Concept explainers
Metallic iron crystallizes in a cubic lattice. The unit cell edge length is 287 pm. The density of iron is 7.87 g/cm3. How many iron atoms are within a unit cell?
Interpretation:
The number of Iron atoms in unit cell of Iron cubic lattice has to be determined.
Concept introduction:
In crystalline solids, the components are packed in regular pattern and neatly stacked. The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing.
Answer to Problem 11.39QP
The number of Iron atoms in unit cell of Iron cubic lattice is
Explanation of Solution
Record the given data:
The unit cell is assumed that of a cubic shape and the edge length of the unit cell is given. Density of Iron is given.
Calculate the volume of one unit cell of cubic lattice of metallic Iron.
Edge length of the cubic unit cell is given. The cubic value of edge length gives the volume of the unit cell.
Calculate the mass of one unit cell of cubic lattice of metallic Iron.
Density of the unit cell is given. The mass of unit cell is calculated using the equation
Calculate the average mass of one Iron atom in unit cell.
The average mass of one Iron atom in its crystal lattice is calculated using the atomic mass value of Iron.
Calculate the number of Iron atoms present in a unit cell.
The average mass of one Iron atom in its crystal lattice is related to number of atoms per unit cell as follows –
Using this equation, the number of Iron atoms present per unit cell has been calculated.
The number of Iron atoms in unit cell of Iron cubic lattice has been determined.
Want to see more full solutions like this?
Chapter 11 Solutions
Chemistry
- 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.arrow_forwardCalculate 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).arrow_forwardCrystalline polonium has a primitive cubic unit cell, lithium has a body-centered cubic unit cell, and calcium has a face-centered cubic unit cell. How many Po atoms belong to one unit cell? How many Li atoms belong to one unit cell? How many Ca atoms belong to one unit cell? Draw each unit cell. Indicate on your drawing what fraction of each atom lies within the unit cell.arrow_forward
- The unit cell of silicon carbide, SiC, is illustrated below. (a) In what type of unit cell are the (dark gray) C atoms arranged? (b) If one edge of the silicon carbide unit cell is 436.0 pm, what is the calculated density of this compound? A portion of the solid-state structure of silicon carbide.arrow_forwardPalladium has a cubic crystal structure in which the edge of the unit cell is 389 pm long. If the density of palladium is 12.02 g/cm3, how many palladium atoms are in a unit cell? In which of the cubic unit cells does palladium crystallize?arrow_forwardSpinel 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?arrow_forward
- Chemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage Learning
- Chemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning