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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

For each of the following pairs of elements \((\mathrm{Mg}\) and \(\mathrm{K}) \quad(\mathrm{F}\) and \(\mathrm{Cl})\) pick the atom with a. more favorable (exothermic) electron affinity. b. higher ionization energy. c. larger size.

Valence electrons are those electrons in the outermost principal quantum level (highest \(n\) level) of an atom in its ground state. Groups \(1 \mathrm{~A}\) to \(8 \mathrm{~A}\) have from 1 to 8 valence electrons. For each group of the representative elements (1A-8A), give the number of valence electrons, the general valence electron configuration, a sample element in that group, and the specific valence electron configuration for that element.

How many valence electrons do each of the following elements have, and what are the specific valence electrons for each element? a. \(\mathrm{Ca}\) b. \(\mathrm{O}\) c. element 117 d. In e. Ar f. \(\mathrm{Bi}\)

Answer the following questions assuming that \(m_{s}\) could have three values rather than two and that the rules for \(n, \ell\), and \(m_{\ell}\) are the normal ones. a. How many electrons would an orbital be able to hold? b. How many elements would the first and second periods in the periodic table contain? c. How many elements would be contained in the first transition metal series? d. How many electrons would the set of 4 forbitals be able to hold?

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{\ell}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{\ell}=1\)
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