To find:
The type of unit cell of the copper.
Answer to Problem 18.47QA
Solution:
The crystalline form of copper has a face-centered unit cell.
Explanation of Solution
1) Concept:
For each type of unit cell, we can determine the number of atoms in the unit cell and calculate the mass of the unit cell using the molar mass of copper. The radius of the atom can be used to calculate the edge length. The volume of the unit cell can be determined from the edge length. Using the mass of the unit cell and its volume, we can determine the density for each type of unit cell. The calculated density that matches with the given density
2) Formula:
i)
ii)
iii)
iv)
v)
3) Given:
i) Density
ii) Radius
4) Calculations:
a. For a simple cubic unit cell:
Number of atoms per unit cell = 1
Mass of 1 atom of copper is calculated as
Calculating the edge length:
Volume of unit cell:
Calculating the density of unit cell:
b. For a bcc unit cell:
Number of atoms per cell = 2
Mass of 2 atoms of copper is calculated as
Calculating the edge length:
Volume of unit cell:
Calculating the density of unit cell:
c. For an fcc unit cell:
Number of atoms per cell = 4
Mass of 4 atoms of copper is calculated as
Calculating the edge length:
Volume of unit cell:
Calculating the density of unit cell:
Thus, the calculated density
in case of fcc unit cell matches with the given density
Thus, the face-centered cubic unit cell is consistent with the given data.
Conclusion:
The type of unit cell is determined by calculating the density of copper in each type of unit cell and comparing it with the given density.
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Chapter 18 Solutions
Chemistry: An Atoms-Focused Approach
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