Discussion
Which of the following cubic structure is most loosely packed ?
Answer: D
The most loosely packed is the diamond structure.
Packing fractions (the fraction of volume filled by touching spheres) are: diamond \( \frac{\sqrt{3}\pi}{16} \approx 0.34 \), simple cubic \( \frac{\pi}{6} \approx 0.52 \), body-centred cubic \( \frac{\sqrt{3}\pi}{8} \approx 0.68 \), and face-centred cubic \( \frac{\sqrt{2}\pi}{6} \approx 0.74 \).
Diamond's atoms have only four nearest neighbours, set by its directed covalent bonds, which leaves much empty space. Simple cubic, with six neighbours, is the loosest of the three Bravais cubic lattices, and FCC is the most closely packed of all.
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