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Chapter 7: Problem 33

Does the minimization of electron-electron repulsions correlate with Hund's rule?

Short Answer

Expert verified
Yes, the minimization of electron-electron repulsions correlates with Hund's rule. Hund's rule ensures that electrons fill degenerate orbitals one at a time with the same spin orientation, thereby maximizing the total spin of the system before pairing up electrons. This arrangement effectively minimizes electron-electron repulsions, as two electrons in the same orbital have increased repulsion due to their close proximity. Distributing electrons among the available orbitals before pairing them reduces these repulsive forces, resulting in the lowest energy and most stable configuration for the atom.

Step by step solution

01

Understand electron-electron repulsions and Hund's rule

Electron-electron repulsions occur between negatively charged electrons in the same atom. In order to minimize these repulsions, electrons should be distributed among available orbitals in an organized manner. Hund's rule is one of the guiding principles in electron configuration, which states that for a given electron configuration, the term with the maximum spin multiplicity has the lowest energy.
02

Electron configuration in an atomic system

According to the Aufbau principle, electrons populate orbitals in order of increasing energy levels. Each orbital can accommodate at most 2 electrons, each with opposite spins denoted by +1/2 and -1/2. When there are multiple degenerate orbitals available (orbitals with the same energy level), electrons start to fill the orbitals one at a time with the same spin orientation. This arrangement abides by Hund's rule as it maximizes the total spin of the system before pairing up electrons in the same orbital.
03

Explanation of Hund's rule's correlation with minimization of electron-electron repulsions

As electrons fill degenerate orbitals one at a time with the same spin orientation, they remain unpaired for as long as possible, which effectively minimizes electron-electron repulsions. Two electrons in the same orbital have increased electron-electron repulsion due to their close proximity. By distributing the electrons among the available orbitals before pairing them, the electron-electron repulsions are reduced. So, the minimization of electron-electron repulsions does correlate with Hund's rule, as Hund's rule ensures that the electrons are arranged in a way that reduces repulsive forces between them, ultimately resulting in the lowest energy (and most stable) configuration for the atom.

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Most popular questions from this chapter

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. \(n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}\)

Calculate the velocities of electrons with de Broglie wavelengths of \(1.0 \times 10^{2} \mathrm{~nm}\) and \(1.0 \mathrm{~nm}\), respectively.

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms? a. The principal quantum number completely determines the energy of a given electron. b. The angular momentum quantum number, \(\ell\), determines the shapes of the atomic orbitals. c. The magnetic quantum number, \(m_{\ell}\), determines the direction that the atomic orbitals point in space.

An excited hydrogen atom emits light with a wavelength of \(397.2 \mathrm{~nm}\) to reach the energy level for which \(n=2\). In which principal quantum level did the electron begin?

The electron affinity for sulfur is more exothermic than that for oxygen. How do you account for this?
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