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

Matter and its Interactions

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The Bohr Model

El modelo planetario describe el átomo de hidrógeno como un diminuto sistema solar, con el electrón orbitando alrededor de un núcleo cargado positivamente. La física clásica sugiere que debido a que el electrón es una partícula cargada que se mueve en una órbita circular, debe irradiar energía continuamente mientras gira en espiral hacia el núcleo cargado positivamente. Eventualmente, el átomo colapsaría.Sin embargo, esto no se observa. Los átomos son estables. Niels Bohr propuso que hay órbitas a determinadas distancias fijas del núcleo.Estas órbitas son enteros numerados etiquetados por el número cuántico principal, n. La órbita más cercana al núcleo es n igual a uno. n puede ser cualquier número entero positivo, pero nunca cero.A medida que n aumenta, también lo hace el radio del orbital. Un electrón que está más lejos del núcleo experimenta una fuerza electrostática más débil y es menos atraído por el protón. Cada órbita corresponde a un nivel o estado de energía particular.Los niveles están cuantificados, lo que significa que la energía entre ellos no es posible. Se dice que un electrón en su estado energético más bajo y estable está en su estado base. Los estados de mayor energía, donde n es mayor que uno, se llaman estados excitados.Un electrón solo puede moverse a un estado energético diferente cuando absorbe energía y salta a un nivel superior o cuando vuelve a bajar a un estado de menor energía y libera el exceso de energía en forma de fotones. La energía absorbida o emitida está relacionado con la diferencia de energía entre los niveles de energía iniciales y finales. Los electrones que se relajan desde un nivel de energía superior emiten luz de una longitud de onda más corta que los electrones que se relajan desde un nivel de energía más bajo.Aunque el modelo de Bohr es adecuado solo para hidrógeno o iones de un solo electrón, sentó las bases para modelos atómicos más precisos.

el modelo de bohr

Siguiendo el trabajo de Ernest Rutherford y sus colegas a principios del siglo XX, la imagen de átomos que consisten en pequeños núcleos densos rodeados por electrones más ligeros e incluso más pequeños que se mueven continuamente por el núcleo estaba bien establecida. Esta imagen se llamaba el modelo planetario, ya que en ella se representaba el átomo como un “sistema solar” en miniatura con los electrones en órbita alrededor del núcleo como planetas en órbita alrededor del sol. El átomo más simple es el hidrógeno, que consiste en un solo protón como el núcleo sobre el cual se mueve un solo electrón. La fuerza electrostática que atrae el electrón al protón depende sólo de la distancia entre las dos partículas. Esta descripción mecánica clásica del átomo es incompleta, sin embargo, ya que un electrón que se mueve en una órbita elíptica estaría acelerando (cambiando de dirección) y, según el electromagnetismo clásico, debería emitir continuamente radiación electromagnética. Esta pérdida de energía orbital debería hacer que la órbita del electrón se reduzca continuamente hasta que se introduzca en espiral en el núcleo, lo que implica que los átomos son inherentemente inestables.
 
 En 1913, Niels Bohr intentó resolver la paradoja atómica ignorando la predicción del electromagnetismo clásico de que el electrón en órbita en el hidrógeno emitiría luz continuamente. En cambio, incorporó la descripción de la mecánica clásica del átomo－ las ideas de Planck sobre la cuantificación y el hallazgo de Einstein de que la luz consiste en fotones cuya energía es proporcional a su frecuencia. Bohr asumió que el electrón que orbitaba el núcleo normalmente no emitiría ninguna radiación (la hipótesis de estado estacionario), pero que emitiría o absorbería un fotón si se movía a una órbita diferente. La energía absorbida o emitida reflejaría las diferencias en las energías orbitales de acuerdo con esta ecuación:
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;" />
 
 Aquí, h es la constante de Planck y Ei y Ef son las energías orbitales inicial y final, respectivamente. Se usa el valor absoluto de la diferencia de energía ya que las frecuencias y las longitudes de onda siempre son positivas. En lugar de permitir valores continuos de energía, Bohr asumió que las energías de estos orbitales de electrones fueron cuantificadas.
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;" />
 
 En esta expresión, k es una constante que comprende constantes fundamentales como la masa y carga de los electrones y la constante de Planck. Insertar la expresión de las energías orbitales en la ecuación de ΔE da
 
 <img alt="Eq3" src="https://www.jovecore.com/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;" />
 
 Una de las leyes fundamentales de la física es que la materia es más estable con la energía más baja posible. Por lo tanto, el electrón en un átomo de hidrógeno generalmente se mueve en la órbita n = 1, la órbita en la que tiene la energía más baja. Cuando el electrón está en esta órbita de energía más baja, se dice que el átomo está en su estado electrónico fundamental (o simplemente en el estado fundamental). Si el átomo recibe energía de una fuente externa, es posible que el electrón se mueva a una órbita con un valor de n más alto y el átomo está ahora en un estado electrónico excitado (o simplemente un estado excitado) con mayor energía. Cuando se produce una transición de electrones desde un estado excitado (órbita de mayor energía) a un estado menos excitado, o estado fundamental, la diferencia de energía es emitida como un fotón. De manera similar, si un fotón es absorbido por un átomo, la energía del fotón mueve un electrón desde una órbita de energía más baja hasta una más excitada. Podemos relacionar la energía de los electrones en los átomos con lo que aprendimos anteriormente acerca de la energía. La ley de conservación de la energía dice que no podemos ni crear ni destruir la energía. Por lo tanto, si una cierta cantidad de energía externa es requerida para excitar un electrón de un nivel de energía a otro, esa misma cantidad de energía será liberada cuando el electrón regrese a su estado inicial.
 
 Dado que el modelo de Bohr involucraba sólo un electrón, también podría aplicarse a los iones de un solo electrón He+, Li2+, Be3+, etc., que difieren del hidrógeno sólo en sus cargas nucleares, y por lo tanto los átomos de un electrón y los iones se denominan colectivamente átomos similares al hidrógeno. 
 
 Este texto ha sido adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Química 2e, Sección 6.2: El modelo Bohr</a>.

El Modelo de Bohr

Siguiendo el trabajo de Ernest Rutherford y sus colegas a principios del siglo XX, la imagen de los átomos formados por diminutos núcleos densos rodeados ...

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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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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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