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: Understanding the Concept:
The packing efficiency of a bcc structure is 68 percent, so 32 percent of the unit cell volume is void space.

Step 2: Calculation:
\[ V_{void} = 0.32\times 8.0\times 10^{-23} = 2.56\times 10^{-23}\text{ cm}^3 \]
The value \(5.44\times10^{-23}\) cm\(^3\) is the volume occupied by atoms (68 percent), so it is not the void volume.

Final Answer:
The void volume is \(2.56\times 10^{-23}\) cm\(^3\), option (D). \[ \boxed{2.56\times 10^{-23}\text{ cm}^3} \]