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
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement140
- Ch.2 - Atoms, Molecules, and Ions192
- Ch.3 - Chemical Reactions and Reaction Stoichiometry172
- Ch.4 - Reactions in Aqueous Solution156
- Ch.5 - Thermochemistry151
- Ch.6 - Electronic Structure of Atoms137
- Ch.7 - Periodic Properties of the Elements127
- Ch.8 - Basic Concepts of Chemical Bonding143
- Ch.9 - Molecular Geometry and Bonding Theories167
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces97
- Ch.12 - Solids and Modern Materials129
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics175
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Acid-Base Equilibria127
- Ch.17 - Additional Aspects of Aqueous Equilibria133
- Ch.18 - Chemistry of the Environment88
- Ch.19 - Chemical Thermodynamics140
- Ch.20 - Electrochemistry137
- Ch.21 - Nuclear Chemistry99
- Ch.22 - Chemistry of the Nonmetals66
- Ch.23 - Transition Metals and Coordination Chemistry69
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry11
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
Chapter 12, Problem 29b
The unit cell of nickel arsenide is shown here. (b) What is the empirical formula?
Verified step by step guidance1
Identify the types of atoms present in the unit cell. In this case, the blue spheres represent nickel (Ni) atoms and the orange spheres represent arsenic (As) atoms.
Count the number of each type of atom within the unit cell. Note that atoms on the corners, edges, and faces are shared with adjacent unit cells.
Determine the contribution of each atom to the unit cell. Corner atoms contribute 1/8, edge atoms contribute 1/4, face atoms contribute 1/2, and atoms entirely within the cell contribute 1.
Calculate the total number of nickel (Ni) atoms in the unit cell by summing the contributions of all Ni atoms.
Calculate the total number of arsenic (As) atoms in the unit cell by summing the contributions of all As atoms.
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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 in a crystal lattice that reflects the symmetry and structure of the entire crystal. It defines the arrangement of atoms, ions, or molecules in three-dimensional space. Understanding the dimensions and contents of the unit cell is crucial for determining the empirical formula of a compound, as it provides insight into the ratio of different types of atoms present.
Empirical Formula
The empirical formula represents the simplest whole-number ratio of the elements in a compound. It is derived from the composition of the unit cell, indicating how many atoms of each element are present in the smallest repeating unit. For compounds like nickel arsenide, determining the empirical formula involves analyzing the number of nickel and arsenic atoms within the unit cell.
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Coordination Number
The coordination number is the number of nearest neighboring atoms surrounding a central atom in a crystal structure. It is essential for understanding the geometry and stability of the crystal lattice. In the case of nickel arsenide, knowing the coordination number helps in identifying how the nickel and arsenic atoms are arranged and how they interact within the unit cell, which is vital for calculating the empirical formula.
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