Textbook Question
The density of a sample of metal was measured to be 6.84 g>cm3. An X-ray diffraction experiment measures the edge of a face-centered cubic cell as 350.7 pm. What is the atomic weight, atomic radius, and identity of the metal?
Ch.12 - Solids and Solid-State Materials
Chapter 12, Problem 50
Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl (Figure 12.11). How many Na+ ions touch each H- ion, and how many H- ions touch each Na+ ion?
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Identify the structure of the face-centered cubic (fcc) unit cell, which is characterized by atoms at each of the eight corners and one atom at the center of each face of the cube.
Recognize that in a NaCl-type structure, the cations (Na+) and anions (H-) alternate positions in the lattice. Each type of ion is surrounded by the other type in the structure.
Determine the coordination number for each ion, which is the number of nearest neighboring ions of the opposite charge that an ion touches directly. In an fcc lattice like NaCl, each ion is surrounded by six ions of the opposite charge.
Apply this understanding to NaH, where Na+ ions and H- ions alternate in the same manner. Each Na+ ion is surrounded by six H- ions and vice versa.
Conclude that in the NaH structure, each Na+ ion touches six H- ions, and each H- ion touches six Na+ ions.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ionic Bonding
Ionic bonding occurs when atoms transfer electrons, resulting in the formation of charged ions. In sodium hydride (NaH), sodium (Na) donates an electron to hydrogen (H), creating Na+ and H- ions. Understanding ionic bonding is crucial for analyzing the interactions between these ions in the crystal lattice.
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Chemical Bonds
Crystal Lattice Structure
A crystal lattice structure is a three-dimensional arrangement of atoms or ions in a crystalline material. In the case of NaH, it adopts a face-centered cubic (FCC) structure similar to NaCl, where each ion occupies specific positions in the lattice. This arrangement influences how ions interact with each other, including how many of one type of ion are in contact with another.
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Coordination Number
The coordination number refers to the number of nearest neighbor ions surrounding a given ion in a crystal lattice. For NaH, determining how many Na+ ions touch each H- ion and vice versa involves calculating the coordination numbers for both ions based on their positions in the FCC structure. This concept is essential for understanding the spatial relationships and interactions between ions in the lattice.
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Related Practice
Textbook Question
If a protein can be induced to crystallize, its molecular structure can be determined by X-ray crystallography. Protein crystals, though solid, contain a large amount of water molecules along with the protein. The protein chicken egg-white lysozyme, for instance, crystallizes with a unit cell having angles of 90° and with edge lengths of 7.9 * 103 pm, 7.9 * 103 pm, and 3.8 * 103 pm. There are eight molecules in the unit cell. If the lysozyme molecule has a molecular weight of 1.44 * 104 and a density of 1.35 g>cm3, what percent of the unit cell is occupied by the protein?
Textbook Question
Iron crystallizes in a body-centered cubic unit cell with an edge length of 287 pm. Iron metal has a density of 7.86 g>cm3 and a molar mass of 55.85 g. Calculate a value for Avogadro's number.
Textbook Question
Cesium chloride crystallizes in a cubic unit cell with Cl- ions at the corners and a Cs+ ion in the center. Count the numbers of + and - charges, and show that the unit cell is electrically neutral.
Textbook Question
If the edge length of an NaH unit cell is 488 pm, what is the length in picometers of an Na¬H bond? (See Problem 12.50.)
Textbook Question
Silicon carbide, SiC, is a covalent network solid with a structuresimilar to that of diamond. Sketch a small portion ofthe SiC structure.