Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 26

Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, \((\mathbf{b})\) hexagonal, \((\mathbf{c})\) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

Short Answer

Expert verified
The correct answer is (c) rhombohedral, as it has three equal edge lengths (a, a, and a) and equal angles between the edges different from \(90^{\circ}\). The orthorhombic, hexagonal, and triclinic unit cells do not have equal edge lengths.

Step by step solution

01

Analyze the orthorhombic unit cell

The orthorhombic unit cell has three unequal edge lengths (a, b, and c) that are mutually perpendicular, meaning the edge lengths are not equal to each other. This makes the answer (a) orthorhombic incorrect.
02

Analyze the hexagonal unit cell

The hexagonal unit cell has three equal edge lengths (a, a, and a) in the basal plane with angles \(120^{\circ}\), and the vertical axis is perpendicular to the basal plane with a different length (c). Therefore, the edge lengths are not all equal to each other, making the answer (b) hexagonal incorrect.
03

Analyze the rhombohedral unit cell

The rhombohedral unit cell has three equal edge lengths (a, a, and a) and angles between the edges are equal and different from \(90^{\circ}\) (given by α,β, and γ). This means that the edge lengths are equal, and the answer (c) rhombohedral is a possible correct choice.
04

Analyze the triclinic unit cell

The triclinic unit cell has three unequal edge lengths (a, b, and c) and none of the angles between the edges are equal to \(90^{\circ}\). This means that the edge lengths are not equal to each other, making the answer (d) triclinic incorrect.
05

Analyze both the rhombohedral and triclinic unit cells

Based on our previous analysis of the rhombohedral and triclinic unit cells, we know that the rhombohedral unit cell has equal edge lengths, while the triclinic unit cell does not. As a result, the answer (e) both rhombohedral and triclinic is incorrect.
06

Final answer

Taking all the information obtained in the previous steps, we find that the only unit cell with equal edge lengths, besides the cubic unit cell, is the rhombohedral unit cell. Therefore, the correct answer is (c) rhombohedral.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

What type of lattice-primitive cubic, body-centered cubic, or face-centered cubic-does each of the following (a) NaF, (b) Ag, (c) Fe, (d) \(\mathrm{CsCl}\) structure types possess: (e) \(\mathrm{ScF}_{3} ?\)

The densities of the elements Cr, Mn, Fe, and Cu are 7.15 , \(7.30,7.87,\) and \(8.96 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. One of these elements crystallizes in a face-centered cubic structure; the other three crystallize in a body-centered cubic structure. Which one crystallizes in the face- centered cubic structure? Justify your answer.

Both covalent-network solids and ionic solids can have melting points well in excess of room temperature, and both can be poor conductors of electricity in their pure form. However, in other ways their properties are quite different. (a) Which type of solid is more likely to dissolve in water? (b) Which type of solid can become a considerably better conductor of electricity via chemical substitution?

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? $(\mathbf{a}) 1,(\mathbf{b}) 2,(\mathbf{c}) 3,(\mathbf{d}) 4,(\mathbf{e}) 5 .$

What molecular structural features cause high-density polyethylene to be denser than low-density polyethylene?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

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.

Sign-up for free