Question

Calculate the void volume in fcc unit cell if total volume of a unit cell is \(6.4\times 10^{-23} \text{cm}^3\) ?

• A. \(3.172\times 10^{-23} \text{cm}^3\)
• B. \(3.911\times 10^{-23} \text{cm}^3\)
• C. \(1.664\times 10^{-23} \text{cm}^3\)
• D. \(2.051\times 10^{-23} \text{cm}^3\)

Hint:

fcc packing efficiency is 74 percent, so voids are 26 percent.

Answer 1

The Correct Option is C

Step 1: Fraction filled:
Atoms in fcc occupy $\frac{\pi}{3\sqrt{2}} = 0.7405$ of the cell volume.

Step 2: Empty fraction:
Empty fraction $= 1 - 0.74 = 0.26$.
$V_{void} = 0.26 \times 6.4 \times 10^{-23} = 1.664 \times 10^{-23}$ cm$^3$.

Final Answer:
Void volume $= 1.664 \times 10^{-23}$ cm$^3$, option (C). \[ \boxed{1.664 \times 10^{-23}\ \text{cm}^3} \]