In the closet packing of atoms, there are:

Options

A. one tetrahedral void and two octahedral voids per atom
B. two tetrahedral voids and one octahedral void per atom
C. two of each tertrahedral and octahedral voids per atom
D. one of each tetrahedral and octahedral voids per atom

Answer

To solve the question regarding the closest packing of atoms and the number of voids present, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Closest Packing**: In the closest packing of atoms, atoms are arranged in a way that maximizes their packing efficiency. The two common arrangements are face-centered cubic (FCC) and hexagonal close-packed (HCP).

2. **Identify the Number of Atoms in Unit Cell**: In a face-centered cubic (FCC) structure, there are 4 atoms per unit cell. In a hexagonal close-packed (HCP) structure, there are also effectively 6 atoms per unit cell when considering the arrangement.

3. **Calculate Tetrahedral Voids**:
- The number of tetrahedral voids in a closest packed structure is given by the formula:
\[ \text{Number of Tetrahedral Voids} = 2n \]
- For FCC, where \( n = 4 \):
\[ \text{Tetrahedral Voids} = 2 \times 4 = 8 \]
- For HCP, where \( n = 6 \):
\[ \text{Tetrahedral Voids} = 2 \times 6 = 12 \]

4. **Calculate Octahedral Voids**:
- The number of octahedral voids in a closest packed structure is given by the formula:
\[ \text{Number of Octahedral Voids} = n \]
- For FCC, where \( n = 4 \):
\[ \text{Octahedral Voids} = 4 \]
- For HCP, where \( n = 6 \):
\[ \text{Octahedral Voids} = 6 \]

5. **Determine the Ratio of Voids to Atoms**:
- For FCC:
- Tetrahedral voids per atom = \( \frac{8}{4} = 2 \)
- Octahedral voids per atom = \( \frac{4}{4} = 1 \)
- For HCP:
- Tetrahedral voids per atom = \( \frac{12}{6} = 2 \)
- Octahedral voids per atom = \( \frac{6}{6} = 1 \)

6. **Choose the Correct Option**: Based on the calculations:
- There are 2 tetrahedral voids and 1 octahedral void per atom in both FCC and HCP arrangements. Therefore, the correct option is:
- **2 tetrahedral voids and 1 octahedral void per atom**.

### Final Answer:
The correct answer is: **2 tetrahedral voids and 1 octahedral void per atom**.

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