Question:
The maximum proportion of available volume that can be filled by hard spheres in diamond is ________.
The maximum proportion of available volume that can be filled by hard spheres in diamond is ________.
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The maximum proportion of available volume that can be filled by hard spheres in diamond is ____.
Updated On: Apr 15, 2026
- 0.52
- 0.34
- 0.32
- 0.68
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Packing fraction is the ratio of the volume occupied by particles to the total volume of the unit cell.
Step 2: Formula
For a diamond cubic structure, the packing efficiency is given by the formula: $\text{Packing fraction} = \frac{\pi\sqrt{3}}{16}$
Step 3: Calculation
$\frac{\pi\sqrt{3}}{16} \approx 0.34$
Step 4: Conclusion
The maximum proportion of volume filled is 0.34 or 34%.
Final Answer: (B)
Packing fraction is the ratio of the volume occupied by particles to the total volume of the unit cell.
Step 2: Formula
For a diamond cubic structure, the packing efficiency is given by the formula: $\text{Packing fraction} = \frac{\pi\sqrt{3}}{16}$
Step 3: Calculation
$\frac{\pi\sqrt{3}}{16} \approx 0.34$
Step 4: Conclusion
The maximum proportion of volume filled is 0.34 or 34%.
Final Answer: (B)
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