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

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Physical Science

Matter and its Interactions

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The Bohr Model

Il modello planetario descrive l'atomo di idrogeno come un minuscolo sistema solare, con l'elettrone in orbita attorno a un nucleo carico positivamente. La fisica classica suggerisce che poiché l'elettrone è una particella carica che si muove in un'orbita circolare, dovrebbe irradiare continuamente energia mentre si muove a spirale nel nucleo carico positivamente. Alla fine, l'atomo collasserebbe.

Tuttavia, questo non viene osservato. Gli atomi sono stabili. Niels Bohr suggerì che ci fossero orbite a determinate distanze fisse dal nucleo.

Queste orbite sono numeri interi numerati indicati dal principale numero quantico, n. L'orbita più vicina al nucleo è n uguale a uno. n può essere qualsiasi numero intero positivo, ma mai zero.

Con l'aumentare di n, aumenta anche il raggio dell'orbitale. Un elettrone che è più lontano dal nucleo subisce una forza elettrostatica più debole ed è attratto meno strettamente dal protone. Ogni orbita corrisponde ad un particolare livello o stato di energia.

I livelli sono quantizzati, il che significa che non sono possibili energie intermedie. Si dice che un elettrone al suo stato energetico più basso e più stabile, con n uguale a uno, sia al suo stato fondamentale. Gli stati energetici superiori, dove n è maggiore di uno, sono detti stati eccitati.

Un elettrone può spostarsi in uno stato energetico diverso solo quando assorbe energia, e salta a un livello più alto, o quando torna indietro a uno stato energetico inferiore e rilascia energia in eccesso sotto forma di un fotone. L'energia assorbita, o emessa, è correlata alla differenza di energia tra il livello di energia finale e quello iniziale. Gli elettroni che si trovano ad un livello di energia più elevato emettono luce di lunghezza d'onda inferiore rispetto agli elettroni che si trovano ad un livello di energia più basso.

Benché il modello di Bohr sia adatto solo per ioni di idrogeno o per elettroni singoli, ha posto le basi per modelli atomici più accurati.

il modello di bohr

Seguendo il lavoro di Ernest Rutherford e dei suoi colleghi all'inizio del XX secolo, l'immagine degli atomi costituiti da minuscoli nuclei densi circondati da elettroni pi leggeri e ancora pi piccoli in continuo movimento attorno al nucleo era ben consolidata. Questimmagine fu chiamata modello planetario poich raffigurava l’atomo come un “sistema solare? in miniatura con gli elettroni che orbitano attorno al nucleo come i pianeti che orbitano attorno al sole. L'atomo pi semplice l'idrogeno, costituito da un singolo protone come nucleo attorno al quale si muove un singolo elettrone. La forza elettrostatica che attrae l'elettrone sul protone dipende solo dalla distanza tra le due particelle. Questa descrizione meccanica classica dell'atomo tuttavia incompleta, poich un elettrone che si muove su un'orbita ellittica accelererebbe (cambiando direzione) e, secondo l'elettromagnetismo classico, dovrebbe emettere continuamente radiazioni elettromagnetiche. Questa perdita di energia orbitale dovrebbe far s che l’orbita dell’elettrone diventi sempre pi piccola fino a quando non si muover a spirale nel nucleo, il che implica che gli atomi sono intrinsecamente instabili.

Nel 1913, Niels Bohr tent di risolvere il paradosso atomico ignorando la previsione dell’elettromagnetismo classico secondo cui l’elettrone orbitante nell’idrogeno avrebbe emesso continuamente luce. Invece, incorpor la descrizione dell’atomo fornita dalla meccanica classica, le idee di quantizzazione di Planck e la scoperta di Einstein secondo cui la luce costituita da fotoni la cui energia proporzionale alla loro frequenza. Bohr ipotizz che l'elettrone in orbita attorno al nucleo normalmente non emetterebbe alcuna radiazione (l'ipotesi dello stato stazionario), ma emetterebbe o assorbirebbe un fotone se si spostasse in un'orbita diversa. L'energia assorbita o emessa rifletterebbe le differenze nelle energie orbitali secondo questa equazione:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;" />

Qui h la costante di Planck ed Ei ed Ef sono rispettivamente l'energia orbitale iniziale e finale. Viene utilizzato il valore assoluto della differenza di energia poich le frequenze e le lunghezze d'onda sono sempre positive. Invece di consentire valori continui di energia, Bohr ipotizz che le energie di questi orbitali elettronici fossero quantizzate.

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;" />

In questa espressione, k una costante che comprende costanti fondamentali come la massa e la carica dell’elettrone e la costante di Planck. Inserendo l'espressione per le energie dell'orbita nell'equazione per ΔE si ottiene

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;" />

Una delle leggi fondamentali della fisica che la materia pi stabile con la pi bassa energia possibile. Pertanto, l'elettrone in un atomo di idrogeno si muove solitamente nell'orbita n = 1, l'orbita in cui ha l'energia pi bassa. Quando l'elettrone si trova in questa orbita a energia pi bassa, si dice che l'atomo si trova nel suo stato elettronico fondamentale (o semplicemente stato fondamentale). Se l'atomo riceve energia da una fonte esterna, possibile che l'elettrone si sposti su un'orbita con un valore n pi alto e l'atomo si trovi ora in uno stato elettronico eccitato (o semplicemente uno stato eccitato) con un'energia pi elevata. Quando avviene una transizione elettronica da uno stato eccitato (orbita ad alta energia) a uno stato meno eccitato, o stato fondamentale, la differenza di energia viene emessa sotto forma di fotone. Allo stesso modo, se un fotone viene assorbito da un atomo, l'energia del fotone sposta un elettrone da un'orbita a energia inferiore fino a un'orbita pi eccitata. Possiamo mettere in relazione l'energia degli elettroni negli atomi con ci che abbiamo imparato in precedenza sull'energia. La legge di conservazione dell’energia dice che non possiamo n creare n distruggere energia. Pertanto, se necessaria una certa quantit di energia esterna per eccitare un elettrone da un livello energetico a un altro, la stessa quantit di energia verr liberata quando l’elettrone ritorner al suo stato iniziale.

Poich il modello di Bohr coinvolgeva solo un singolo elettrone, potrebbe essere applicato anche agli ioni a singolo elettrone He^+, Li^2^+, Be^3^+ e cos via, che differiscono dall’idrogeno solo per la loro carica nucleare, e quindi gli atomi e gli ioni a un elettrone sono collettivamente detti atomi simili all’idrogeno.



Questo testo adattato da <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Chemistry 2e, Section 6.2: The Bohr Model</a>.

Il modello di Bohr

Seguendo il lavoro di Ernest Rutherford e dei suoi colleghi all'inizio del XX secolo, l'immagine di atomi costituiti da minuscoli nuclei densi circondati ...

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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

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