/*! 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 15 Atoms are assumed to touch in cl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 15

Atoms are assumed to touch in closest packed structures, yet every closest packed unit cell contains a significant amount of empty space. Why?

Short Answer

Expert verified
The presence of empty space in closest packed structures, such as face-centered cubic (fcc) and hexagonal closest packed (hcp) arrangements, is due to the spherical shape of atoms. Even when atoms are packed as closely as possible, their spherical nature results in empty spaces called interstitial spaces between them. These unoccupied spaces account for approximately 26% of the total volume in closest packed structures, making the packing efficiency about 74%. It is impossible to fill these spaces with additional atoms without expanding the lattice or changing the arrangement of existing atoms.

Step by step solution

01

Closest packed structures of atoms

Closest packed structures are arrangements of atoms in crystal lattice where the atoms are packed as closely as possible. There are two main types of closest packed structures: hexagonal closest packed (hcp) and face-centered cubic (fcc) structures. In both these structures, the atoms occupy a certain pattern which minimizes the interstitial spaces between them.
02

Properties of closest packed structures

In closest packed structures, each atom has 12 nearest neighbors (in fcc and hcp). The packing efficiency, which is the ratio of the volume occupied by the atoms to the total volume of the crystal, is approximately 74% for both fcc and hcp structures. This means that approximately 26% of the crystal volume is empty space.
03

Reason for empty space in closest packed structures

The reason for the existence of empty space in closest packed structures is due to the fact that atoms are spherical in shape. When arranging spheres in the most compact way possible (face-centered cubic or hexagonal close-packed arrangement), there will still be some leftover space, called interstitial space, between the spheres. It is impossible to completely fill this space with additional atoms without expanding the lattice or altering the arrangement of the existing atoms. So, even in the densest arrangement, the closest packed structures will always contain some amount of empty space.

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

When 1 mol benzene is vaporized at a constant pressure of \(1.00\) atm and at its boiling point of \(353.0 \mathrm{~K}, 30.79 \mathrm{~kJ}\) of energy (heat) is absorbed and the volume change is \(+28.90 \mathrm{~L}\). What are \(\Delta E\) and \(\Delta H\) for this process?

Selenium is a semiconductor used in photocopying machines. What type of semiconductor would be formed if a small amount of indium impurity is added to pure selenium?

Which are stronger, intermolecular or intramolecular forces for a given molecule? What observation(s) have you made that support this? Explain.

\(\mathrm{X}\) rays of wavelength \(2.63\) 脜 were used to analyze a crystal. The angle of first-order diffraction \((n=1\) in the Bragg equation) was \(15.55\) degrees. What is the spacing between crystal planes, and what would be the angle for second-order diffraction \((n=2)\) ?

Predict which substance in each of the following pairs would have the greater intermolecular forces. a. \(\mathrm{CO}_{2}\) or \(\mathrm{OCS}\) b. \(\mathrm{SeO}_{2}\) or \(\mathrm{SO}_{2}\) c. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) or \(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) d. \(\mathrm{CH}_{3} \mathrm{CH}_{3}\) or \(\mathrm{H}_{2} \mathrm{CO}\) e. \(\mathrm{CH}_{3} \mathrm{OH}\) or \(\mathrm{H}_{2} \mathrm{CO}\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

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.