Question

Calculate the volume occupied by all particles in bcc unit cell if the volume of unit cell is \(8.0 \times 10^{-23} \mathrm{~cm}^3\).

• A. \(3.19\times 10^{-23}\text{ }\mathrm{cm}^{3}\)
• B. \(2.72\times 10^{-23}\text{ }\mathrm{cm}^{3}\)
• C. \(5.44\times 10^{-23}\text{ }\mathrm{cm}^{3}\)
• D. \(1.48\times 10^{-23}\text{ }\mathrm{cm}^{3}\)

Hint:

The packing efficiency of a bcc lattice is 68 percent of the unit cell volume.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Packing efficiency is the fraction of the cell volume occupied by particles.

Step 2: bcc Value
For bcc, packing efficiency \(= \dfrac{\sqrt{3}\pi}{8} \approx 0.68\).

Step 3: Calculation
Volume occupied \(= 0.68\times 8.0\times 10^{-23} = 5.44\times 10^{-23}\ \text{cm}^3\)

Final Answer:
The particles occupy \(5.44\times 10^{-23}\ \text{cm}^3\). \[ \boxed{\text{(C) }5.44\times 10^{-23}\text{ cm}^{3}} \]