Name: bohr’s quantized atomic orbits
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 2 min 18 s
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Physical Science

Matter and its Interactions

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The Bohr Model

Das Planetenmodell beschreibt das Wasserstoffatom als winziges Sonnensystem, in dem das Elektron um einen positiv geladenen Kern kreist. Die klassische Physik legt nahe, da das Elektron ein geladenes Teilchen ist, das sich auf einer kreisförmigen Umlaufbahn bewegt, kontinuierlich Energie abgeben sollte während es sich in den positiv geladenen Zellkern schraubt. Am Ende würde das Atom zusammenbrechen.Dies wird jedoch nicht beobachtet. Die Atome sind stabil. Niels Bohr schlug vor, dass es Umlaufbahnen in bestimmten, festgelegten Abständen vom Kern gebe.Diese Bahnen sind nummerierte ganze Zahlen beschriftet mit der Hauptquantenzahl n. Die dem Kern am nächsten liegende Umlaufbahn ist n gleich eins. Das n kann eine beliebige positive ganze Zahl sein, aber niemals Null.Mit zunehmendem n vergrößert sich auch der Radius der Umlaufbahn. Ein Elektron, das weiter vom Kern entfernt ist erfährt eine schwächere elektrostatische Kraft und wird weniger stark vom Proton angezogen. Jede Umlaufbahn entspricht eines bestimmten Energieniveaus oder zustands.Die Energiezustände sind quantisiert, d.h. keine Energien dazwischen sind möglich. Ein Elektron in seinem niedrigsten, stabilsten Energiezustand bei n gleich eins sollte sich im Grundzustand befinden.Die höheren Energiezustände, wobei n größer als eins ist, werden die angeregten Zustände genannt. Ein Elektron kann sich in einen anderen Energiezustand bewegen entweder wenn es Energie absorbiert und auf einen höheren Energiezustand springt oder wenn es wieder in einen niedrigeren Energiezustand übergeht und setzt überschüssige Energie in Form eines Photons frei. Die absorbierte oder abgegebene Energie steht im Zusammenhang mit der Energiedifferenz zwischen dem abschließenden und dem anfänglichen Energiezustandes.Elektronen, die von einem höheren Energiezustand transferieren emittieren Licht mit kürzerer Wellenlänge als Elektronen, die von einem niedrigeren Energiezustand entspannen. Obwohl das Bohr'sche Modell nur für Wasserstoff und einfach geladene Ionen geeignet ist, schuf es die Grundlage für genauere atomare Modelle.

das bohr-modell

Nach der Arbeit von Ernest Rutherford und seinen Kollegen im frühen 20. Jahrhundert wurden Atomen als aus winzigen dichten Kernen bestehend, von leichteren und noch winzigeren Elektronen umgebend welche sich ständig um den Kern bewegen betrachtet. Dieses Bild wurde als Planetenmodell bezeichnet, da es das Atom als Miniatur-Sonnensystem darstellte, in dem die Elektronen den Kern wie Planeten die Sonne umkreisen. Das einfachste Atom ist Wasserstoff und besteht aus einem Proton als Kern um den sich ein einzelnes Elektron bewegt. Die elektrostatische Kraft, die das Elektron zum Proton zieht, hängt nur vom Abstand zwischen den beiden Teilchen ab. Diese klassische mechanische Beschreibung des Atoms ist jedoch unvollständig, da ein Elektron, das sich auf einer elliptischen Umlaufbahn bewegt, (durch Richtungsänderung) beschleunigt würde und gemäß dem klassischen Elektromagnetismus kontinuierlich elektromagnetische Strahlung aussenden müsste. Dieser Verlust an Bahnenergie müsste dazu führen, dass die Umlaufbahn des Elektrons immer kleiner wird, bis es spiralförmig in den Kern eindringt was bedeutet, dass Atome von Natur aus instabil wären. Im Jahr 1913 versuchte Niels Bohr, das Atomparadoxon zu lösen, indem er die Vorhersage des klassischen Elektromagnetismus ignorierte welche besgt, dass das umlaufende Elektron im Wasserstoff kontinuierlich Licht emittieren würde. Stattdessen bezog er in die Beschreibung des Atoms die klassische Mechanik mit ein – Plancks Ideen der Quantisierung und Einsteins Entdeckung, dass Licht aus Photonen besteht deren Energie proportional zu ihrer Frequenz ist. Bohr ging davon aus, dass das Elektron, das den Kern umkreist, normalerweise keine Strahlung aussendet (Hypothese des stationären Zustands), aber ein Photon aussendet oder absorbiert wenn es sich in eine anderes Orbital bewegt. Die absorbierte oder emittierte Energie würde Unterschiede in den Orbitalenergien gemäß folgender Gleichung widerspiegeln: <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;"> Hier ist h die Planck Konstante und E_i und E_f die Anfangs- bzw. Endenergie des Orbitals. Da Frequenzen und Wellenlängen immer positiv sind, wird der Absolutwert der Energiedifferenz verwendet. Anstatt kontinuierliche Energiewerte zu berücksichtigen, ging Bohr davon aus, dass die Energien dieser Elektronenorbitale quantisiert seien. <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;"> In diesem Ausdruck ist k eine Konstante, die grundlegende Konstanten wie die Elektronenmasse und -ladung sowie das Plancksche Wirkungsquantum miteinbezieht. Durch Einsetzen des Ausdrucks für die Bahnenergien in die Gleichung für ΔE erhält man: <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;"> Eines der Grundgesetze der Physik ist, dass Materie in ihrem niedrigst möglichen Energiezustand am stabilsten ist. Daher bewegt sich das Elektron in einem Wasserstoffatom normalerweise in dem n = 1 Orbital, der Umlaufbahn in der es die niedrigste Energie hat. Wenn sich das Elektron in diesem Orbital mit der niedrigsten Energie befindet, befindet sich das Atom in seinem elektronischen Grundzustand (oder einfach im Grundzustand). Wenn das Atom Energie von einer externen Quelle erhält, kann sich das Elektron in ein Orbital mit einem höheren n-Wert bewegen und das Atom befindet sich in einem angeregten elektronischen Zustand (oder in einem angeregten Zustand) mit höherer Energie. Wenn ein Elektronenübergang von einem angeregten Zustand (Umlaufbahn mit höherer Energie) in einen weniger angeregten Zustand oder Grundzustand erfolgt, wird die Energiedifferenz als Photon emittiert. Wenn ein Photon von einem Atom absorbiert wird, bewegt die Energie des Photons ein Elektron von einem energieärmeren Orbital in ein energetisch höheres. Wir können die Energie der Elektronen in Atomen nun mit dem was zuvor über Energie gesagt wurde in Beziehung setzen. Der Energieerhaltungssatz besagt, dass wir Energie weder erzeugen noch vernichten können. Wenn also eine bestimmte Menge externer Energie erforderlich ist, um ein Elektron von einem Energieniveau auf ein anderes anzuregen, wird dieselbe Energiemenge freigesetzt, wenn das Elektron in seinen Ausgangszustand zurückkehrt. Da Bohrs Modell ein einzelnes Elektron umfasste, konnte es auch auf die Einelektronen-Ionen He+, Li2+, Be3+ usw. angewendet werden, die sich von Wasserstoff nur durch ihre Kernladungen unterscheiden. So werden Ein-Elektronen-Atome und -Ionen kollektiv als wasserstoffähnliche Atome bezeichnet. Dieser Text wurde angepasst von <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Chemistry 2e, Section 6.2: The Bohr Model</a>.

Das Bohr-Modell

In Anlehnung an die Arbeit von Ernest Rutherford und seinen Kollegen im frühen zwanzigsten Jahrhundert wurde das Bild von Atomen, die aus winzigen dichten Kernen bestehen, die von ...

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bohr’s quantized atomic orbits

Bohr’s quantized atomic orbits explain why hydrogen atoms can stay stable. Early in the twentieth century, Ernest Rutherford and his colleagues described atoms as tiny dense nuclei with lighter electrons moving around them. This picture was called the planetary model because it compared the atom to a miniature solar system, with electrons orbiting the nucleus like planets around the sun.

The simplest atom is hydrogen. It has one proton in the nucleus and one electron moving around it. In the classical view, the electrostatic force between the proton and electron depends only on the distance between them. That description is incomplete, though. If the electron moved in an elliptical orbit, it would be accelerating because its direction changes.

Classical electromagnetism says an accelerating charged particle should continually emit electromagnetic radiation. If that happened, the electron would lose orbital energy. Its orbit would keep shrinking until it spiraled into the nucleus. That would make atoms unstable, so the classical picture creates an atomic paradox.

In 1913, Niels Bohr proposed a different model to address this problem. He ignored the classical prediction that the orbiting electron in hydrogen should constantly emit light. Instead, he used classical mechanics together with Planck’s idea of quantization and Einstein’s idea that light is made of photons with energy proportional to frequency. Bohr also proposed the stationary state hypothesis, which says the electron does not normally emit radiation while it stays in one orbit.

Bohr said light is emitted or absorbed only when the electron moves between orbits. The energy change follows the difference between the initial and final orbital energies, and the absolute value is used because frequency and wavelength are always positive. He also assumed the allowed electron energies are quantized, not continuous. In his energy equation, k is a constant that includes fundamental constants such as electron mass, electron charge, and Planck’s constant.

For hydrogen, the n = 1 orbit has the lowest energy. Because matter is most stable at the lowest possible energy, the electron usually stays in this orbit. This is the ground electronic state, or ground state. If the atom absorbs energy from outside, the electron can move to a higher n orbit. The atom then enters an excited electronic state, or excited state.

When an electron drops from an excited state to a less excited state or back to the ground state, the energy difference is released as a photon. The reverse also happens. If the atom absorbs a photon, that photon’s energy can move the electron from a lower orbit to a more excited one. This matches the law of conservation of energy, which says energy is neither created nor destroyed.

Because Bohr’s model was built for a single electron, it also applies to single-electron ions such as He+, Li2+, and Be3+. These species differ from hydrogen only in their nuclear charges. For that reason, hydrogen and these one-electron ions are called hydrogen-like atoms.

Bohr’s Quantized Atomic Orbits

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Bohr’s quantized atomic orbits explain why hydrogen atoms can stay stable. Early in the twentieth century, Ernest Rutherford and his colleagues described atoms as tiny dense nuclei with lighter electrons moving around them. This picture was called the planetary model because it compared the atom to a miniature solar system, with electrons orbiting the nucleus like planets around the sun. The simplest atom is hydrogen. It has one proton in the nucleus and one electron moving around it. In the...

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Learn how Bohr explained hydrogen stability with quantized orbits, ground and excited states, and photon absorption and emission in hydrogen-like atoms.

Bohr’s Quantized Atomic Orbits | JoVE K12

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The Uncertainty Principle

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Understand types, properties, and structure of matter.

Bohr’s Quantized Atomic Orbits

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