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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 1s虏, 2s虏, 2p_x鹿, 2p_y鹿, 2p_z鈦�, 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: 1s虏, 2s虏, 2p鈦�. 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: 1s虏, 2s虏, 2p_x鹿, 2p_y鹿, 2p_z鈦� 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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electron-Electron Repulsion
Electrons are negatively charged particles, and because like charges repel each other, they are prone to experience electron-electron repulsion. In an atom, multiple electrons try to arrange themselves in such a way that they can minimize this repulsion. This is crucial because it can affect how electrons are distributed within an atom and can influence energy levels. Minimizing repulsion leads to a more stable atom since electrons will position themselves to be as far apart as possible. This principle is particularly important when understanding why electrons occupy orbitals in certain ways to achieve lower energy states.
Degenerate Orbitals
Degenerate orbitals refer to orbitals that have the same energy level. This usually occurs in sublevels like p, d, or f, where there are multiple orbitals of the same type. For example, the three p orbitals in a p subshell are degenerate. When electrons populate these orbitals, they do so by following Hund's rule. - Electrons will fill each degenerate orbital singly before any of them receives a second electron. - Placing electrons in separate orbitals reduces electron-electron repulsion and helps achieve a more energetically favored configuration. By maximizing the distance between electrons, atoms can maintain greater stability and lower energy.
Electron Configuration
Electron configuration describes the arrangement of electrons in an atom's orbitals. It follows a specific order governed by principles like the Aufbau principle, Pauli exclusion principle, and Hund's rule. For example, in an oxygen atom, the configuration is 1s虏 2s虏 2p鈦�. The electrons first fill the lowest energy orbitals (1s), then move to the higher ones (2s, 2p) while obeying Hund's rule when filling the 2p orbitals. - Electrons prefer to occupy orbitals singly within degenerate orbitals until pairing is necessary. - This system ensures that electron-electron repulsions are minimized, contributing to the stability of the atom's electron configuration.
Total Spin
Total spin refers to the cumulative spin of all electrons in an atom. Spin is a fundamental property of electrons, usually depicted as either "up" or "down". Hund's rule relates strongly to this concept as it dictates that electrons will fill degenerate orbitals in a way that maximizes total spin, meaning they will have parallel spins. - More parallel spins in degenerate orbitals leads to a lower energy state. - It also minimizes repulsion as electrons spread out in separate orbitals first. By doing this, the atom reaches a state of lower energy and thus greater stability, as interactions between electrons are controlled.
Atomic Stability
Stability in an atom is about achieving the lowest possible energy configuration. Atoms strive to minimize repulsions between electrons, which makes the arrangement of electrons across orbitals crucial in determining stability. - By spreading electrons across degenerate orbitals before pairing them up, atoms reduce the repulsive forces between electrons. - This careful distribution in adherence to Hund's rule ensures that energy levels remain minimal, enhancing stability. The concept of atomic stability is a central theme in chemical bonding and reactions, as atoms are energetically driven to reach a stable state, reducing reactivity and increasing persistence.

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Most popular questions from this chapter

Four blocks of elements in a periodic table refer to various atomic orbitals being filled. What are the four blocks and the corresponding orbitals? How do you get the energy ordering of the atomic orbitals from the periodic table? What is the aufbau principle? Hund's rule? The Pauli exclusion principle? There are two common exceptions to the ground-state electron configuration for elements \(1-36\) as predicted by the periodic table. What are they?

An ionic compound of potassium and oxygen has the empirical formula KO. Would you expect this compound to be potassium(II) oxide or potassium peroxide? Explain.

An unknown element is a nonmetal and has a valence electron configuration of \(n s^{2} n p^{4}\). a. How many valence electrons does this element have? b. What are some possible identities for this element? c. What is the formula of the compound this element would form with potassium? d. Would this element have a larger or smaller radius than barium? e. Would this element have a greater or smaller ionization energy than fluorine?

The four most abundant elements by mass in the human body are oxygen, carbon, hydrogen, and nitrogen. These four elements make up about \(96 \%\) of the human body. The next four most abundant elements are calcium, phosphorus, magnesium, and potassium. Write the expected ground-state electron configurations for these eight most abundant elements in the human body.

A particle has a velocity that is \(90 . \%\) of the speed of light. If the wavelength of the particle is \(1.5 \times 10^{-15} \mathrm{~m}\), calculate the mass of the particle.
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