Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 25

Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is \(90^{\circ}\) ? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

Short Answer

Expert verified
The correct answer is (e) both rhombohedral and triclinic lattices, as they are the only ones among the given lattice types where none of the internal angles is equal to 90°.

Step by step solution

01

Orthorhombic lattice

In an orthorhombic lattice, all three axes are mutually perpendicular, which means that the internal angles are exactly 90°. So, an orthorhombic lattice does not match the required conditions.
02

Hexagonal lattice

In a hexagonal lattice, the angle between the a and b axes is 120°, while the angle between the a and c axes and between the b and c axes is 90°. By definition, the hexagonal lattice has at least one angle equal to 90°, so it doesn't satisfy the conditions.
03

Rhombohedral lattice

In a rhombohedral lattice, the angles between each pair of axes are equal and not 90° (they are equal to α). As this lattice has all internal angles not equal to 90°, it meets the required conditions. Therefore, it could be one of the answers.
04

Triclinic lattice

In a triclinic lattice, all three axes are different in length and the internal angles between them are α, β, and γ, where none of these angles is equal to 90°. Therefore, this lattice also meets the required conditions and could be another answer.
05

Both rhombohedral and triclinic

Since both rhombohedral and triclinic lattices meet the required conditions, the correct answer is (e) both rhombohedral and triclinic.

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

Silicon is the fundamental component of integrated circuits. Si has the same structure as diamond. (a) Is Si a molecular, metallic, ionic, or covalent- network solid? (b) Silicon readily reacts to form silicon dioxide, \(\mathrm{SiO}_{2,}\) which is quite hard and is insoluble in water. Is \(\mathrm{SiO}_{2}\) most likely a molecular, metallic, ionic, or covalent- network solid?

Which statement correctly describes a difference between graphene and graphite? (a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms. (c) Graphene is an insulator but graphite is a metal. (d) Graphite is pure carbon but graphene is not. \((\mathbf{e})\) The carbons are $s p^{2}\( hybridized in graphene but \)s p^{3}$ hybridized in graphite.

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

Determine if each statement is true or false: (a) Substitutional alloys are solid solutions, but interstitial alloys are heterogenous alloys. (b) Substitutional alloys have "solute" atoms that replace "solvent" atoms in a lattice, but interstitial alloys have "solute" atoms that are in between the "solvent" atoms in a lattice. (c) The atomic radii of the atoms in a substitutional alloy are similar to each other, but in an interstitial alloy, the interstitial atoms are a lot smaller than the host lattice atoms.

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) \(\mathrm{ScF}_{3} ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

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