What is its new energy? In what part of the electromagnetic spectrum do we find this radiation? The difference in energy between the two states is given by this expression:. The wavelength of a photon with this energy is found by the expression. Rearrangement gives:. From Figure 2 in Chapter 6.
It does introduce several important features of all models used to describe the distribution of electrons in an atom. These features include the following:. Of these features, the most important is the postulate of quantized energy levels for an electron in an atom.
As a consequence, the model laid the foundation for the quantum mechanical model of the atom. Bohr won a Nobel Prize in Physics for his contributions to our understanding of the structure of atoms and how that is related to line spectra emissions. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms.
Bohr Model of the Atom - Overview and Examples
Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Transitions between these allowed orbits result in the absorption or emission of photons. When an electron moves from a higher-energy orbit to a more stable one, energy is emitted in the form of a photon.
To move an electron from a stable orbit to a more excited one, a photon of energy must be absorbed. Using the Bohr model, we can calculate the energy of an electron and the radius of its orbit in any one-electron system.
Quantized energy means that the electrons can possess only certain discrete energy values; values between those quantized values are not permitted. Both involve a relatively heavy nucleus with electrons moving around it, although strictly speaking, the Bohr model works only for one-electron atoms or ions.
If the requirements of classical electromagnetic theory that electrons in such orbits would emit electromagnetic radiation are ignored, such atoms would be stable, having constant energy and angular momentum, but would not emit any visible light contrary to observation. If classical electromagnetic theory is applied, then the Rutherford atom would emit electromagnetic radiation of continually increasing frequency contrary to the observed discrete spectra , thereby losing energy until the atom collapsed in an absurdly short time contrary to the observed long-term stability of atoms.
The Bohr model retains the classical mechanics view of circular orbits confined to planes having constant energy and angular momentum, but restricts these to quantized values dependent on a single quantum number, n. Skip to content Increase Font Size. Chapter 6. Electronic Structure and Periodic Properties of Elements. Learning Objectives By the end of this section, you will be able to: Describe the Bohr model of the hydrogen atom Use the Rydberg equation to calculate energies of light emitted or absorbed by hydrogen atoms.
Example 1 Calculating the Energy of an Electron in a Bohr Orbit Early researchers were very excited when they were able to predict the energy of an electron at a particular distance from the nucleus in a hydrogen atom. Answer: 6. Chemistry End of Chapter Exercises Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?
What does it mean to say that the energy of the electrons in an atom is quantized? Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom. Show your calculations. The electron volt eV is a convenient unit of energy for expressing atomic-scale energies.
6.3: Line Spectra and the Bohr Model
How are the Bohr model and the Rutherford model of the atom similar? The analysis of these simple systems is carried out with techniques that are analogous to those that were first applied to simple atomic spectra. More complex structures, such as clusters of atoms, and bulk condensed matter, such as solids and liquids , also have energy levels describable by quantum mechanics.
The energy levels in these complex systems, however, are so closely spaced that they smear into a continuous band of energies.
- The Theory of Atomic Structure and Spectra.
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Transitions between these bands allow researchers to discern many important properties of a given material. The location and properties of the energy states are often referred to as the electronic structure of the material.
If an atom in its ground state is given some amount of energy so that it is promoted to an excited state, the atom will release that extra energy spontaneously as it moves back into lower states, eventually returning to the ground state. For an isolated atom, the energy is emitted as electromagnetic radiation. Conversely, the relationship allows the energy states of an atom to be determined from measurements of its frequency or wavelength spectrum. The analysis of the discrete wavelengths emitted or absorbed by an atom or molecule was historically carried out using prism or grating spectrometers; because of the appearance of the separated light in these instruments, these discrete wavelengths are sometimes called spectral lines.
The basis for analytical spectroscopy is the discovery, made in by the German physicist Gustav R. Kirchhoff , that each pure substance has its own characteristic spectrum. These dark lines, sometimes called Fraunhofer lines , are also collectively referred to as an absorption spectrum. The spectra of materials that were heated in flames or placed in electric-gas discharges were studied by many scientists during the 18th and 19th centuries. These spectra were composed of numerous bright discrete lines, indicating that only certain wavelengths were present in the emitted light.
They are called brightline, or emission, spectra. Although the possibility that each chemical element has a unique characteristic spectrum had been considered by numerous investigators, the early studies were hampered by the difficulty of obtaining relatively pure substances.
Atomic Structure and Spectra
Any sample could contain impurities that would result in the simultaneous production of many spectra. By using carefully purified substances, Kirchhoff demonstrated characteristic spectra and initiated the technique of spectroscopic analysis of the chemical composition of matter. Before the 20th century, there was no theory that could satisfactorily explain the origin of the spectra of the elements or the reason why different elements have different spectra.
The quantitative understanding of the elemental spectra needed the development of a fundamentally new physical theory, and the spectra of the simplest atoms played the key role in the development of this theory. Many of the major developments in 20th-century physics were motivated by an ever-increasing accuracy in the measurement of the spectra of the hydrogen atom; highlights include the discovery in by the Swiss scientist Johann J. Balmer that the frequency spectrum of hydrogen followed a simple numerical pattern, later revised by the Swedish physicist Johannes R.
In the Danish physicist Niels Bohr presented the first theoretical model that could give quantized energy levels that were in quantitative agreement with measurements of the hydrogen spectrum. Despite the success of the Bohr theory in describing the hydrogen spectrum, the theory failed badly when applied to the next simplest atom, helium , which contains two electrons. It was also incapable of predicting the likelihood of transitions between energy levels. This theory, known as quantum mechanics , was extended by the Austrian-born Swiss physicist Wolfgang Pauli , the German physicist Max Born , and others.
It has been remarkably successful in describing the spectra of complex atoms, ions, simple molecules, and solids.