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Copper has the face centred cubic struct...

Copper has the face centred cubic structure. The coordination number of each ion is:
a) 4
b) 12
c) 14
d) 8

A

4

B

12

C

14

D

8

Text Solution

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The correct Answer is:
To determine the coordination number of copper in a face-centered cubic (FCC) structure, we can follow these steps: ### Step 1: Understand the FCC Structure In a face-centered cubic structure, atoms are located at each of the corners of the cube and at the center of each face of the cube. ### Step 2: Identify the Atoms Surrounding a Central Atom The coordination number is defined as the number of nearest neighboring atoms surrounding a particular atom. For an atom located at the center of a face in the FCC structure, we need to identify how many atoms are closest to it. ### Step 3: Visualize the Arrangement 1. **Corner Atoms**: There are 8 corner atoms in the cube, each shared by 8 adjacent cubes. However, for the coordination number, we consider only the atoms that are in direct contact with the central atom. 2. **Face-Centered Atoms**: The atom at the center of the face is surrounded by 4 corner atoms on that face and 4 additional atoms from the opposite face. ### Step 4: Count the Nearest Neighbors For an atom at the face center: - It has 4 nearest neighbors from the same face. - It also has 4 nearest neighbors from the opposite face. - Therefore, the total number of nearest neighbors is \(4 + 4 = 8\). ### Step 5: Consider the Edge Atoms In addition to the face-centered atoms, we also need to consider the atoms that are located along the edges of the cube. Each edge atom is shared between two adjacent cubes, but they also contribute to the coordination number. ### Step 6: Final Count of Coordination Number In total, for an atom in the FCC structure, the nearest neighbors count up to 12: - 4 from the same face, - 4 from the opposite face, - 4 from the edges. Thus, the coordination number of copper in the FCC structure is **12**. ### Conclusion The correct answer is **b) 12**. ---

To determine the coordination number of copper in a face-centered cubic (FCC) structure, we can follow these steps: ### Step 1: Understand the FCC Structure In a face-centered cubic structure, atoms are located at each of the corners of the cube and at the center of each face of the cube. ### Step 2: Identify the Atoms Surrounding a Central Atom The coordination number is defined as the number of nearest neighboring atoms surrounding a particular atom. For an atom located at the center of a face in the FCC structure, we need to identify how many atoms are closest to it. ...
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