Consider the body-centered cubic unit cell shown in this image. How many corner atoms are shown in the image? number of corner atoms: 8 How many body atoms are shown in the image? number of body atoms: 1 Each body atom is fully inside the boundaries of the cube. What fraction of each corner atom is inside the boundaries of the cube? 1 3 Incorrect If all the whole atoms and fractions of atoms are summed, how many atoms are actually inside a body-centered cubic unit cell? number of atoms: Incorrect

Consider the body-centered cubic unit cell shown in this image. How many corner atoms are shown in the image? number of corner atoms: 8 How many body atoms are shown in the image? number of body atoms: 1 Each body atom is fully inside the boundaries of the cube. What fraction of each corner atom is inside the boundaries of the cube? 1 3 Incorrect If all the whole atoms and fractions of atoms are summed, how many atoms are actually inside a body-centered cubic unit cell? number of atoms: Incorrect

Chemistry

9th Edition

ISBN:9781133611097

Author:Steven S. Zumdahl

Publisher:Steven S. Zumdahl

Chapter10: Liquids And Solids

Section: Chapter Questions

Problem 5RQ: What is a lattice? What is a unit cell? Describe a simple cubic unit cell. How many net atoms are...

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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.
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).
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).
Spinel is a mineral that contains 37.9% aluminum, 17.1% magnesium, and 45.0% oxygen, by mass, and has a density of 3.57 g/cm3.The edge of the cubic unit cell measures 809 pm. How many of each type of ion are present in the unit cell?
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.
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.)
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?
Aluminum metal crystallizes with a face-centered cubic unit cell. The volume of the cell is 0.0662 nm3. (a) What is the atomic radius of aluminum in cm? (b) What is the volume of a single aluminum atom? (c) What is the density of a single aluminum atom? (d) In face-centered cubic cell packing, the fraction of empty space is 26.0%. When this is factored in, what is the calculated density of aluminum?
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.
Lead has a face-centered cubic lattice with all atoms at lattice points and a unit-cell edge length of 495.0 pm. Its atomic mass is 207.2 amu. What is the density of lead?
In an FCC structure, the atoms are found on the corners of the cubic unit cell and at the center of each face. The unit cell has an edge whose length is the distance from the center of one corner atom to the center of another corner atom on the same edge. The atoms on the diagonal of any face are touching. One of the faces of the unit cell is shown below in the following: a. Show the distance dO on the sketch. Draw the boundaries of the unit cell. b. What is the relationship between the length of the face diagonal and the radius of the atoms in the cell? Face diagonal = ______________ c. How is the radius of the atoms related to dO? r= ______________ d. Silver metal crystals have an FCC structure. The unit cell edge in silver is 0.4086nm long. What is the radius of a silver atom? ______________nm
MnO has either the NaCI type structure or the CsCI type structure (see Exercise 69). The edge length of the MnO unit cell is 4.47 10-8 cm and the density of MnO is 5.28 g/cm3. a. Does MnO crystallize in the NaCl or the CsCl type structure? b. Assuming that the ionic radius of oxygen is 140. pm, estimate the ionic radius of manganese.