The total number of octahedral void (s) per atom present in a cubic close packed structure is

Options

A. 2
B. 4
C. 1
D. 3

Answer

To determine the total number of octahedral voids per atom in a cubic close-packed (CCP) structure, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure**:
- Recognize that a cubic close-packed (CCP) structure is equivalent to a face-centered cubic (FCC) unit cell.

2. **Calculate the Number of Atoms in the Unit Cell**:
- In an FCC unit cell, atoms are located at the corners and the face centers.
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell. Therefore, the contribution from the corners is:
\[ 8 \times \frac{1}{8} = 1 \text{ atom} \]
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom to the unit cell. Therefore, the contribution from the face centers is:
\[ 6 \times \frac{1}{2} = 3 \text{ atoms} \]
- Adding these contributions together gives:
\[ 1 + 3 = 4 \text{ atoms} \]

3. **Identify the Octahedral Voids**:
- In an FCC structure, octahedral voids are located at the body center and the edge centers.
- There is 1 body-centered void, which contributes fully (100%):
\[ 1 \text{ (body center)} \]
- There are 12 edge centers, each contributing \( \frac{1}{4} \) of a void. Therefore, the contribution from the edge centers is:
\[ 12 \times \frac{1}{4} = 3 \text{ voids} \]
- Adding these contributions together gives:
\[ 1 + 3 = 4 \text{ octahedral voids} \]

4. **Calculate the Number of Octahedral Voids per Atom**:
- Since there are 4 octahedral voids for 4 atoms in the unit cell, the number of octahedral voids per atom is:
\[ \frac{4 \text{ octahedral voids}}{4 \text{ atoms}} = 1 \text{ octahedral void per atom} \]

5. **Final Answer**:
- Therefore, the total number of octahedral voids per atom in a cubic close-packed structure is **1**.