici.

Ogni orbitale corrisponde ad un principale fisso momento angolare, o azimutale, ed a valori numerici quantistici magnetici. Per esempio, un elettrone nell'orbitale 1s ha sempre un numero quantico principale di uno e numeri quantici azimutali e magnetici pari a zero. Di conseguenza, gli elettroni devono avere diversi valori del numero quantico di spin, o spin, per risiedere nello stesso orbitale atomico.

Ricordate che il numero quantico di spin ha solo due possibili valori:1/2 e 1/2. Pertanto, solo due elettroni possono occupare lo stesso orbitale. Dunque, ogni subshell s, che ha un orbitale, può ospitare solo due elettroni, e ogni subshell p, che ha tre orbitali, può contenere sei elettroni.

Ciascuno dei subshell d ed f ha una capacità massima di dieci e quattordici elettroni, rispettivamente. La distribuzione degli elettroni tra gli orbitali atomici di un atomo è rappresentata dalla sua configurazione di elettroni, in forma di testo o diagramma. Considerate un atomo di idrogeno allo stato fondamentale, in cui un elettrone occupa l'orbitale a più bassa energia:1 s.

La configurazione elettronica scritta indica ciascun subshell occupato con il numero del guscio/shelle corrispondente, la lettera del subshell e un numero in apice, che specifica il numero di elettroni nel subshell. Lo stile del diagramma orbitale della configurazione degli elettroni indica ogni orbitale all'interno di un subshell occupato come una scatola o una linea, e ogni elettrone come una freccia. Una freccia verso l'alto indica un 1/2 giro, o spin-up, e una freccia verso il basso indica un 1/2 spin, o spin-down.

Il diagramma orbitale dell'idrogeno, quindi, ha una freccia verso l'alto. La configurazione elettronica dell'elio è 1s 2. I due elettroni hanno tre numeri quantici identici, poiché appartengono allo stesso shell e subshell.

I loro numeri quantici di spin sono diversi, in accordo con il principio di esclusione di Pauli. Gli elettroni con spin opposti sono definiti accoppiati"se occupano lo stesso orbitale. Per il litio, che ha un numero atomico di tre, i due elettroni nell'orbitale 1s sono accoppiati e l'elettrone nell'orbitale 2s è spaiato.

Convenzionalmente, gli elettroni spaiati sono rappresentati come spin-up.

il principio di esclusione di pauli

La disposizione degli elettroni negli orbitali di un atomo chiamata configurazione elettronica. Descriviamo una configurazione elettronica con un simbolo che contiene tre informazioni:

<ol>
	<li>Il numero del guscio quantistico principale, n,</li>
	<li>La lettera che designa il tipo orbitale (il sottoguscio, l), e</li>
	<li>Un numero in apice che indica il numero di elettroni in quel particolare sottoguscio.</li>
</ol>

Ad esempio, la notazione 2p4 indica quattro elettroni in un sottolivello p (l = 1) con un numero quantico principale (n) pari a 2. La notazione 3d 8 indica otto elettroni nel sottolivello d (l = 2) del livello principale per il quale n = 3.

Anche se i tre numeri quantici funzionano bene per descrivere gli orbitali elettronici, alcuni esperimenti hanno dimostrato che non erano sufficienti a spiegare tutti i risultati osservati. stato dimostrato negli anni '20 che quando gli spettri delle linee dell'idrogeno vengono esaminati ad altissima risoluzione, alcune linee non sono in realt picchi singoli ma, piuttosto, coppie di linee ravvicinate. Questa la cosiddetta struttura fine dello spettro e implica che vi siano ulteriori piccole differenze nelle energie degli elettroni anche quando si trovano nello stesso orbitale. Queste osservazioni portarono Samuel Goudsmit e George Uhlenbeck a proporre che gli elettroni abbiano un quarto numero quantico. Lo chiamavano numero quantico di spin o ms.

In un campo magnetico applicato, un elettrone ha due possibili orientamenti con energie diverse, uno con spin verso l'alto, allineato con il campo magnetico, e uno con spin verso il basso, allineato contro di esso.

Il quarto numero quantico, il numero quantico di spin (ms) descrive questi due diversi stati di spin di un elettrone. Un numero quantico di spin ha due valori possibili, −1/2 (spin verso il basso) e +1/2 (spin verso l'alto).

Lo spin dell'elettrone descrive una "rotazione" o "filatura" intrinseca dell'elettrone. Ogni elettrone agisce come un minuscolo magnete o un minuscolo oggetto rotante dotato di momento angolare, o come un anello percorso da una corrente elettrica, anche se questa rotazione o corrente non pu essere osservata in termini di coordinate spaziali.

L'entit dello spin complessivo dell’elettrone pu avere solo un valore e un elettrone pu “ruotare? solo in uno dei due stati quantizzati. Uno chiamato stato “spin” dove la componente z dello spin nella direzione positiva dell'asse z. Ci corrisponde al numero quantico di spin ms = +1/2. L'altro chiamato stato β, con la componente z dello spin negativa e ms = −1/2.

Qualsiasi elettrone, indipendentemente dall'orbitale atomico in cui si trova, pu avere solo uno di questi due valori del numero quantico di spin. Le energie degli elettroni con spin diversi sono diverse se viene applicato un campo magnetico esterno.

Un elettrone in un atomo completamente descritto da quattro numeri quantici: n, l, ml e ms. I primi tre numeri quantici definiscono l'orbitale e sono interdipendenti, mentre il quarto numero quantico indipendente da altri numeri quantici poich descrive una propriet intrinseca dell'elettrone chiamata spin. Il fisico austriaco Wolfgang Pauli (Premio Nobel per la fisica: 1945) ha formulato un principio generale che fornisce l'ultima informazione di cui abbiamo bisogno per comprendere il comportamento generale degli elettroni negli atomi. Il principio di esclusione di Pauli pu essere formulato come segue: due elettroni nello stesso atomo non possono avere esattamente lo stesso insieme di tutti e quattro i numeri quantici. Ci significa che due elettroni possono condividere lo stesso orbitale (lo stesso insieme di numeri quantici n, l e ml) solo se i loro numeri quantici di spin hanno valori diversi. Poich il numero quantico di spin (ms) pu avere solo due valori +1/2 e -1/2, non pi di due elettroni possono occupare lo stesso orbitale (e se due elettroni si trovano nello stesso orbitale, devono avere spin opposti ). Pertanto, qualsiasi orbitale atomico pu essere popolato solo da zero, uno o due elettroni.

Lo stile del diagramma orbitale della configurazione elettronica rappresenta ciascun orbitale all'interno di un sottoguscio occupato come una scatola o linea e ciascun elettrone come una freccia. Il diagramma orbitale dell'idrogeno, che ha una configurazione elettronica di 1s1, :

<img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;" />

Una freccia rivolta verso l'alto indica pi di met rotazione, o rotazione verso l'alto, mentre una freccia verso il basso indica meno di met rotazione, o rotazione verso il basso. Il diagramma orbitale dell'idrogeno, quindi, ha una freccia rivolta verso l'alto.

La configurazione elettronica dell'elio 1s2. I due elettroni hanno tre numeri quantici identici, poich appartengono allo stesso livello e sottolivello. I loro numeri quantici di spin sono diversi, in accordo con il principio di esclusione di Pauli. Gli elettroni con spin opposti si dicono accoppiati se occupano lo stesso orbitale.

<img alt="Figure2" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;" />

Questo testo adattato da Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory.

Il principio di esclusione di Pauli

La disposizione degli elettroni negli orbitali di un atomo è chiamata configurazione elettronica. Descriviamo una configurazione elettronica con un simbolo che ...

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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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