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

Os orbitais atômicos são as regiões onde os elétrons de um átomo são mais prováveis de serem encontrados. Mas quantos elétrons pode cada orbital aguentar, o princípio da exclusão Pauli responde a esta pergunta, pois significa que não existem dois elétrons num átomo que possam ter o mesmo conjunto de quatro números quânticos. Cada orbital corresponde a um princípio fixo;momento angular, ou azimutal;e valores do número quântico magnético.Por exemplo, um elétron no orbital 1s tem sempre um número quântico principal de um e números quânticos azimutais e magnéticos de zero. Consequentemente, os elétrons devem ter valores do número quântico de centrifugação diferentes, ou centrifugações, para residirem no mesmo orbital atômico. Recorde-se que o número quântico da centrifugação tem apenas dois valores possíveis:1/2 e 1/2.Portanto, apenas dois elétrons podem ocupar a mesma orbital. Assim, cada subcamada, que tem um orbital, pode acomodar apenas dois elétrons, e cada subcamada p, que tem três orbitais, pode conter seis elétrons. Cada uma das subcasas d e f tem uma capacidade máxima de dez e catorze elétrons, respetivamente.A distribuição de elétrons entre os orbitais atômicos de um átomo é representada pela sua configuração de elétrons em forma de texto ou diagrama. Consideremos um átomo de hidrogênio em estado de solo, onde um elétron ocupa o orbital de energia mais baixa:1s. A configuração de elétrons escrita denota cada subcamada ocupada com o número da camada correspondente, a letra da subcapa, e um número sobrescrito especificando o número de elétrons na subcapa.O estilo do diagrama orbital da configuração dos elétrons denota cada orbital dentro de uma subcapacidade ocupada como uma caixa ou linha e cada elétron como uma seta. Uma seta para cima indica uma rotação de 1/2, ou rotação para cima, e uma seta para baixo significa uma rotação 1/2, ou rotação para baixo. O diagrama orbital do hidrogênio, portanto, tem uma seta para cima.A configuração de elétrons do hélio é de 1s^2. Os dois elétrons têm três números quânticos idênticos, uma vez que pertencem à mesma camada e subcamada. Os seus números quânticos de centrifugação são diferentes, de acordo com o princípio de exclusão Pauli.Os elétrons com centrifugações opostas são chamados de emparelhados"se ocuparem a mesma órbita. Para o lítio, que tem um número atômico de três, os dois elétrons no orbital 1s estão emparelhados e o elétron na órbita dos 2s não está emparelhado. Convencionalmente, os elétrons não emparelhados são representados como centrifugação para cima.

o princípio da exclusão de pauli

A disposição dos eletrões nas orbitais de um átomo é denominada a sua configuração eletrónica. Descrevemos uma configuração eletrónica com um símbolo que contém três partes de informação:

<ol>
<li>O número da camada quântica principal, n,</li>
<li>A letra que designa o tipo de orbital, l), e</li>
<li>Um número sobrescrito que designa o número de eletrões nessa subcamada em particular.</li>
</ol>

Por exemplo, a notação 2p4 indica quatro eletrões em uma subcamada p (l = 1) com um número quântico principal (n) de 2. A notação 3d 8 indica oito eletrões na subcamada d (l = 2) da estrutura principal para a qual n = 3.

Embora os três números quânticos funcionem bem para descrever orbitais de eletrões, algumas experiências mostraram que não eram suficientes para explicar todos os resultados observados. Foi demonstrado na década de 1920 que quando os espectros de linha do hidrogénio são examinados em resolução extremamente alta, algumas linhas não são realmente picos únicos mas, em vez disso, pares de linhas com espaçamento próximo. Esta é a chamada estrutura fina do espectro, e implica que há pequenas diferenças adicionais nas energias dos eletrões mesmo quando estão localizadas na mesma orbital. Estas observações levaram Samuel Goudsmit e George Uhlenbeck a propor que os eletrões têm um quarto número quântico. Eles chamaram a isto o número quântico de spin ou ms.

Em um campo magnético aplicado, um eletrão tem duas orientações possíveis com energias diferentes, uma com rotação para cima, alinhada com o campo magnético e outra com rotação para baixo, alinhada contra ele.

O quarto número quântico, o número quântico de spin (ms) descreve estes dois estados de rotação diferentes de um eletrão. Um número quântico de spin tem dois valores possíveis, −1/2 (rotação para baixo) e +1/2 (rotação para cima).

O spin de um eletrão descreve uma "rotação" intrínseca do eletrão ou "spinning". Cada eletrão atua como um pequeno íman ou um pequeno objeto rotativo com um momentum angular, ou como um laço com uma corrente elétrica, mesmo que essa rotação ou corrente não possa ser observada em termos de coordenadas espaciais.

A magnitude do spin total de um eletrão só pode ter um valor, e um eletrão só pode “rodar” em um dos dois estados quantizados. Um é chamado de estado α, com o componente z do spin estando na direção positiva do eixo z. Isto corresponde ao número quântico de spin ms = +1/2. O outro é chamado de estado β, com o componente z do spin sendo negativo e ms = −1/2.

Qualquer eletrão, independentemente da orbital atómica em que está localizado, só pode ter um desses dois valores de número quântico de spin. As energias de eletrões com diferentes spins são diferentes se for aplicado um campo magnético externo.

Um eletrão em um átomo é completamente descrito por quatro números quânticos: n, l, ml, e ms. Os três primeiros números quânticos definem a orbital, e são interdependentes, enquanto que o quarto número quântico é independente de outros números quânticos, pois descreve uma propriedade intrínseca de eletrões chamada spin. Um físico Austríaco Wolfgang Pauli (Prémio Nobel de Física: 1945) formulou um princípio geral que dá a última informação de que precisamos para entender o comportamento geral de eletrões em átomos. O princípio da exclusão de Pauli pode ser formulado da seguinte forma: Nenhuns dois eletrões no mesmo átomo podem ter exatamente o mesmo conjunto de todos os quatro números quânticos. O que isto significa é que dois eletrões podem partilhar a mesma orbital (o mesmo conjunto dos números quânticos n, l, e ml) apenas se os seus números quânticos de spin tiverem valores diferentes. Como o número quântico de spin (ms) pode ter apenas dois valores de +1/2 e -1/2, não mais de dois eletrões podem ocupar a mesma orbital (e se dois eletrões estiverem localizados na mesma orbital, devem ter spins opostos). Portanto, qualquer orbital atómica pode ser preenchida apenas por zero, um, ou dois eletrões.

O estilo do diagrama orbital da configuração eletrónica representa cada orbital dentro de uma subcamada ocupada como uma caixa ou linha e cada eletrão como uma seta. O diagrama orbital do hidrogénio, com uma configuração eletrónica de 1s1, é:

<img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;" />

Uma seta para cima indica um meio spin positivo, ou spin para cima, e uma seta para baixo significa um meio spin negativo, ou spin para baixo. O diagrama orbital do hidrogénio, tem portanto, uma seta para cima.

A configuração eletrónica do hélio é 1s2. Os dois eletrões têm três números quânticos idênticos, uma vez que pertencem à mesma camada e subcamada. Os seus números quânticos de spin são diferentes, de acordo com o princípio de exclusão de Pauli. Os eletrões com spins opostos são chamados emparelhados se ocuparem a mesma orbital.

<img alt="Figure2" src="https://www.jove.com/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;" />

Este texto é adaptado de <a 6-3-development-of-quantum-theory="" books="" chemistry-2e="" href="" https:="" openstax.org="" pages="">Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory. </a>

O Princípio da Exclusão de Pauli

O arranjo dos elétrons nos orbitais de um átomo é chamado de configuração eletrônica. Descrevemos uma configuração eletrônica com um símbolo que ...

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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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