Question

Calculate the total volume occupied by all particles in fcc unit cell if volume of unit cell is $6.4 \times 10^{-23}$ cm$^3$.

• A. $3.321 \times 10^{-23}$ cm$^3$
• B. $4.350 \times 10^{-23}$ cm$^3$
• C. $5.126 \times 10^{-23}$ cm$^3$
• D. $4.736 \times 10^{-23}$ cm$^3$

Hint:

Memorize the packing efficiencies for instant calculations:
- Simple Cubic (sc) = 52.4%
- Body-Centered Cubic (bcc) = 68%
- Face-Centered Cubic (fcc) ccp hcp = 74%

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Packing Efficiency (P.E.) of a unit cell is the ratio of the volume occupied by particles to the total volume of the unit cell.

Step 2: Formula Application:
For a Face-Centered Cubic (fcc) unit cell, the packing efficiency is 74% or 0.74. Total Volume of Particles = Packing Efficiency $\times$ Volume of Unit Cell.

Step 3: Explanation:
Volume $= 0.74 \times (6.4 \times 10^{-23} \text{ cm}^3)$ Volume $= 4.736 \times 10^{-23} \text{ cm}^3$.

Step 4: Final Answer:
The total volume occupied by particles is $4.736 \times 10^{-23}$ cm$^3$.