/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 Many times the claim is made tha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{\ell}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{\ell}=1\)

Consider the following statement: "The ionization energy for the potassium atom is negative, because when \(\mathrm{K}\) loses an electron to become \(\mathrm{K}^{+}\), it achieves a noble gas electron configuration." Indicate everything that is correct in this statement. Indicate everything that is incorrect. Correct the incorrect information and explain.

One of the emission spectral lines for \(\mathrm{Be}^{3+}\) has a wavelength of \(253.4 \mathrm{~nm}\) for an electronic transition that begins in the state with \(n=5 .\) What is the principal quantum number of the lowerenergy state corresponding to this emission? (Hint: The Bohr model can be applied to one- electron ions. Don't forget the \(Z\) factor: \(Z=\) nuclear charge \(=\) atomic number. \()\)

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?
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Analysis

Read Explanation

Chemistry Branches

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.