Question

Ratio of packing factor of an FCC crystal to the packing factor of a simple cubic crystal is:

• A. 1.0
• B. 0.702
• C. 1.423
• D. 2.502

Hint:

FCC has a packing efficiency of about 74%, while SC has about 52%, making their ratio approximately \textbf{1.423}.

Answer 1

The Correct Option is C

Step 1: Understanding Packing Factor (PF)
Packing factor or packing efficiency is defined as the fraction of volume in a crystal structure that is occupied by constituent particles (atoms). Step 2: PF for Simple Cubic (SC)
- Number of atoms per unit cell: 1
- PF = \( \frac{\text{Volume occupied by atoms}}{\text{Volume of unit cell}} = \frac{\pi}{6} \approx 0.52 \) Step 3: PF for Face-Centered Cubic (FCC)
- Number of atoms per unit cell: 4
- PF = \( \frac{4 \times \frac{4}{3} \pi r^3}{a^3} = \frac{\pi \sqrt{2}}{6} \approx 0.74 \) Step 4: Finding the Ratio
\[ \text{Ratio} = \frac{\text{PF of FCC}}{\text{PF of SC}} = \frac{0.74}{0.52} \approx 1.423 \] Conclusion: The ratio of the packing factor of FCC to SC is approximately 1.423.