Question

which of the following cubic unit cells has the highest packing efficiency?

face-centered cubic
simple cubic
they all have the same packing efficiency.
body-centered cubic

Explanation:

Define packing efficiency

Using the Crystal Lattice knowledge point

$$ \text{Packing Efficiency} = \frac{\text{Volume occupied by spheres in unit cell}}{\text{Total volume of unit cell}} \times 100\% $$

Compare cubic unit cells

We evaluate the packing efficiencies of the three standard cubic unit cells:

• Simple cubic (SC): \(52\%\)
• Body-centered cubic (BCC): \(68\%\)
• Face-centered cubic (FCC): \(74\%\)

Identify the highest efficiency

Comparing the values:

$$ 74\% > 68\% > 52\% $$

Thus, face-centered cubic has the highest packing efficiency.

Answer:

• face-centered cubic (Correct answer)
• simple cubic
• They all have the same packing efficiency.
• body-centered cubic