Textbook Question
What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.
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Ch.12 - Solids and Modern Materials
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement111
- Ch.2 - Atoms, Molecules, and Ions166
- Ch.3 - Chemical Reactions and Reaction Stoichiometry138
- Ch.4 - Reactions in Aqueous Solution127
- Ch.5 - Thermochemistry104
- Ch.6 - Electronic Structure of Atoms109
- Ch.7 - Periodic Properties of the Elements107
- Ch.8 - Basic Concepts of Chemical Bonding102
- Ch.9 - Molecular Geometry and Bonding Theories120
- Ch.10 - Gases122
- Ch.11 - Liquids and Intermolecular Forces79
- Ch.12 - Solids and Modern Materials102
- Ch.13 - Properties of Solutions99
- Ch.14 - Chemical Kinetics153
- Ch.15 - Chemical Equilibrium83
- Ch.16 - Acid-Base Equilibria109
- Ch.17 - Additional Aspects of Aqueous Equilibria117
- Ch.18 - Chemistry of the Environment60
- Ch.19 - Chemical Thermodynamics109
- Ch.20 - Electrochemistry113
- Ch.21 - Nuclear Chemistry79
- Ch.22 - Chemistry of the Nonmetals52
- Ch.23 - Transition Metals and Coordination Chemistry57
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry7
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 12, Problem 33a
Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms?
Verified step by step guidance1
Identify the type of unit cell for each structure: A, B, and C.
Determine the number of atoms per unit cell for each structure.
Calculate the packing efficiency for each type of unit cell.
Compare the packing efficiencies to determine which structure(s) have the densest packing.
Conclude which structure(s) correspond to the densest packing of atoms based on the highest packing efficiency.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Cell
A unit cell is the smallest repeating unit of a crystal lattice that reflects the overall symmetry and structure of the entire crystal. It defines the arrangement of atoms in a solid and can vary in shape, such as cubic, tetragonal, or hexagonal. Understanding unit cells is crucial for analyzing the packing efficiency and density of different crystalline structures.
Atomic Packing Efficiency
Atomic packing efficiency (APE) refers to the fraction of volume in a crystal structure that is occupied by atoms. It is calculated by comparing the volume occupied by the atoms to the total volume of the unit cell. Higher packing efficiency indicates a denser arrangement of atoms, which is important for understanding the physical properties of metals and their stability.
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Atom Structure
Close-Packed Structures
Close-packed structures, such as face-centered cubic (FCC) and hexagonal close-packed (HCP), are arrangements where atoms are packed together as closely as possible. These structures maximize atomic density and are characterized by specific coordination numbers and packing efficiencies. Identifying these structures is essential for determining which metallic arrangements provide the densest packing.
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Related Practice
Textbook Question
Calcium crystallizes in a body-centered cubic structure at 467°C. (a) How many Ca atoms are contained in each unit cell?
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Textbook Question
Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (b) Which structure(s) corresponds to the least dense packing of atoms?
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Textbook Question
The unit cell of nickel arsenide is shown here. (b) What is the empirical formula?
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