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

The planetary model describes the hydrogen atom as a tiny solar system, with the electron orbiting a positively-charged nucleus. 

Classical physics suggests that because the electron is a charged particle moving in a circular orbit, it should continuously radiate energy while spiraling into the positively-charged nucleus. Eventually, the atom would collapse. 

However, this isn&#8217;t observed. Atoms are stable. 

Niels Bohr proposed that there are orbits at certain, fixed distances from the nucleus. These orbits are numbered integers labeled by the principal quantum number, n. The orbit closest to the nucleus is n = 1. n can be any positive integer, but never zero. 

As n increases, so does the radius of the orbital. An electron that is farther away from the nucleus experiences a weaker electrostatic force and is less tightly attracted to the proton. 

Each orbit corresponds to a particular energy level or state. The levels are quantized, meaning no energies in between are possible.

An electron at its lowest, most stable energy state, at n = 1, is said to be at its ground state.

The higher energy states, where n &#62; 1, are called the excited states.

An electron can only move to a different energy state either when it absorbs energy &#8212; and jumps to a higher level &#8212; or when it transitions back down to a lower energy state and releases excess energy in the form of a photon. 

The energy absorbed &#8212; or emitted &#8212; is related to the difference in energy between the final and initial energy levels. 

Electrons relaxing from a higher energy level emit shorter-wavelength light than electrons relaxing from a lower energy level.

Although Bohr&#8217;s model is suitable only for hydrogen or single electron ions, it set the groundwork for more accurate atomic models.

the 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 by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature &#8220;solar system&#8221; with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus about which a single electron moves. The electrostatic force attracting the electron to the proton depends only on the distance between the two particles. This classical mechanics description of the atom is incomplete, however, since an electron moving in an elliptical orbit would be accelerating (by changing direction) and, according to classical electromagnetism, it should continuously emit electromagnetic radiation. This loss in orbital energy should result in the electron&#8217;s orbit getting continually smaller until it spirals into the nucleus, implying that atoms are inherently unstable.

In 1913, Niels Bohr attempted to resolve the atomic paradox by ignoring classical electromagnetism&#8217;s prediction that the orbiting electron in hydrogen would continuously emit light. Instead, he incorporated classical mechanics&#8217; description of the atom &#65293; Planck&#8217;s ideas of quantization and Einstein&#8217;s finding that light consists of photons whose energy is proportional to their frequency. Bohr assumed that the electron orbiting the nucleus would not normally emit any radiation (the stationary state hypothesis), but it would emit or absorb a photon if it moved to a different orbit. The energy absorbed or emitted would reflect differences in the orbital energies according to this equation:

<img alt="Energy transition equation &#916;E=Ef&#8722;Ei=h&#957;=hc/&#955;, formula in quantum mechanics, diagram." src="/files/core/CDNSource/lessons/978/978_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

Here, h is Planck&#8217;s constant and Ei and Ef are the initial and final orbital energies, respectively. The absolute value of the energy difference is used since frequencies and wavelengths are always positive. Instead of allowing for continuous values of energy, Bohr assumed the energies of these electron orbitals were quantized.

<img alt="Energy levels formula \(E_n = -\frac{k}{n^2}\), physics, hydrogen atom, educational diagram." src="/files/core/CDNSource/lessons/978/978_Equations-02.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq2" />

In this expression, k is a constant comprising fundamental constants such as the electron mass and charge and Planck&#8217;s constant. Inserting the expression for the orbit energies into the equation for &#916;E gives

<img alt="Energy difference equation &#916;E in physics, relates spectral lines, shown as a mathematical formula." src="/files/core/CDNSource/lessons/978/978_Equations-03.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq3" />

One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the n = 1 orbit, the orbit in which it has the lowest energy. When the electron is in this lowest energy orbit, the atom is said to be in its ground electronic state (or simply ground state). If the atom receives energy from an outside source, it is possible for the electron to move to an orbit with a higher n value and the atom is now in an excited electronic state (or simply an excited state) with higher energy. When an electron transition occurs from an excited state (higher energy orbit) to a less excited state, or ground state, the difference in energy is emitted as a photon. Similarly, if a photon is absorbed by an atom, the energy of the photon moves an electron from a lower energy orbit up to a more excited one. We can relate the energy of electrons in atoms to what we learned previously about energy. The law of conservation of energy says that we can neither create nor destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, that same amount of energy will be liberated when the electron returns to its initial state.

Since Bohr&#8217;s model involved only a single electron, it could also be applied to the single-electron ions He+, Li2+, Be3+, and so forth, which differ from hydrogen only in their nuclear charges, and so one-electron atoms and ions are collectively referred to as hydrogen-like atoms. 

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/6-2-the-bohr-model">Openstax, Chemistry 2e, Section 6.2: The Bohr Model</a>.

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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Learn how Bohr explained hydrogen stability with quantized orbits, ground and excited states, and photon absorption and emission in hydrogen-like atoms.

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Bohr’s Quantized Atomic Orbits

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