Question

The packing factor for the FCC unit cell is

• A. 0.52
• B. 0.68
• C. 0.74
• D. 0.99

Hint:

The FCC structure has a packing factor of 0.74 (or 74%), the highest among common cubic structures. This makes FCC ideal for dense materials. The close-packed arrangement minimizes empty space, enhancing material strength and stability.

Answer 1

The Correct Option is C

The packing factor is calculated as:
\[\text{Packing Factor} = \frac{\text{Volume of atoms in a unit cell}}{\text{Volume of the unit cell}}\]
For FCC, the packing factor is:
\[\text{Packing Factor} = \frac{4 \times \frac{4}{3} \pi r^3}{a^3} = 0.74\]
where \(a = \frac{4r}{\sqrt{2}}\). This indicates that \(74\%\) of the unit cell volume is occupied by atoms.