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

Het planetaire model beschrijft het waterstofatoom als een klein zonnestelsel, waarbij het elektron in een baan om een positief geladen kern draait. De klassieke natuurkunde suggereert dat, omdat het elektron een geladen deeltje is dat in een cirkelvormige baan beweegt, het continu energie moet uitstralen terwijl het in de positief geladen kern beweegt. Uiteindelijk zou het atoom instorten.Dit wordt echter niet waargenomen. Atomen zijn stabiel. Niels Bohr stelde voor dat er banen zijn op bepaalde, vaste afstanden van de kern.Deze banen zijn genummerde gehele getallen gelabeld door het hoofdkwantumnummer, n. De baan die het dichtst bij de kern ligt is n gelijk aan één. n kan elk positief geheel getal zijn, maar nooit nul.Naarmate n toeneemt, neemt ook de straal van de orbitaal toe. Een elektron dat verder van de kern verwijderd is, ervaart een zwakkere elektrostatische kracht en wordt minder sterk aangetrokken door het proton. Elke baan komt overeen met een bepaald energieniveau of een bepaalde toestand.De niveaus zijn gekwantiseerd, wat betekent dat er geen energieën tussenin mogelijk zijn. Een elektron in zijn laagste, meest stabiele energietoestand op n gelijk aan één zou zich in zijn grondtoestand bevinden. De hogere energietoestanden, waarbij n groter is dan één, worden de aangeslagen toestanden genoemd.Een elektron kan alleen naar een andere energietoestand gaan wanneer het energie absorbeert en naar een hoger niveau springt of wanneer het teruggaat naar een lagere energietoestand en overtollige energie vrijgeeft in de vorm van een foton. De geabsorbeerde of uitgezonden energie is gerelateerd aan het verschil in energie tussen het uiteindelijke en initiële energieniveau. Elektronen die ontspannen vanaf een hoger energieniveau, zenden licht met een kortere golflengte uit dan elektronen die ontspannen vanaf een lager energieniveau.Hoewel Bohr's model alleen geschikt is voor waterstof-of enkelvoudige elektronionen, heeft het de basis gelegd voor nauwkeurigere atomaire modellen.

het bohr-model

Na het werk van Ernest Rutherford en zijn collega's in het begin van de twintigste eeuw was het beeld van atomen bestaande uit kleine, dichte atoomkernen omgeven door lichtere en zelfs nog kleinere elektronen die voortdurend door de atoomkern bewegen, goed ingeburgerd. Dit beeld werd het planetenmodel genoemd, omdat het het atoom voorstelde als een miniatuur “zonnestelsel” waarbij de elektronen rond de atoomkern cirkelden zoals planeten rond de zon. Het eenvoudigste atoom is waterstof, bestaande uit een enkel proton als atoomkern waaromheen een enkel elektron beweegt. De elektrostatische kracht die het elektron naar het proton trekt, hangt alleen af van de afstand tussen de twee deeltjes. Deze klassieke mechanische beschrijving van het atoom is echter onvolledig, aangezien een elektron dat zich in een elliptische baan beweegt, zou versnellen (door van richting te veranderen) en, volgens het klassieke elektromagnetisme, voortdurend elektromagnetische straling zou moeten uitzenden. Dit verlies aan orbitale energie zou ertoe moeten leiden dat de baan van het elektron steeds kleiner wordt totdat deze in de atoomkern spiraalt, wat impliceert dat atomen inherent onstabiel zijn. In 1913 probeerde Niels Bohr de atomaire paradox op te lossen door de voorspelling van het klassieke elektromagnetisme te negeren dat het in een baan om de aarde draaiende elektron in waterstof continu licht zou uitzenden. In plaats daarvan verwerkte hij de beschrijving van het atoom uit de klassieke mechanica – de ideeën van Planck over kwantisering en de bevinding van Einstein dat licht bestaat uit fotonen waarvan de energie evenredig is aan hun frequentie. Bohr ging ervan uit dat het elektron dat in een baan om de atoomkern draait normaal gesproken geen straling zou uitzenden (de stationaire toestandshypothese), maar dat het een foton zou uitzenden of absorberen als het naar een andere baan zou bewegen. De geabsorbeerde of uitgezonden energie zou verschillen in de orbitale energieën weerspiegelen volgens deze vergelijking: <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;"> Hier is h de constante van Planck en zijn Ei en Ef respectievelijk de initiële en uiteindelijke orbitale energie. De absolute waarde van het energieverschil wordt gebruikt, omdat frequenties en golflengten altijd positief zijn. In plaats van continue energiewaarden toe te staan, ging Bohr ervan uit dat de energieën van deze elektronenorbitalen gekwantiseerd waren. <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;"> In deze uitdrukking is k een constante die fundamentele constanten omvat, zoals de elektronenmassa en lading en de constante van Planck. Het invoegen van de uitdrukking voor de baanenergieën in de vergelijking voor ΔE geeft <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;"> Een van de fundamentele wetten van de natuurkunde is dat materie het meest stabiel is met de laagst mogelijke energie. Het elektron in een waterstofatoom beweegt dus gewoonlijk in de baan n = 1, de baan waarin het de laagste energie heeft. Wanneer het elektron zich in deze baan met de laagste energie bevindt, wordt gezegd dat het atoom zich in zijn elektronische grondtoestand bevindt (of eenvoudigweg grondtoestand). Als het atoom energie ontvangt van een externe bron, is het mogelijk dat het elektron naar een baan met een hogere n-waarde beweegt en het atoom zich nu in een aangeslagen elektronische toestand (of eenvoudigweg een aangeslagen toestand) met hogere energie bevindt. Wanneer er een elektronenovergang plaatsvindt van een aangeslagen toestand (baan met hogere energie) naar een minder aangeslagen toestand of grondtoestand, wordt het verschil in energie uitgezonden als een foton. Op dezelfde manier, als een foton door een atoom wordt geabsorbeerd, verplaatst de energie van het foton een elektron van een baan met lagere energie naar een meer aangeslagen baan. We kunnen de energie van elektronen in atomen in verband brengen met wat we eerder over energie hebben geleerd. De Wet van Behoud van Energie zegt dat we energie niet kunnen creëren of vernietigen. Als er dus een bepaalde hoeveelheid externe energie nodig is om een elektron van het ene energieniveau naar het andere te exciteren, zal diezelfde hoeveelheid energie vrijkomen wanneer het elektron terugkeert naar zijn oorspronkelijke toestand. Omdat het model van Bohr slechts één elektron betrof, kon het ook worden toegepast op de één-elektron-ionen He+, Li2+, Be3+, enzovoort, die alleen verschillen van waterstof in hun nucleaire lading, en dus zijn één-elektron-atomen en ionen gezamenlijk waterstofachtige atomen genoemd. Deze tekst is aangepast van <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Chemistry 2e, Sectie 6.2: Het Bohr-model</a>.

Het Bohr-model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded ...

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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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the bohr model

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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key terms and concepts

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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Understand types, properties, and structure of matter.

Bohr’s Quantized Atomic Orbits

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