Domanda del libro di testo
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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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 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?
Guida verificata passo dopo passo1
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.
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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.
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01:27
Simple Cubic Unit Cell
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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02:10Atom 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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01:42Resonance Structures
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Domanda del libro di testo
Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3. (a) Use this information and Avogadro’s number (NA = 6.022 × 1023/mol) to estimate the atomic radius of sodium. (b) If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on water?
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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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