In the closest packing of is N atoms . There are

Options

A. N' Tetrahedral voids and '2N' octahedral voids
B. 2N' Tetrahedral voids and 'N' octahedral voids
C. 2N' Tetrahedral voids and '2N' octahedral voids
D. N' Tetrahedral voids and 'N' octahedral voids

Answer

To solve the question regarding the number of tetrahedral and octahedral voids formed in the closest packing of N atoms, we can follow these steps:

### Step 1: Understanding Closest Packing
In closest packing arrangements, atoms are packed together as closely as possible. The two common types of closest packing are Face-Centered Cubic (FCC) and Hexagonal Close Packing (HCP).

### Step 2: Identifying the Number of Tetrahedral and Octahedral Voids
1. **Tetrahedral Voids**: In a closest packing arrangement, for every atom, there are 2 tetrahedral voids formed. Therefore, if there are N atoms, the number of tetrahedral voids (T) can be calculated as:
\[ T = 2N \]

2. **Octahedral Voids**: For every atom in the closest packing, there is 1 octahedral void formed. Therefore, the number of octahedral voids (O) can be calculated as:
\[ O = N \]

### Step 3: Conclusion
Based on the calculations:
- The number of tetrahedral voids formed is \( 2N \).
- The number of octahedral voids formed is \( N \).

### Final Answer
In the closest packing of N atoms, there are \( 2N \) tetrahedral voids and \( N \) octahedral voids.

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