Question

Calculate the void volume of bcc unit cell if volume of unit cell is \(8\cdot 0\times 10^{-23}\text{ cm}^3\)

• A. \(3\cdot 08\times 10^{-23}\text{ cm}^3\)
• B. \(4\cdot 16\times 10^{-23}\text{ cm}^3\)
• C. \(5\cdot 44\times 10^{-23}\text{ cm}^3\)
• D. \(2\cdot 56\times 10^{-23}\text{ cm}^3\)

Hint:

Packing efficiency of bcc is 68 percent, so 32 percent is empty.

Answer 1

The Correct Option is D

Step 1: Derive the packing fraction:
In bcc, $\sqrt{3}a = 4r$, and there are 2 atoms: $\text{fraction} = \frac{2\times\frac{4}{3}\pi r^3}{a^3} = \frac{\sqrt{3}\pi}{8} = 0.68$.

Step 2: Void part:
Void fraction = 1 - 0.68 = 0.32. Void volume = $0.32\times 8.0\times 10^{-23} = 2.56\times 10^{-23}$ cm$^3$ (D).

Final Answer:
$2.56\times 10^{-23}$ cm$^3$. \[ \boxed{2.56\times 10^{-23}\text{ cm}^3} \]