For a simple cubic unit cell, what percentage of the space in the cell is occupied by the atoms at thecorners of the cell?

The packing fraction is the percentage of total space in the unit cell occupied by constituent…

Answered: For a simple cubic unit cell, what…

Chemistry: The Molecular Science

5th Edition

ISBN:9781285199047

Author:John W. Moore, Conrad L. Stanitski

Publisher:John W. Moore, Conrad L. Stanitski

Chapter9: Liquids, Solids, And Materials

Section9.6: Crystalline Solids

Problem 9.14E

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Similar questions

A portion of the crystalline lattice for potassium is illustrated below. (a) In what type of unit cell are the K atoms arranged? A portion of the solid-state structure of potassium. (b) If one edge of the potassium unit cell is 533 pm, what is the density of potassium?
Silicon carbide, SiC, is a very hard, high-melting solid. What kind of crystal forces account for these properties?
The CsCl structure is a simple cubic array of chloride ions with a cesium ion at the center of each cubic array (see Exercise 69). Given that the density of cesium chloride is 3.97 g/cm3, and assuming that the chloride and cesium ions touch along the body diagonal of the cubic unit cell, calculate the distance between the centers of adjacent Cs+ and Cl ions in the solid. Compare this value with the expected distance based on the sizes of the ions. The ionic radius of Cs+ is 169 pm, and the ionic radius of Cl is 181 pm.
Calculate the percent of volume that is actually occupied by spheres in a body-centered cubic lattice of identical spheres You can do this by first relating the radius of a sphere, r, to the length of an edge of a unit cell, l. (Note that the spheres do not touch along an edge but do touch along a diagonal passing through the body-centered sphere.) Then calculate the volume of a unit cell in terms of r. The volume occupied by spheres equals the number of spheres per unit cell times the volume of a sphere (4r3/3).
Tungsten crystallizes in the unit cell shown here. Unit cell for tungsten (a) What type of unit cell is this? (b) How many tungsten atoms occur per unit cell? (c) If the edge of the unit cell is 316.5 pm, what is the radius of a tungsten atom? (Hint: The W atoms touch each other along the diagonal line from one comer of the unit cell to the opposite comer of the unit cell.)
Calculate the percent of volume that is actually occupied by spheres in a face-centered cubic lattice of identical spheres. You can do this by first relating the radius of a sphere, r, to the length of an edge of a unit cell, l. (Note that the spheres do not touch along an edge but do touch along the diagonal of a face.) Then calculate the volume of a unit cell in terms of r. The volume occupied by spheres equals the number of spheres per unit cell times the volume of a sphere (4r3/3).
What is a lattice? What is a unit cell? Describe a simple cubic unit cell. How many net atoms are contained in a simple cubic unit cell? How is the radius of the atom related to the cube edge length for a simple cubic unit cell? Answer the same questions for the body-centered cubic unit cell and for the face-centered unit cell.
The structures of some common crystalline substances are shown below. Show that the net composition of each unit cell corresponds to the correct formula of each substance.
8.48 Why must the vapor pressure of a substance be measured only after dynamic equilibrium is established?
Shown below is the cubic unit cell of an ionic compound. Answer the questions by referring to this structure. Be careful to note that some atoms are hidden by those in front. a One of the spheres (red or green) represents a monatomic, metallic ion. The other color sphere represents a monatomic, nonmetal ion. Which spheres probably represent the metal ion? Explain. b How many red spheres are there in the unit cell? How many green ones? c From the information you have, deduce the general formula of the compound, using M for the metallic element and X for the nonmetallic element. What are the formulas of the ions? d Give an example of a compound that might have this structure. Explain why you think this compound might have this structure. Which ion of this compound would be represented by the red spheres?
Explain in words how Avogadros number could be obtained from the unit-cell edge length of a cubic crystal. What other data are required?
Rubidium chloride has the sodium chloride structure at normal pressures but assumes the cesium chloride structure at high pressures. (See Exercise 69.) What ratio of densities is expected for these two forms? Does this change in structure make sense on the basis of simple models? The ionic radius is 148 pm for Rb+ and 181 pm for CI.

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For a simple cubic unit cell, what percentage of the space in the cell is occupied by the atoms at the corners of the cell?