Domanda del libro di testo
Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres.
(c) The unit cell edge length is 5.550 Å. Determine the density of Na2O.
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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 114b
Energy bands are considered continuous due to the large number of closely spaced energy levels. The range of energy levels in a crystal of copper is approximately 1 × 10–19 J. Assuming equal spacing between levels, the spacing between energy levels may be approximated by dividing the range of energies by the number of atoms in the crystal. (b) Determine the average spacing in J between energy levels in the copper metal in part (a).
Guida verificata passo dopo passo1
Identify the given information: the range of energy levels in the copper crystal is approximately \(1 \times 10^{-19}\) J.
Assume that the energy levels are equally spaced.
To find the average spacing between energy levels, divide the total range of energy levels by the number of atoms in the crystal.
Express the formula for average spacing as: \( \text{Average spacing} = \frac{\text{Total energy range}}{\text{Number of atoms}} \).
Substitute the given values into the formula to calculate the average spacing.
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Energy Bands
Energy bands in solids arise from the overlap of atomic orbitals in a crystal lattice, leading to a continuum of energy levels. In metals like copper, these bands allow for the conduction of electricity as electrons can move freely between closely spaced energy levels. Understanding energy bands is crucial for analyzing the electrical and thermal properties of materials.
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03:13
Intepreting the Band of Stability
Energy Level Spacing
The spacing between energy levels in a solid can be approximated by dividing the total range of energy levels by the number of available states, which is often related to the number of atoms in the crystal. This concept is essential for determining how energy is quantized in a material and influences its electronic properties, such as conductivity and band gap.
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01:26Nature of Energy
Crystal Structure
The arrangement of atoms in a crystal structure significantly affects its physical properties, including energy levels and band formation. In metals like copper, the face-centered cubic (FCC) structure allows for a high density of atoms, contributing to the close spacing of energy levels. Understanding crystal structure is vital for predicting how materials will behave under various conditions.
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01:42Resonance Structures