If the number of close packed sphere be N, then the number of octahedral and tetrahedral voids generated respectively are A and B that refers to

Options

A. 2N, N
B. 3N, N
C. 4N, N
D. N, 2N

Explanation

To solve the problem of determining the number of octahedral and tetrahedral voids generated when the number of close-packed spheres is \( N \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Close-Packed Structures**:
In a close-packed structure, spheres are arranged in a way that maximizes the packing efficiency. The two common types of close-packed structures are face-centered cubic (FCC) and hexagonal close-packed (HCP).

2. **Identifying the Number of Voids**:
- For every \( N \) close-packed spheres, the number of **octahedral voids** is equal to \( N \).
- The number of **tetrahedral voids** is equal to \( 2N \).

3. **Formulating the Results**:
- Therefore, if the number of close-packed spheres is \( N \):
- The number of octahedral voids \( A = N \)
- The number of tetrahedral voids \( B = 2N \)

4. **Conclusion**:
The final answer can be summarized as:
- The number of octahedral voids \( A = N \)
- The number of tetrahedral voids \( B = 2N \)

### Final Answer:
The number of octahedral voids is \( N \) and the number of tetrahedral voids is \( 2N \).

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