
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Transcribed Image Text:**Title: Calculating Atoms in a Unit Cell**
**Question:**
Calculate the total number of atoms contained within this unit cell.
**Diagram:**
The diagram shows a cubic unit cell structure with atoms represented by circles. The vertices of the cube and the centers of the cube faces are occupied by atoms. This configuration typically represents a face-centered cubic (FCC) lattice.
**Answer Choices:**
A) 8 atoms
B) 4 atoms
C) 2 atoms
D) 1 atom
**Explanation:**
In a face-centered cubic (FCC) lattice:
- Each corner atom is shared by 8 adjacent unit cells.
- Each face-centered atom is shared by 2 adjacent unit cells.
- There are 8 corner atoms (each contributing 1/8th of an atom) and 6 face-centered atoms (each contributing 1/2 of an atom).
To calculate the total number of atoms in one FCC unit cell:
- Contributions from corner atoms: \(8 \times \frac{1}{8} = 1\) atom
- Contributions from face-centered atoms: \(6 \times \frac{1}{2} = 3\) atoms
- Total number of atoms: \(1 + 3 = 4\) atoms
Thus, the correct answer is **B) 4 atoms**.
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