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Chapter 7: Problem 35

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

Short Answer

Expert verified
The minimization of electron-electron repulsions does correlate with Hund's rule. Hund's rule states that when occupying degenerate orbitals, electrons will fill the orbitals in a way that maximizes the total spin, resulting in the lowest possible energy. This distribution of electrons minimizes the electron-electron repulsions and increases the stability of the atom. For example, in the case of oxygen, the electron configuration is 1s², 2s², 2p_x¹, 2p_y¹, 2p_z⁰, where the 2p electrons have parallel spins and occupy separate orbitals, minimizing repulsive forces between them according to Hund's rule.

Step by step solution

01

Understanding electron-electron repulsions

Electron-electron repulsion is the force that occurs between two electrons due to their negative charges, causing them to repel each other. In an atom, electrons are more stable when they are farther apart, reducing the repulsive forces between them. This is a key factor in understanding Hund's rule, which relates to how electrons fill degenerate orbitals in order to minimize electron-electron repulsions and have the lowest possible energy.
02

Hund's Rule: Occupying orbitals maximizes total spin

Hund's rule states that when filling degenerate orbitals (orbitals with the same energy level), electrons will occupy the orbitals in a manner that maximizes the total spin of the electrons. The reasoning behind Hund's rule involves allowing electrons to occupy separate orbitals before pairing up, which reduces electron-electron repulsions and makes the atom more stable.
03

Applying Hund's Rule: An Example using Oxygen (O)

Oxygen has 8 electrons: 1s², 2s², 2p⁴. The first 6 electrons fill up the lower-energy 1s and 2s orbitals, while the remaining 2 electrons need to occupy the three degenerate 2p orbitals. According to Hund's rule, these electrons will not pair up in a single orbital but occupy separate orbitals with parallel spins. The electron configuration of oxygen will be: 1s², 2s², 2p_x¹, 2p_y¹, 2p_z⁰ The electrons in the 2p orbitals have parallel spins and are in separate orbitals, which minimizes electron-electron repulsions and follows Hund's rule.
04

Correlation between electron-electron repulsions and Hund's rule

The minimization of electron-electron repulsions indeed correlates with Hund's rule. Hund's rule helps ensure that electrons in an atom have the lowest possible total energy by filling degenerate orbitals in a way that maximizes the total spin. This distribution of electrons minimizes the electron-electron repulsions, making the atom more stable.

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Most popular questions from this chapter

Which of elements 1-36 have two unpaired electrons in the ground state?

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

Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers \(p, q, r\), and \(s\). The rules for these quantum numbers are as follows: \(p=1,2,3,4,5, \ldots\) \(q\) takes on positive odd integers and \(q \leq p\). \(r\) takes on all even integer values from \(-q\) to \(+q\). (Zero is considered an even number.) \(s=+\frac{1}{2}\) or \(-\frac{1}{2}\) a. Sketch what the first four periods of the periodic table will look like in this universe. b. What are the atomic numbers of the first four elements you would expect to be least reactive? c. Give an example, using elements in the first four rows, of ionic compounds with the formulas XY, \(\mathrm{XY}_{2}, \mathrm{X}_{2} \mathrm{Y}, \mathrm{XY}_{3}\), and \(\mathrm{X}_{2} \mathrm{Y}_{3}\). d. How many electrons can have \(p=4, q=3 ?\) e. How many electrons can have \(p=3, q=0, r=0\) ? f. How many electrons can have \(p=6\) ?

An excited hydrogen atom with an electron in the \(n=5\) state emits light having a frequency of \(6.90 \times 10^{14} \mathrm{~s}^{-1}\). Determine the principal quantum level for the final state in this electronic transition.

The wave function for the \(2 p_{z}\) orbital in the hydrogen atom is $$ \psi_{2 p_{i}}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{Z}{a_{0}}\right)^{3 / 2} \sigma \mathrm{e}^{-\sigma / 2} \cos \theta $$ where \(a_{0}\) is the value for the radius of the first Bohr orbit in meters \(\left(5.29 \times 10^{-11}\right), \sigma\) is \(Z\left(r / a_{0}\right), r\) is the value for the distance from the nucleus in meters, and \(\theta\) is an angle. Calculate the value of \(\psi_{2 p_{z}}^{2}\) at \(r=a_{0}\) for \(\theta=0^{\circ}(z\) axis \()\) and for \(\theta=90^{\circ}\) \((x y\) plane).
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