Name: electron regions in atomic orbitals
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 44 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

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Chemistry and Physics

IPC.7

IPC.7.E

Atomic Orbitals

Der dichteste Bereich der Elektronenwolke wo ein Elektron am wahrscheinlichsten zu finden ist wird in Form von Atomorbitalen beschrieben. Die Form eines Atomorbitales ist bestimmt durch die Drehimpulsquantenzahl l. Erinnern Sie sich, dass die Werte von l auf der Hauptquantenzahl n basieren-mit möglichen Werte für l die von 0 bis n 1 reichen.Wenn n größer als eins ist, existieren mehrere Unterebenen. Jeder Wert von l entspricht entweder einem s-p-d-oder f-Orbital. Das Orbital mit der niedrigsten Energie ist das 1s-Orbital.Dies ist ein kugelsymmetrisches Orbital. Die Wahrscheinlichkeitsdichte eines 1s-Orbitals zeigt, dass das Elektron am wahrscheinlichsten beim Atomkern zu finden ist. Angesichts der elektrostatischen Kräfte zwischen den Protonen und Elektronen, ist das jedoch unwahrscheinlich.Multiplikation der Wahrscheinlichkeitsdichte durch das Volumen von dünnen Kugelhüllen mit den Radien r ist jedoch repräsentativer. Die Gesamtwahrscheinlichkeit, dass ein Elektron innerhalb der dünnen Hülle mit einem Abstand r vom Kern zu finden, nennt sich radiale Verteilungsfunktion. Beim Wasserstoff, ist die größte Wahrscheinlichkeit bei 52, 9 Picometern, für die Entfernung des Elektrons vom dem Kern.So ist die Form des 1s-Atomorbitals für Wasserstoff kugelförmig, mit einem Radius von 52, 9 Picometern. Die zwei-und dreiseitigen Orbitale sind ebenfalls kugelförmig. Sie sind größer und haben Knotenpunkte.An einem Knoten ist die Wahrscheinlichkeit, ein Elektron zu finden, gleich Null. Hauptebenen mit n gleich zwei oder mehr enthalten auch drei p-Orbitale. Diese sind hantelförmig mit einem Knoten am Kern.Ihre Orientierung wird durch den Wert von m-l beschrieben. Die drei p-Orbitale sind orthogonal zueinander angeordnet. Hauptzustände von n gleich drei oder mehr haben ebenfalls fünf d-Orbitale.Die d-Orbitale haben die Form einer gekreuzten Doppelhantel, die aus vier elektronendichten Hanteln und zwei senkrechte Knotenebenen bestehen. Eines der d-Orbitale ist ein wenig anders. Die f-Orbitale haben mehr Hanteln und Knoten.Diese Orbitale existieren für die Hauptebenen n gleich vier oder mehr. Wenn die Orbitale übereinander liegen, entsteht eine grob kugelförmige Form. Aus diesem Grund werden Atome im Allgemeinen als Kugeln dargestellt.

atomorbitale

Ein Atomorbital stellt die dreidimensionalen Bereiche in einem Atom dar, in denen sich ein Elektron mit der höchsten Wahrscheinlichkeit aufhält. Die radiale Verteilungsfunktion gibt die Gesamtwahrscheinlichkeit an, ein Elektron innerhalb der dünnen Hülle im Abstand r vom Kern zu finden. Die Atomorbitale haben unterschiedliche Formen, die durch l, die Drehimpulsquantenzahl, bestimmt wird. Die Orbitale werden oft mit einer Grenzfläche gezeichnet, welche die dichtesten Regionen der Wolke umschließt.

 Die Drehimpulsquantenzahl ist eine ganze Zahl, die die Werte l = 0, 1, 2, …, n – 1 annehmen kann. Ein Orbital mit der Hauptquantenzahl 1 (n = 1) kann nur einen Wert von l haben ( l = 0), wohingegen eine Hauptquantenzahl von 2 (n = 2) l = 0 und l = 1 zulässt. Orbitale mit dem gleichen Wert von l bezeichnen eine Unterschale.

 Orbitale mit l = 0 heißen s-Orbitale und bilden die s-Unterschalen. Der Wert l = 1 entspricht den p-Orbitalen. Für ein gegebenes n bilden p-Orbitale eine p-Unterschale (d. h. 3p, wenn n = 3). Die Orbitale mit l = 2 heißen d-Orbitale. Die Orbitale mit l = 3, 4 und 5 sind die f-, g- und h-Orbitale.

 Das Orbital mit der niedrigsten Energie ist das 1s-Orbital. Dies ist ein kugelsymmetrisches Orbital. Die Wahrscheinlichkeitsdichte (ψ2) eines 1s-Orbitals zeigt, dass sich das Elektron am wahrscheinlichsten in direkter Nähe des Kerns befindet. Angesichts der elektrostatischen Kräfte zwischen Protonen und Elektronen gibt dies den realen Zustand jedoch nicht treffend wieder. Stattdessen wird die Radialverteilungsfunktion verwendet, welche eine Darstellung der Gesamtwahrscheinlichkeit ist, ein Elektron in einem Orbital entlang eines gegebenen Radius r zu finden. Die radiale Verteilungsfunktion wird durch Multiplikation der Wahrscheinlichkeitsdichte mit dem Volumen dünner Kugelschalenabschnitte der Radien r ermittelt. Für das 1s-Orbital von Wasserstoff hat die radiale Verteilungsfunktion am Kern einen Wert von Null, der auf ein Maximum bei 52,9 Pikometern ansteigt, bevor er mit zunehmendem r abnimmt.

 Es gibt bestimmte Entfernungen vom Kern, bei denen die Wahrscheinlichkeitsdichte, ein Elektron in einem bestimmten Orbital zu finden, Null ist. Mit anderen Worten, der Wert der Wellenfunktion ψ ist in dieser Entfernung für dieses Orbital Null. Ein solcher Wert von r wird als Radialknoten bezeichnet. Die Anzahl der Radialknoten in einem Orbital beträgt n – l – 1. Für 2s-Orbitale mit n = 1 gibt es einen Radialknoten, während 3s-Orbitale zwei Radialknoten haben.

 Jedes Hauptniveau mit n = 2 oder mehr enthält drei p-Orbitale. Die drei p-Orbitale bestehen jeweils aus zwei gegenüber liegenden Keulen und einem Knotenpunkt im Kern. Die Orientierung von p-Orbitalen im Raum wird durch den Wert ml beschrieben. Die drei p-Orbitale stehen zueinander senkrecht (orthogonal). Die höheren p-Orbitale (3p, 4p, 5p und höher) haben ähnliche Formen, sind jedoch größer und verfügen über zusätzliche radiale Knotenpunkte.

 Hauptniveaus mit n = 3 oder mehr enthalten fünf d-Orbitale. Vier dieser Orbitale haben die Form eines Kleeblatts mit vier elektronendichten Keulen. Es gibt zwei senkrechte Knotenebenen, die sich im Kern schneiden. An diesen Knotenebenen ist die Elektronendichte Null. Eines der d-Orbitale hat eine etwas andere Form und weist zwei in der z-Achse ausgerichtete Keulen mit einem ringförmigen Ring in der xy-Ebene auf. Hauptniveaus mit n = 4 und größer enthalten sieben f-Orbitale welche komplexere Formen aufweisen. Diese Orbitale haben mehr Knoten und Keulen als d-Orbitale.

 <img alt="Figure1" src="https://www.jove.com/files/core/CDNSource/lessons/983/983Image 1.png" style="width: 700px;">

 Abbildung 1: Beispiele für s-, p-, d- und f-Orbitale.

 Diese unterschiedlichen Formen der Atomorbitale stellen die dreidimensionalen Bereiche dar, in denen sich das Elektron mit einer hohen Wahrscheinlichkeit befindet. Alle Orbitale zusammen bilden eine annähernd kugelartige Form, weshalb Atome im Allgemeinen auch als Kugeln dargestellt werden.

 Dieser Text wurde adaptiert von <a href="https://openstax.org/books/chemistry-2e/pages/6-3-development-of-quantum-theory">Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory.</a>

Atomorbitale

Ein Atomorbital stellt die dreidimensionalen Bereiche in einem Atom dar, in denen sich ein Elektron mit der höchsten Wahrscheinlichkeit befindet. Die radiale Verteilung ...

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electron regions in atomic orbitals

Electron regions in atomic orbitals show where an electron is most likely to be found in an atom. These three-dimensional regions are often drawn as boundary surfaces around the densest part of the cloud.

The shape of an orbital depends on the angular momentum quantum number, l. This value can range from 0 to n - 1, where n is the principal quantum number. For n = 1, only l = 0 is allowed. For n = 2, both l = 0 and l = 1 are allowed.

Orbitals with the same value of l form a subshell. The l = 0 orbitals are s orbitals, and they make up s subshells. The l = 1 orbitals are p orbitals, which form a p subshell such as 3p when n = 3. The l = 2 orbitals are d orbitals. The l = 3, 4, and 5 orbitals are called f, g, and h orbitals.

The lowest-energy orbital is the 1s orbital. It is spherically symmetric. The probability density, ψ², suggests that an electron is most likely found at the nucleus. But this does not fully match electron behavior. The radial distribution function gives the total probability of finding an electron at a distance r from the nucleus. It is found by multiplying the probability density by the volume of thin spherical shells.

For the 1s orbital of hydrogen, the radial distribution function is zero at the nucleus. It rises to a maximum at 52.9 picometers and then decreases as r increases. Some distances from the nucleus have zero probability density for a given orbital. These points are called radial nodes. The number of radial nodes is n - l - 1. A 2s orbital has one radial node, and a 3s orbital has two.

Each principal level with n = 2 or more contains three p orbitals. Each p orbital has two lobes and a node at the nucleus. Their orientation in space is described by m_l. The three p orbitals are mutually perpendicular. Higher p orbitals, such as 3p, 4p, and 5p, have the same general shape but are larger and contain additional radial nodes.

Principal levels with n = 3 or more contain five d orbitals. Four of them have a cloverleaf shape with four electron-dense lobes. They also have two perpendicular nodal planes that meet at the nucleus. The fifth d orbital has two lobes along the z-axis and a donut-shaped ring in the xy plane.

Principal levels with n = 4 and greater contain seven f orbitals. These orbitals have complex shapes with more nodes and lobes than d orbitals. Together, s, p, d, and f orbitals help explain why atoms are often drawn as spheres, even though the electron regions inside them have distinct shapes.

Electron Regions in Atomic Orbitals

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Electron Regions in Atomic Orbitals

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