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

K12 Standards

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Chemistry and Physics

IPC.7

IPC.7.E

The Pauli Exclusion Principle

Los orbitales atómicos son las regiones donde es más probable que se encuentren los electrones de un átomo. Pero, cuántos electrones puede contener cada orbital? El principio de exclusión de Pauli responde a esta pregunta, ya que significa que no hay dos electrones en un átomo que puedan tener el mismo conjunto de cuatro números cuánticos.Cada orbital corresponde a un principal fijo;momento angular o azimutal;y a valores de un número cuántico magnético. Por ejemplo, un electrón en el orbital 1s siempre tiene un número cuántico principal de uno y números cuánticos azimutales y magnéticos de cero. En consecuencia, los electrones deben tener valores cuánticos de espín diferentes, o espines, para residir en el mismo orbital atómico.Recuerde que el número cuántico de espín tiene solo dos valores posibles:1/2 y 1/2. Por tanto, solo dos electrones pueden ocupar el mismo orbital. Por lo tanto, cada subcapa s, que tiene un orbital, puede acomodar solo dos electrones, y cada subcapa p, que tiene tres orbitales, puede contener seis electrones.Cada una de las subcapas d y f tiene una capacidad máxima de diez y catorce electrones, respectivamente. La distribución de los electrones entre los orbitales atómicos de un átomo está representada por su configuración de electrones en forma de texto o diagrama. Considere un átomo de hidrógeno en estado base, donde un electrón ocupa el orbital de menor energía:1s.La configuración de electrones escrita denota cada subcapa ocupada con el número de la capa correspondiente, la letra de la subcapa, y un número en superíndice que especifica el número de electrones en la subcapa. El estilo de diagrama orbital de la configuración de los electrones denota cada orbital dentro de una subcapa ocupada como una caja o línea y cada electrón como una flecha. Una flecha hacia arriba indica 1/2 giro, o giro hacia arriba, y una flecha hacia abajo significa un giro de 1/2 o un giro hacia abajo.El diagrama orbital del hidrógeno, por lo tanto, tiene una flecha hacia arriba. La configuración de los electrones del helio es 1s 2. Los dos electrones tienen tres números cuánticos idénticos, ya que pertenecen a la misma capa y subcapa.Sus números cuánticos de espín son diferentes, de acuerdo con el principio de exclusión de Pauli. Los electrones con espines opuestos se denominan emparejados"si ocupan el mismo orbital. Para el litio, que tiene un número atómico de tres, los dos electrones en el orbital 1s están emparejados y el electrón en el orbital 2s no está apareado.Convencionalmente, los electrones no apareados se representan como espines hacia arriba.

el principio de exclusión de pauli

La disposición de los electrones en los orbitales de un átomo se denomina configuración de los electrones de ese átomo. Describimos una configuración de electrones con un símbolo que contiene tres piezas de información:
 
 <ol>
 <li>El número de la capa cuántica principal, n,</li>
 <li>La letra que designa el tipo de orbital (la subcapa, l), y</li>
 <li>Número de superíndice que designa el número de electrones en esa subcapa en particular.</li>
 </ol>
 
 Por ejemplo, la notación 2p4 indica cuatro electrones en una subcapa p (l = 1) con un número cuántico principal (n) de 2. La notación 3d 8 indica ocho electrones en la subcapa d (l = 2) de la capa principal para la cual n = 3.
 
 Mientras que los tres números cuánticos funcionan bien para describir los orbitales de electrones, algunos experimentos demostraron que no eran suficientes para explicar todos los resultados observados. En la década de 1920 se demostró que cuando los espectros de líneas de hidrógeno se examinan a una resolución extremadamente alta, algunas líneas no son picos únicos, sino pares de líneas poco espaciadas. Esta es la llamada estructura fina del espectro, e implica que hay pequeñas diferencias adicionales en las energías de los electrones incluso cuando están ubicados en el mismo orbital. Estas observaciones llevaron a Samuel Goudsmith y George Uhlenbeck a proponer que los electrones tienen un cuarto número cuántico. Ellos lo llamaron el número cuántico de espín o de giro ms.
 
 En un campo magnético aplicado, un electrón tiene dos orientaciones posibles con diferentes energías, una con giro hacia arriba, alineada con el campo magnético, y otra con giro hacia abajo, alineada en contra de él.
 
 El cuarto número cuántico, el número cuántico de espín (ms) describe estos dos estados de espín diferentes de un electrón. Un número cuántico de espín tiene dos valores posibles, −1/2 (giro hacia abajo) y +50 (giro hacia arriba).
 
 El espín de los electrones describe una “rotación” o “giro” intrínseca de los electrones. Cada electrón actúa como un imán diminuto o un objeto giratorio diminuto con impulso angular, o como un bucle con una corriente eléctrica, aunque esta rotación o corriente no se puede observar en términos de coordenadas espaciales.
 
 La magnitud del giro total de un electrón sólo puede tener un valor, y un electrón sólo puede “girar” en uno de los dos estados cuantizados. Uno se llama el estado α, con el componente z del giro en la dirección positiva del eje z. Esto corresponde al número cuántico de espín ms = +1/2. El otro se llama el estado β, siendo el componente z del espín negativo y ms = −1/2.
 
 Cualquier electrón, independientemente del orbital atómico en el que se encuentre, puede tener sólo uno de esos dos valores del número cuántico de espín. Si se aplica un campo magnético externo las energías de los electrones que tienen diferentes espines son diferentes.
 
 Un electrón en un átomo es completamente descrito por cuatro números cuánticos: n, l, ml y ms. Los primeros tres números cuánticos definen el orbital, y son interdependientes, mientras que el cuarto número cuántico es independiente de los otros números cuánticos ya que describe una propiedad intrínseca de los electrones llamada giro o espín. Un físico austriaco Wolfgang Pauli (Premio Nobel de Física: 1945) formuló un principio general que aporta la última pieza de información que necesitamos para entender el comportamiento general de los electrones en los átomos. El principio de exclusión de Pauli puede formularse de la siguiente manera: No hay dos electrones en el mismo átomo que puedan tener exactamente el mismo conjunto de los cuatro números cuánticos. Lo que esto significa es que dos electrones pueden compartir el mismo orbital (el mismo conjunto de los números cuánticos n, l y ml) sólo si sus números cuánticos de espín tienen valores diferentes. Dado que el número cuántico de espín (ms) sólo puede tener dos valores +50 y −1/2, un mismo orbital no puede ser ocupado por más de dos electrones (y si dos electrones están ubicados en el mismo orbital, deben tener espines opuestos). Por lo tanto, cualquier orbital atómico puede estar poblado únicamente por cero, uno o dos electrones.
 
 El estilo del diagrama de orbitales de la configuración de los electrones representa cada orbital dentro de una subcapa ocupada como una caja o línea y cada electrón como una flecha. El diagrama de orbitales del hidrógeno, con una configuración de electrones de 1s1, es:
 
 <img alt="Figure1" src="https://www.jovecore.com/CDNSource/lessons/984/984Image_1.png" style="height: 40px;" />
 
 Una flecha hacia arriba indica medio giro más, o un giro hacia arriba, y una flecha hacia abajo significa medio giro menos, o un giro hacia abajo. El diagrama de orbitales del hidrógeno, por lo tanto, tiene una flecha hacia arriba.
 
 La configuración de los electrones del helio es 1s2. Los dos electrones tienen tres números cuánticos idénticos, ya que pertenecen a la misma capa y subcapa. Sus números cuánticos de espín son diferentes, de acuerdo con el principio de exclusión de Pauli. A los electrones con espines opuestos se les llama emparejados si los mismos ocupan el mismo orbital.
 
 <img alt="Figure2" src="https://www.jovecore.com/CDNSource/lessons/984/984Image_2.png" style="height: 40px;" />
 
 Este texto ha sido adaptado de <a 6-3-development-of-quantum-theory=" books=" chemistry-2e=" href=" https:=" openstax.org=" pages=">Openstax, Química 2e, Sección 6.3: Desarrollo de la Teoría Cuántica.  </a>

El Principio de Exclusión de Pauli

La disposición de los electrones en los orbitales de un átomo se denomina configuración electrónica. Describimos una configuración electrónica con un 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.

Electron Spin and Orbital Pairing

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Electron Spin and Orbital Pairing

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