Europium crystallizes in a body-centered cubic lattice (the Eu atoms occupy only the lattice points). The density of Eu is 5.26 g/cm3. Calculate the unit cell edge length in picometers.
Interpretation:
The edge length of unit cell of Europium crystal lattice has to be calculated.
Concept Introduction:
In packing of atoms in a crystal structure, the atoms are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing forms two types of lattices – body – centered lattice and face – centered lattice.
In body-centered cubic unit cell, each of the six corners is occupied by every single atom. Center of the cube is occupied by one atom. Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared. Thus the number of atoms per unit cell in BCC unit cell is,
Answer to Problem 12.31QP
The edge length of unit cell of Europium is calculated as
Explanation of Solution
Record the given data.
Density of Europium is given which is related to mass and volume by the following equation
Calculate the mass of unit cell of Europium.
Each unit cell contains 2 Europium atoms. Therefore two times the average mass of one Europium atom gives mass of a unit cell of Europium.
Calculate the volume of unit cell of Ti.
Density of
Determine the edge length of unit cell of
Volume of the bcc unit cell of Europium is calculated in the previous step. Cube root of the volume of a bcc unit cell, gives the edge length of bcc unit cell of Europium.
The edge length of the unit cell of Europium is determined.
Want to see more full solutions like this?
Chapter 12 Solutions
Chemistry: Atoms First
- Silicon carbide, SiC, is a very hard, high-melting solid. What kind of crystal forces account for these properties?arrow_forwardThe 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_forwardThe 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_forward
- The coordination number of uniformly sized spheres in a cubic closest-packing (FCC) array is 12. Give the coordination number of each atom in (a) a simple cubic lattice. (b) a body-centered cubic lattice.arrow_forward• describe the arrangement of atoms in the common cubic crystal lattices and calculate the packing efficiency for a lattice.arrow_forward
- Chemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningPrinciples of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning
- Chemistry for Engineering StudentsChemistryISBN:9781337398909Author:Lawrence S. Brown, Tom HolmePublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning