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Chapter 7: Problem 27

Many times the claim is made that subshells half-filled with electrons are particularly stable. Can you suggest a possible physical basis for this claim?

Short Answer

Expert verified
Electron configuration, which describes the distribution of electrons in orbitals, is related to the stability of subshells. Half-filled subshells are particularly stable due to three factors: minimization of electron-electron repulsion, symmetry, and exchange energy. In a half-filled subshell, electrons are spread out evenly, minimizing repulsive forces. Additionally, symmetry in electron configuration ensures even charge distribution and contributes to stability. Lastly, exchange energy, which arises due to electrons with the same spin occupying different orbitals, is at its maximum in half-filled subshells. An example of this stability can be seen in Chromium's electron configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鈦� 4s鹿, where the 3d subshell is half-filled, increasing its stability.

Step by step solution

01

Introduction to electron configuration

Electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. The arrangement is in ascending order of energy levels, with a maximum of two electrons in each orbital, thanks to the Pauli Exclusion Principle (each electron in an atom must have a unique set of quantum numbers).
02

Understanding subshells and their stability

Subshells are the subdivisions of electron shells, which are labeled as s, p, d, or f, with a specific number of orbitals and maximum electrons. For example, the s subshell has 1 orbital and can hold a maximum of 2 electrons, while the p subshell has 3 orbitals and can hold a maximum of 6 electrons. A half-filled subshell means having exactly half of the maximum number of electrons possible in a subshell. The stability of subshells is attributed to three factors: electron-electron repulsion minimization, symmetry, and exchange energy.
03

Describing physical basis for stability in half-filled subshells

1. Minimization of electron-electron repulsion: When a subshell is half-filled, the electrons in it have minimal repulsion, as they are spread out evenly among the available orbitals. This even distribution reduces the total repulsive force acting on the electrons, which increases the stability of the subshell. 2. Symmetry: Half-filled subshells are symmetrical in their electron configuration, which adds to their stability. Symmetry ensures an even distribution of charge and minimizes the energy associated with the system. 3. Exchange energy: Exchange energy arises from the requirement that electrons with the same spin must have different spatial quantum numbers in order to occupy the same orbital. In half-filled subshells, the exchange energy is at its maximum, which results in greater stability.
04

Example of a half-filled subshell

Let's consider the electron configuration of Chromium (Cr) with an atomic number of 24: Expected electronic configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鈦� 4s虏 Actual electronic configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鈦� 4s鹿 In the case of Chromium, it promotes one electron from the 4s orbital to the 3d orbital. This results in a half-filled 3d subshell (3d鈦�), which is more stable due to the reasons discussed above. This analysis demonstrates the physical basis behind the claim for stability in half-filled subshells and provides an example of an element that exhibits this stability.

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Most popular questions from this chapter

Choose the best response for the following. The ionization energy for the chlorine atom is equal in magnitude to the electron affinity for a. the \(\mathrm{Cl}\) atom. b. the \(\mathrm{Cl}^{-}\) ion. c. the \(\mathrm{Cl}^{+}\) ion. d. the \(\mathrm{F}\) atom. e. none of these. Explain each choice. Justify your choice, and for the choices you did not select, explain what is incorrect about them.

How many orbitals in an atom can have the designation \(5 p, 3 d_{z^{2}}\), \(4 d, n=5, n=4 ?\)

Which of the following orbital designations are incorrect: \(1 s, 1 p\), \(7 d, 9 s, 3 f, 4 f, 2 d ?\)

An ion having a \(4+\) charge and a mass of \(49.9\) amu has 2 electrons with principal quantum number \(n=1,8\) electrons with \(n=2\), and 10 electrons with \(n=3 .\) Supply as many of the properties for the ion as possible from the information given. (Hint: In forming ions for this species, the \(4 s\) electrons are lost before the \(3 d\) electrons.) a. the atomic number b. total number of \(s\) electrons c. total number of \(p\) electrons d. total number of \(d\) electrons e. the number of neutrons in the nucleus f. the ground-state electron configuration of the neutral atom

Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground-state electron configuration where appropriate. a. \(1 s^{2} 2 s^{2} 3 p^{1}\) b. \(1 s^{2} 2 s^{2} 2 p^{6}\) c. \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\) d. \([\mathrm{Ar}] 4 s^{2} 3 d^{5} 4 p^{1}\) How many unpaired electrons are present in each of these species?
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