Domanda del libro di testo
Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is 90? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.
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Ch.12 - Solids and Modern Materials
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 12, Problema 28
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.
Guida verificata passo dopo passo1
Understand that a face-centered cubic (FCC) lattice is a type of crystal structure where atoms are located at each of the corners and the centers of all the faces of the cube.
In a face-centered cubic unit cell, there are 8 corner atoms and 6 face-centered atoms.
Each corner atom is shared by 8 adjacent unit cells, so each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
Each face-centered atom is shared by 2 adjacent unit cells, so each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
Calculate the total number of atoms in the unit cell by adding the contributions from the corner atoms and the face-centered atoms: \( 8 \times \frac{1}{8} + 6 \times \frac{1}{2} \).
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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 in the crystal and can vary in shape and size. Understanding the unit cell is crucial for determining the properties of the material, including its density and packing efficiency.
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01:27
Simple Cubic Unit Cell
Face-Centered Cubic (FCC) Lattice
A face-centered cubic lattice is a type of crystal structure where atoms are located at each corner of the cube and at the center of each face. This arrangement leads to a high packing efficiency, with each unit cell containing four atoms. The FCC structure is common in metals like copper and aluminum, influencing their physical properties.
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Percorso guidato
00:51Face Centered Cubic Example
Atomic Coordination Number
The coordination number refers to the number of nearest neighbor atoms surrounding a central atom in a crystal structure. In a face-centered cubic lattice, the coordination number is 12, indicating that each atom is in contact with 12 others. This concept is important for understanding the stability and reactivity of the material.
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00:27Coordination Numbers
Pratica correlata
Domanda del libro di testo
The unit cell of nickel arsenide is shown here. (b) What is the empirical formula?
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Domanda del libro di testo
The unit cell of a compound containing potassium, aluminum, and fluorine is shown here. (a) What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)?
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