Which the following is true about the size of tetrahedral and octahedral voids ?

Options

A. Size of tetrahedral void = Size of octahedral void
B. Size of tetrahedral void `gt` Size of octahedral void
C. Size of tetrahedral void `lt` Size of octahedral void
D. Size of voids depends on the size of atoms present in packing

Answer

To determine the relationship between the sizes of tetrahedral and octahedral voids, we can follow these steps:

### Step 1: Understand the Types of Voids
- Tetrahedral and octahedral voids are types of interstitial spaces found in crystal lattices.
- Tetrahedral voids are formed when four spheres (atoms) are arranged at the corners of a tetrahedron, while octahedral voids are formed when six spheres are arranged at the corners of an octahedron.

**Hint:** Remember the geometric arrangement of spheres in tetrahedral and octahedral voids.

### Step 2: Count the Number of Voids
- In a close-packed structure with 'n' spheres:
- The number of tetrahedral voids is 2n.
- The number of octahedral voids is n.

**Hint:** Keep in mind the relationship between the number of spheres and the number of voids.

### Step 3: Compare the Sizes of Voids
- The size of the voids can be compared using the radius ratio (r/R), where 'r' is the radius of the void and 'R' is the radius of the spheres.
- For tetrahedral voids, the radius ratio (r/R) is approximately 0.225.
- For octahedral voids, the radius ratio (r/R) is approximately 0.414.

**Hint:** Focus on the radius ratios to understand the relative sizes of the voids.

### Step 4: Analyze the Implications of the Ratios
- Since the radius ratio for octahedral voids (0.414) is greater than that for tetrahedral voids (0.225), it indicates that octahedral voids are larger than tetrahedral voids.

**Hint:** Larger radius ratios imply larger void sizes.

### Step 5: Conclusion
- Based on the analysis, we conclude that the size of tetrahedral voids is less than the size of octahedral voids. Therefore, the correct statement is that tetrahedral voids are smaller than octahedral voids.

**Hint:** Summarize your findings to reinforce the conclusion.

### Final Answer
The correct statement is: "The size of tetrahedral voids is less than the size of octahedral voids."