Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 38

Calculate the number of spheres that would be found within a simple cubic, a body-centered cubic, and a face-centered cubic cell. Assume that the spheres are the same.

Short Answer

Expert verified
A simple cubic cell contains 1 sphere, a body-centered cubic cell contains 2 spheres, and a face-centered cubic cell contains 4 spheres.

Step by step solution

01

Analyze a Simple Cubic Cell

A simple cubic cell has one sphere at each of its eight corners. However, these spheres are shared among eight different cells. Therefore, only 1/8 of each sphere is within one cell. To get the number of spheres in a single simple cubic cell, the 1/8 is multiplied by the total number of corners, which is 8. This results in a value of 1, meaning 1 sphere is found in a simple cubic cell.
02

Analyze a Body-Centered Cubic Cell

A body-centered cubic cell has the same spheres at its corners as a simple cubic cell, but with an additional sphere at the center of the cell. This center sphere is totally within the cell and isn't shared with any other cells. Therefore, the total number of spheres in a body-centered cubic cell is the 1 sphere from the corners (like the simple cubic cell) plus the 1 sphere at the center, for a total of 2 spheres.
03

Analyze a Face-Centered Cubic Cell

A face-centered cubic cell has spheres at its corners like the simple cubic cell, plus an additional sphere at the center of each of its six faces. Each of these face-center spheres is shared with exactly one other adjacent cube. Therefore, it counts as half (1/2) of a sphere within the cell. To get the total number of spheres, add the 1 sphere from the corners, plus 1/2 sphere for each of the 6 faces, for a total value of 1 (from corners) + 3 (from faces) = 4 spheres.

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

A solid is hard, brittle, and electrically nonconducting. Its melt (the liquid form of the substance) and an aqueous solution containing the substance conduct electricity. Classify the solid.

Crystalline silicon has a cubic structure. The unit cell edge length is \(543 \mathrm{pm}\). The density of the solid is \(2.33 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the number of Si atoms in one unit cell.

Explain how water's phase diagram differs from those of most substances. What property of water causes the difference?

What is a phase change? Name all possible changes that can occur among the vapor, liquid, and solid phases of a substance.

Freeze-dried coffee is prepared by freezing brewed coffee and then removing the ice component with a vacuum pump. Describe the phase changes taking place during these processes.
See all solutions

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

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