Concept explainers
Interpretation:
The density of nickel having face-centered cubic unit cell is given and its atomic radius has to be determined.
Concept introduction:
In packing of atoms in a crystal structure, the atoms are imagined as spheres and closely packed in a regular pattern. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.
In face-centered cubic unit cell, each of the six corners is occupied by every single atom. Each face of the cube is occupied by one atom.
Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells. Thus the number of atoms per unit cell in FCC unit cell is,
Answer to Problem 52E
Answer
The radius of nickel atom is
Explanation of Solution
Explanation
Calculate the mass of a unit cell.
Each unit cell contains 4 Ni atoms. Therefore four times the average mass of one Ni atom gives mass of a unit cell.
Calculate the volume and edge length of the unit cell.
The volume ‘a3’ of the unit cell is calculated using
Calculate the radius of Ni atom.
The side length of fcc unit cell is given as
Conclusion
The radius of the nickel atom is determined using the concept of side length of the FCC unit cell and its relation with density given.
Want to see more full solutions like this?
Chapter 9 Solutions
CHEMISTRY:AN ATOMS FIRST...>CUSTOM PKG<
- (a) Determining an Atom Radius from Lattice Dimensions: Gold has a face-centered unit cell, and its density is 19.32 g/cm3. Calculate the radius of a gold atom. (b) The Structure of Solid Iron: Iron has a density of 7.8740 g/cm3, and the radius of an iron atom is 126 pm. Verify that solid iron has a body-centered cubic unit cell. (Be sure to note that the atoms in a body-centered cubic unit cell touch along the diagonal across the cell. They do not touch along the edges of the cell.) (Hint: The diagonal distance across the unit cell = edge 3.)arrow_forwardThe 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_forwardThe radius of gold is 144 pm, and the density is 19.32 g/cm3. Does elemental gold have a face-centered cubic structure or a body-centered cubic structure?arrow_forward
- Chemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning
- Chemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning