Concept explainers
Consider the three types of cubic units cells.
- (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cube’s edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)πr3, where r is the radius of the sphere.)
- (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?
(a)
Interpretation:
Percentage of occupied space within the unit cell has to be calculated.
Concept introduction:
Answer to Problem 50GQ
Percentage of occupied space within the unit cell is given below
More dense is FCC and least dense is simple primitive
Explanation of Solution
Calculate the packing efficiency of primitive cell
Calculate the packing efficiency of FCC
One unit cell of the fcc contains four atoms therefore,
Calculate the packing efficiency of BCC
By comparing packing efficiency percentage of the above three unit cell more the percentage, more the dense, therefore,
More dense is FCC and least dense is simple primitive
(b)
Interpretation:
On comparing the percentage of occupied space in PC with BCC and FCC, most dense and least dense has to be identified.
Concept introduction:
Answer to Problem 50GQ
More dense is FCC and least dense is simple primitive
Explanation of Solution
Percentage of occupied space within the unit cell is given below
By comparing packing efficiency percentage of the above three unit cell more the percentage, more the dense, therefore,
More dense is FCC and least dense is simple primitive
Want to see more full solutions like this?
Chapter 12 Solutions
Chemistry & Chemical Reactivity
Additional Science Textbook Solutions
General, Organic, and Biological Chemistry - 4th edition
Organic Chemistry (8th Edition)
Introduction to Chemistry
Chemistry: Atoms First
Fundamentals of Heat and Mass Transfer
- Palladium 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_forwardIf an ionic solid has an fcc lattice of anions (X) and all of the tetrahedral holes are occupied by metal cations (M), is the formula of the compound MX, MX2, or M2X?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
- What is the relationship between the structures of buckminsterfullerene and carbon nanotubes?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_forwardDescribe the structural units in (a) C (graphite) (b) SiC (c) FeCl2 (d) C2H2arrow_forward
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher: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: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningPhysical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,