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Chapter 7: Problem 1

Defend and criticize Bohr's model. Why was it reasonable that such a model was proposed, and what evidence was there that it "works"? Why do we no longer "believe" in it?

Short Answer

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Bohr's model was proposed as a simple representation of an atom to address the inconsistencies of Rutherford's model and successfully explained the hydrogen spectrum, providing evidence for quantized energy levels in atoms. However, its limitations, such as being unable to accurately predict energy levels or spectral lines for multi-electron atoms, led to its replacement by the more advanced quantum mechanical model. The quantum mechanical model, which treats electrons as wave-like entities and provides a more complete picture of atomic structure, is now the widely accepted understanding of atomic behavior.

Step by step solution

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1. Overview of Bohr's model

Bohr's model is a highly simplified representation of an atom, which was proposed by Danish physicist Niels Bohr in 1913. In this model, electrons orbit the nucleus in well-defined, circular paths called orbits or shells. The nucleus contains protons and neutrons, and the orbits are described by a principle called the "quantum rule", which states that the angular momentum of an electron in a stable orbit is an integer multiple of a fundamental constant (Planck's constant divided by 2蟺).
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2. Reasons for proposing Bohr's model

Bohr's model was proposed to address some of the inconsistencies and problems with the earlier Rutherford's model. Rutherford's model could not explain how atoms could emit specific frequencies of light when heated. It also failed to explain the stability of atoms, as according to classical electromagnetic theory, accelerating electrons should continuously lose energy and eventually fall into the nucleus. Bohr's model, based on the principles of quantum mechanics, resolved these issues by introducing the concept of quantized orbits and restricting electron transitions between particular energy levels.
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3. Evidence supporting Bohr's model

Bohr's model was able to accurately predict the energy levels and spectral lines of hydrogen. It was capable of explaining the observed line spectrum of hydrogen, which was previously a mystery using Rutherford's model. This success in describing the hydrogen spectrum provided strong evidence that Bohr's model "works" and lent credibility to the idea of quantized energy levels in atoms.
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4. Criticisms and limitations of Bohr's model

Despite its initial success, Bohr's model had several shortcomings. It was unable to accurately predict the energy levels or spectral lines for atoms with more than one electron. The model's assumption of circular electron orbits was an oversimplification, which led to inaccuracies in predicting the behavior of larger atoms. Furthermore, the model could not account for the observed fine structure and Zeeman effect in the hydrogen spectrum.
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5. Why we no longer "believe" in Bohr's model

Bohr's model was eventually replaced by a more advanced understanding of atomic structure, known as the quantum mechanical model. This model, developed by physicists such as Schr枚dinger and Heisenberg, treats electrons as wave-like entities and relies on more complex mathematics and probabilistic descriptions of electron behavior. The quantum mechanical model provides a more accurate and complete picture of atomic structure, including the behavior of multi-electron atoms and the fine structure of atomic spectra. While Bohr's model was an essential step in the development of atomic theory, its limitations and shortcomings led to its replacement by this more sophisticated model.

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Most popular questions from this chapter

Predict the atomic number of the next alkali metal after francium and give its ground-state electron configuration.

An electron is excited from the \(n=1\) ground state to the \(n=3\) state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true. a. It takes more energy to ionize (completely remove) the electron from \(n=3\) than from the ground state. b. The electron is farther from the nucleus on average in the \(n=3\) state than in the \(n=1\) state. c. The wavelength of light emitted if the electron drops from \(n=3\) to \(n=2\) will be shorter than the wavelength of light emitted if the electron falls from \(n=3\) to \(n=1\). d. The wavelength of light emitted when the electron returns to the ground state from \(n=3\) will be the same as the wavelength of light absorbed to go from \(n=1\) to \(n=3\). e. For \(n=3\), the electron is in the first excited state.

Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground-state electron configuration where appropriate. a. \(1 s^{2} 2 s^{2} 3 p^{1}\) b. \(1 s^{2} 2 s^{2} 2 p^{6}\) c. \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\) d. \([\mathrm{Ar}] 4 s^{2} 3 d^{5} 4 p^{1}\) How many unpaired electrons are present in each of these species?

The elements \(\mathrm{Si}\), Ga, As, Ge, Al, \(\mathrm{Cd}, \mathrm{S}\), and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configuration for these atoms.

One bit of evidence that the quantum mechanical model is "correct" lies in the magnetic properties of matter. Atoms with unpaired electrons are attracted by magnetic fields and thus are said to exhibit paramagnetism. The degree to which this effect is observed is directly related to the number of unpaired electrons present in the atom. Consider the ground-state electron configurations for \(\mathrm{Li}, \mathrm{N}, \mathrm{Ni}, \mathrm{Te}, \mathrm{Ba}\), and \(\mathrm{Hg} .\) Which of these atoms would be expected to be paramagnetic, and how many unpaired electrons are present in each paramagnetic atom?
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