Question

Calculate the volume occupied by particle in simple cubic unit cell if volume of unit cell is $5.5 \times 10^{-22} \text{ cm}^3$.

• A. $2.88 \times 10^{-22} \text{ cm}^3$
• B. $1.87 \times 10^{-22} \text{ cm}^3$
• C. $1.02 \times 10^{-22} \text{ cm}^3$
• D. $3.44 \times 10^{-22} \text{ cm}^3$

Hint:

Simple cubic: Packing efficiency = $52.4\%$

Answer 1

The Correct Option is A

Concept: In a simple cubic unit cell:
• Only 1 atom per unit cell
• Packing efficiency = $52.4\%$

Step 1: Use packing efficiency. \[ \text{Volume occupied} = 0.524 \times \text{volume of unit cell} \]

Step 2: Substitute values. \[ = 0.524 \times 5.5 \times 10^{-22} \]

Step 3: Calculate. \[ = 2.882 \times 10^{-22} \text{ cm}^3 \]

Step 4: Conclusion.
Volume occupied $\approx 2.88 \times 10^{-22} \text{ cm}^3$ Final Answer: Option (A)