Question

The volume of simple unit cell is \( x \times 10^{-23} \text{ cm}^3 \). Calculate the value of \( x \) if volume occupied by a particle in it is \( 2.1 \times 10^{-23} \text{ cm}^3 \).

• A. 3.0
• B. 3.5
• C. 4.0
• D. 4.5

Hint:

Simple Cubic = \(52%\), BCC = \(68%\), FCC = \(74%\) volume occupied.

Answer 1

The Correct Option is C

Step 1: Concept
Packing efficiency defines the percentage of total volume occupied by particles in a unit cell.

Step 2: Meaning
For a simple cubic unit cell, the packing efficiency is approximately \(52.4%\).

Step 3: Analysis
Packing Efficiency = \(\frac{\text{Volume of particle}}{\text{Volume of unit cell}} \times 100\).
\(52.4 = \frac{2.1 \times 10^{-23}}{x \times 10^{-23}} \times 100\).
\(x = \frac{2.1 \times 100}{52.4} \approx 4.0\).

Step 4: Conclusion
The value of \(x\) is \(4.0\). Final Answer: (C)