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

Model planetarny opisuje atom wodoru jako maleńki układ słoneczny, w którym elektron krąży wokół dodatnio naładowanego jądra. 

Fizyka klasyczna sugeruje, że ponieważ elektron jest naładowaną cząstką poruszającą się po kołowej orbicie, powinien stale emitować energię, jednocześnie wpadając spiralnie do dodatnio naładowanego jądra. W końcu atom by się zapadł .

Jednak nie jest to obserwowane. Atomy są stabilne. 

Niels Bohr zaproponował, że istnieją orbity w pewnych, stałych odległościach od jądra. Orbity te są ponumerowanymi liczbami całkowitymi oznaczonymi główną liczbą kwantową, n. Orbita najbliższa jądru wynosi n = 1. n może być dowolną dodatnią liczbą całkowitą, ale nigdy zerem. 

Wraz ze wzrostem n zwiększa się promień orbity. Elektron, który znajduje się dalej od jądra, doświadcza słabszej siły elektrostatycznej i jest mniej mocno przyciągany do protonu. 

Każda orbita odpowiada określonemu poziomowi energii lub stanowi energii. Poziomy są skwantowane, co oznacza, że nie są możliwe żadne energie pomiędzy nimi.

Mówi się, że elektron w swoim najniższym, najbardziej stabilnym stanie energetycznym, przy n = 1, jest w stanie podstawowym.

Wyższe stany energetyczne, gdzie n  > 1, nazywane są stanami wzbudzonymi.

Elektron może przejść do innego stanu energetycznego tylko wtedy, gdy pochłonie energię – i przeskoczy na wyższy poziom – lub gdy przejdzie z powrotem do niższego stanu  energetycznego i uwolni nadmiar energii w postaci fotonu. 

Energia pochłonięta – lub wyemitowana – jest związana z różnicą energii między końcowym a początkowym poziomem energii. 

Elektrony relaksujące się z wyższego poziomu energetycznego emitują światło o krótszej długości fali niż elektrony relaksujące się z niższego poziomu energetycznego.

Chociaż model Bohra jest odpowiedni tylko dla wodoru lub jonów pojedynczych elektronów, położył podwaliny pod dokładniejsze modele atomowe.

model bohra

Dzięki pracom Ernesta Rutherforda i jego współpracowników z początku XX wieku ugruntowany został obraz atomów składających się z maleńkich, gęstych jąder otoczonych lżejszymi i jeszcze mniejszymi elektronami, stale po nim się poruszającymi. Obraz ten nazwano modelem planetarnym, ponieważ przedstawiał atom jako miniaturowy „układ słoneczny” z elektronami krążącymi po jądrze niczym planety krążące wokół Słońca. Najprostszym atomem jest wodór, składający się z pojedynczego protonu będącego jądrem, wokół którego porusza się pojedynczy elektron. Siła elektrostatyczna przyciągająca elektron do protonu zależy tylko od odległości między dwiema cząstkami. Ten klasyczny opis atomu w mechanice klasycznej jest jednak niekompletny, ponieważ elektron poruszający się po eliptycznej orbicie miałby przyspieszanie (poprzez zmianę kierunku) i zgodnie z klasycznym elektromagnetyzmem powinien w sposób ciągły emitować promieniowanie elektromagnetyczne. Ta utrata energii orbitalnej powinna skutkować ciągłym zmniejszaniem się orbity elektronu, aż do momentu, gdy zacznie ona krążyć po spirali w jądrze, co oznacza, że atomy są z natury niestabilne.

W 1913 roku Niels Bohr podjął próbę rozwiązania paradoksu atomowego, ignorując przewidywania klasycznego elektromagnetyzmu, że elektron krążący wokół wodoru będzie w sposób ciągły emitował światło. Zamiast tego połączył opis atomu z mechaniki klasycznej – ideę kwantyzacji Plancka i odkrycie Einsteina, że światło składa się z fotonów, których energia jest proporcjonalna do ich częstotliwości. Bohr założył, że elektron krążący wokół jądra normalnie nie emituje żadnego promieniowania (hipoteza stanu stacjonarnego), ale wyemituje lub zaabsorbuje foton, jeśli przejdzie na inną orbitę. Energia pochłonięta lub wyemitowana odzwierciedlałaby różnice w energiach orbit zgodnie z tym równaniem:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;">

Tutaj h jest stałą Plancka, a Ei i Ef to odpowiednio początkowa i końcowa energia orbity. Stosowana jest wartość bezwzględna różnicy energii, ponieważ częstotliwości i długości fal są zawsze dodatnie. Zamiast uwzględniać ciągłe wartości energii, Bohr założył, że energie tych orbitali elektronowych są skwantowane.

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;">

W tym wyrażeniu k jest stałą zawierającą podstawowe stałe, takie jak masa i ładunek elektronu oraz stała Plancka. Wstawienie wyrażenia na energie orbit do równania na ΔE daje

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;">

Jednym z podstawowych praw fizyki jest to, że materia jest najbardziej stabilna przy najniższej możliwej energii. Zatem elektron w atomie wodoru zwykle porusza się po orbicie n = 1, na której ma najniższą energię. Kiedy elektron znajduje się na orbicie o najniższej energii, mówi się, że atom znajduje się w podstawowym stanie elektronowym (lub po prostu w stanie podstawowym). Jeśli atom otrzymuje energię z zewnętrznego źródła, elektron może przenieść się na orbitę o wyższej wartości n i atom znajdzie się w wzbudzonym stanie elektronowym (lub po prostu stanie wzbudzonym) o wyższej energii. Kiedy następuje przejście elektronu ze stanu wzbudzonego (orbita o wyższej energii) do stanu mniej wzbudzonego, czyli stanu podstawowego, różnica energii jest emitowana w postaci fotonu. Podobnie, jeśli foton zostanie zaabsorbowany przez atom, energia fotonu przesuwa elektron z orbity o niższej energii na orbitę bardziej wzbudzoną. Możemy powiązać energię elektronów w atomach z tym, czego dowiedzieliśmy się wcześniej o energii. Prawo zachowania energii mówi, że energii nie możemy ani wytworzyć, ani zniszczyć. Zatem, jeśli do wzbudzenia elektronu z jednego poziomu energii na drugi wymagana jest pewna ilość energii zewnętrznej, ta sama ilość energii zostanie uwolniona, gdy elektron powróci do stanu początkowego.

Ponieważ model Bohra uwzględniał tylko pojedynczy elektron, można go również zastosować do jednoelektronowych jonów He+, Li2+, Be3+ i tak dalej, które różnią się od wodoru jedynie ładunkami jądrowymi, w związku z czym jednoelektronowe atomy i jony są zbiorowo zwane atomami wodoru.

Model Bohra

Podążając za pracami Ernesta Rutherforda i jego współpracowników na początku XX wieku, obraz atomów składających się z maleńkich gęstych jąder otoczonych ...

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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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Understand types, properties, and structure of matter.

Bohr’s Quantized Atomic Orbits

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