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Chapter 7: Problem 24

The Bohr model only works for one electron species. Why do we discuss it in this text (what's good about it)?

Short Answer

Expert verified
The Bohr model is discussed in physics and chemistry texts due to its simplicity, ease of calculation for hydrogen-like atoms, foundational role in quantum mechanics, its ability to explain spectral lines in the hydrogen atom, and its educational value as an excellent starting point for understanding atomic structure. Even though the model has limitations and has been surpassed by more advanced models like the Schr枚dinger model, it helps students build a strong foundation for further learning in atomic and quantum physics.

Step by step solution

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1. Introduction to the Bohr Model

The Bohr model, proposed by Niels Bohr in 1913, is an early model of atomic structure and only works for one-electron species like hydrogen and hydrogen-like ions (such as He+ and Li虏鈦�). The model successfully explains the hydrogen atom's energy levels, electron orbits, and quantized energy emissions.
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2. Simplicity and Calculation

One of the key advantages of the Bohr model is its simplicity. It offers a straightforward way to calculate the energy levels of hydrogen-like atoms. Using the Bohr model, we can easily determine the electron's energy in each orbit around the nucleus using the formula \(E_n = -\frac{13.6 eV}{n^2}\), where n is the principal quantum number (integer n鈮�1).
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3. Foundation for Quantum Mechanics

Even though the Bohr model has limitations, it sets the stage for the development of quantum mechanics. The idea of quantized energy levels and the wave-particle duality introduced by the model are fundamental concepts in quantum theory. These concepts were further elaborated and refined by scientists like Erwin Schr枚dinger, Werner Heisenberg, and Max Born, who contributed to the development of the modern quantum mechanics theory.
04

4. Spectral Lines of Hydrogen Atom

The Bohr model accurately predicts the hydrogen atoms' spectral lines, also known as the hydrogen emission spectrum. The model explains the observed spectral lines by the electrons absorbing or emitting photons. As the electrons transition between energy levels (orbits), they absorb or emit energy corresponding to the difference in energy levels. This energy difference is observed as discrete lines in the emission spectrum.
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5. Educational Value

Despite its limitations, the Bohr model is widely discussed in educational settings because it serves as an excellent starting point for introducing the concept of atomic structure. The model's simplicity and visualization of electron orbits help students easily grasp the essentials of atomic theory. In conclusion, even though the Bohr model has its limitations, it is discussed in physics and chemistry texts because of its simplicity, ease of calculation, foundational role in quantum mechanics, the explanation of spectral lines in the hydrogen atom, and its educational value. While more advanced models like the Schr枚dinger model have surpassed the Bohr model, understanding the Bohr model helps students build a strong foundation for further learning in atomic and quantum physics.

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Most popular questions from this chapter

Write the expected ground-state electron configuration for each of the following. a. the lightest halogen atom b. the alkali metal with only \(2 p\) and \(3 p\) electrons c. the Group \(3 \mathrm{~A}\) element in the same period as \(\mathrm{Sn}\) d. the nonmetallic elements in Group \(4 \mathrm{~A}\)

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect. a. \(n=3, \ell=3, m_{\ell}=0, m_{s}=-\frac{1}{2}\) b. \(n=4, \ell=3, m_{\ell}=2, m_{s}=-\frac{1}{2}\) c. \(n=4, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-1\) e. \(n=5, \ell=-4, m_{\ell}=2, m_{s}=+\frac{1}{2}\) f. \(n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}\)

From the information below, identify element \(\mathrm{X}\). a. The wavelength of the radio waves sent by an FM station broadcasting at \(97.1 \mathrm{MHz}\) is \(30.0\) million \(\left(3.00 \times 10^{7}\right)\) times greater than the wavelength corresponding to the energy difference between a particular excited state of the hydrogen atom and the ground state. b. Let \(V\) represent the principal quantum number for the valence shell of element \(X\). If an electron in the hydrogen atom falls from shell \(V\) to the inner shell corresponding to the excited state mentioned above in part a, the wavelength of light emitted is the same as the wavelength of an electron moving at a speed of \(570 . \mathrm{m} / \mathrm{s}\) c. The number of unpaired electrons for element \(\mathrm{X}\) in the ground state is the same as the maximum number of electrons in an atom that can have the quantum number designations \(n=2\), \(m_{\ell}=-1\), and \(m_{s}=-\frac{1}{2}\) d. Let \(A\) equal the charge of the stable ion that would form when the undiscovered element 120 forms ionic compounds. This value of \(A\) also represents the angular momentum quantum number for the subshell containing the unpaired electron(s) for element \(\mathrm{X}\).

The elements \(\mathrm{Cu}, \mathrm{O}, \mathrm{La}, \mathrm{Y}, \mathrm{Ba}, \mathrm{Tl}\), and \(\mathrm{Bi}\) are all found in high- temperature ceramic superconductors. Write the expected electron configuration for these atoms.

Write equations corresponding to the following. a. the fourth ionization energy of Se b. the electron affinity of \(\mathrm{S}^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of \(\mathrm{Mg}\)
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