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

O modelo planetário descreve o átomo de hidrogênio como um sistema solar minúsculo, com o elétron em órbita e um núcleo com carga positiva. A física clássica sugere que, porque o elétron é uma partícula carregada em movimento numa órbita circular, deve irradiar energia continuamente enquanto se espalha para o núcleo com carga positiva. Eventualmente, o átomo entraria em colapso.No entanto, isto não é observado. Os átomos são estáveis. Niels Bohr propôs que existem órbitas a determinadas e fixas distâncias do núcleo.Estas órbitas são números inteiros rotulados pelo número quântico principal, n. A órbita mais próxima do núcleo é n igual a um. n pode ser qualquer número inteiro positivo, mas nunca zero.À medida que n aumenta, aumenta também o raio do orbital. Um elétron que está mais afastado do núcleo tem uma força eletrostática mais fraca e é menos atraído pelo próton. Cada órbita corresponde a um nível ou estado de energia específica.Os níveis são quantificados, o que significa que não são possíveis energias no meio. Um elétron no seu estado energético mais baixo e estável n igual a um diz-se que está no seu estado inicial. Os estados de energia superior, onde n é maior do que um, são chamados os estados excitados.Um elétron só pode mover-se para um estado energético diferente quando absorve energia e salta para um nível superior ou quando regressa a um estado de energia inferior e liberta energia em excesso sob a forma de um fóton. A energia absorvida ou emitida está relacionada com a diferença de energia entre os níveis finais e iniciais de energia. Os elétrons a relaxarem a partir de um nível de energia mais elevado emitem luz com menor comprimento de onda do que os elétrons a relaxarem a partir de um nível de energia mais baixo.Embora o modelo de Bohr seja apenas adequado para o hidrogênio ou íons de elétrons simples, preparou-se o terreno para modelos atómicos mais precisos.

o modelo de bohr

Após o trabalho de Ernest Rutherford e seus colegas no início do século XX, a imagem dos átomos consistindo de pequenos núcleos densos cercados por eletrões mais leves e até mesmo mais pequenos que se movimentam continuamente à volta do núcleo estava bem estabelecida. Esta imagem foi chamada de modelo planetário, uma vez que retratava o átomo como um “sistema solar” em miniatura, com os eletrões a orbitar o núcleo como planetas a orbitar o sol. O átomo mais simples é o hidrogénio, que consiste em um único protão como núcleo à volta do qual um único eletrão se move. A força eletrostática que atrai o eletrão para o protão depende apenas da distância entre as duas partículas. Esta descrição clássica da mecânica do átomo está incompleta, no entanto, uma vez que um eletrão que se move em órbita elíptica estaria a acelerar (mudando de direção) e, de acordo com o eletromagnetismo clássico, deveria emitir continuamente radiação eletromagnética. Esta perda na energia orbital deveria resultar na diminuição contínua da órbita dos eletrões até entrar em espiral até ao núcleo, o que implica que os átomos são inerentemente instáveis.

Em 1913, Niels Bohr tentou resolver o paradoxo atómico ignorando a previsão do eletromagnetismo clássico de que o eletrão em órbita do hidrogénio emitiria continuamente luz. Em vez disso, incorporou a descrição da mecânica clássica do átomo － as ideias de quantização de Planck e a descoberta de Einstein de que a luz consiste em fotões cuja energia é proporcional à sua frequência. Bohr assumiu que o eletrão que orbita o núcleo normalmente não emitiria nenhuma radiação (a hipótese do estado estacionário), mas emitiria ou absorveria um fotão se mudasse para uma órbita diferente. A energia absorvida ou emitida refletiria diferenças nas energias orbitais de acordo com esta equação:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;" />

Aqui, h é a constante de Planck e Ei e Ef são as energias orbitais inicial e final, respectivamente. O valor absoluto da diferença de energia é utilizado uma vez que as frequências e os comprimentos de onda são sempre positivos. Em vez de permitir valores contínuos de energia, Bohr assumiu que as energias dessas orbitais de eletrões eram quantizadas.

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;" />

Nesta expressão, k é uma constante que compreende constantes fundamentais como a massa e carga do eletrão e a constante de Planck. Inserindo a expressão para as energias de órbita na equação de ΔE obtemos

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;" />

Uma das leis fundamentais da física é que a matéria é mais estável com a menor energia possível. Assim, o eletrão em um átomo de hidrogénio move-se geralmente na órbita n = 1, a órbita em que tem a energia mais baixa. Quando o eletrão está nesta órbita de energia mais baixa, diz-se que o átomo está no seu estado eletrónico fundamental (ou simplesmente estado fundamental). Se o átomo receber energia de uma fonte externa, é possível que o eletrão se mova para uma órbita com um valor n superior, ficando o átomo então em um estado eletrónico excitado (ou simplesmente um estado excitado) com maior energia. Quando ocorre uma transição de eletrão de um estado excitado (órbita de energia mais alta) para um estado menos excitado, ou estado fundamental, a diferença de energia é emitida como um fotão. Da mesma forma, se um fotão for absorvido por um átomo, a energia do fotão move um eletrão de uma órbita de energia inferior para uma órbita mais excitada. Podemos relacionar a energia dos eletrões nos átomos com o que aprendemos anteriormente sobre a energia. A lei da conservação da energia diz que não podemos nem criar nem destruir a energia. Assim, se uma determinada quantidade de energia externa for necessária para excitar um eletrão de um nível de energia para outro, essa mesma quantidade de energia será libertada quando o eletrão retornar ao seu estado inicial.

Como o modelo de Bohr envolvia apenas um único eletrão, ele também poderia ser aplicado aos iões com um único eletrão He+, Li2+, Be3+, e assim por diante, que diferem do hidrogénio apenas nas suas cargas nucleares, pelo que os átomos e iões de eletrão único são colectivamente referidos como átomos hidrogenóides. 

Este texto é adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Chemistry 2e, Section 6.2: The Bohr Model</a>.

O Modelo de Bohr

Seguindo o trabalho de Ernest Rutherford e seus colegas no início do século XX, a imagem de átomos consistindo de minúsculos núcleos densos cercados ...

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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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