In the closest packing of atoms

Options

A. Coordination number of particles placed in tetrahedral voids is smaller than octahedral voids.
B. Size of tetrahedral void is larger than that of octahedral void
C. Size of voids depend upon size of atoms of atoms and tetrahedral void is smaller than octahedral void
D. Radius ratio for tetrahedral voids is smaller than octahedral void

Answer

To solve the question regarding the closest packing of atoms, we will analyze the characteristics of tetrahedral and octahedral voids in terms of their sizes and relationships with the radii of cations and anions.

### Step-by-Step Solution:

1. **Understand the Concept of Closest Packing**:
Closest packing refers to the arrangement of atoms in a solid where they occupy the least amount of space. In this arrangement, there are two types of voids formed: tetrahedral and octahedral voids.

2. **Identify the Radii Relationships**:
- For tetrahedral voids, the relationship between the radius of the cation (R⁺) and the radius of the anion (R⁻) is given by:
\[ \frac{R^+}{R^-} = 0.225 \]
- For octahedral voids, the relationship is:
\[ \frac{R^+}{R^-} = 0.414 \]

3. **Interpret the Relationships**:
- From the above equations, we can deduce that the radius of the cation in relation to the anion is smaller in the case of tetrahedral voids compared to octahedral voids. This indicates that the tetrahedral voids are smaller than the octahedral voids.

4. **Compare the Sizes of the Voids**:
- Since the size of the tetrahedral voids is determined by the smaller ratio (0.225), and the size of the octahedral voids is determined by the larger ratio (0.414), we conclude:
\[ \text{Size of octahedral voids} > \text{Size of tetrahedral voids} \]

5. **Select the Correct Option**:
- Based on the analysis, the correct statement is that the size of the octahedral voids is larger than that of the tetrahedral voids. Therefore, the correct answer is option number three.

### Final Answer:
The size of octahedral voids is larger than the size of tetrahedral voids.

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