Question

Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is $1.6 \times 10^{-23} \text{ cm}^3$.

• A. $5.44 \times 10^{-24} \text{ cm}^3$
• B. $2.96 \times 10^{-24} \text{ cm}^3$
• C. $8.37 \times 10^{-24} \text{ cm}^3$
• D. $6.15 \times 10^{-24} \text{ cm}^3$

Hint:

For FCC: Volume of 1 atom $= \frac{0.74 \times \text{Volume of Unit Cell}}{4}$.

Answer 1

The Correct Option is B

Step 1: Formula
Packing Efficiency of FCC = 74% = 0.74.
Packing Efficiency $= \frac{\text{Volume of all atoms in unit cell}}{\text{Total volume of unit cell}}$
Step 2: Volume of 4 atoms
Total volume of unit cell $= 1.6 \times 10^{-23} \text{ cm}^3$.
Total volume of 4 particles $= 0.74 \times 1.6 \times 10^{-23} = 1.184 \times 10^{-23} \text{ cm}^3$.
Step 3: Volume of 1 particle
Since FCC has 4 atoms per unit cell:
Volume of 1 particle $= \frac{1.184 \times 10^{-23}}{4}$
Volume $= 0.296 \times 10^{-23} = 2.96 \times 10^{-24} \text{ cm}^3$.
Final Answer: (B)