Q71 · CSIR-NET Chemistry, June 2018

Paper: CSIR-NET June 2018 · Subject: Physical Chemistry · Chapter: Solid State Chemistry · Topic: Crystal Systems Lattices · Marks: 2 · Difficulty: Medium

If all the lattice points of an FCC structure are occupied by uniform hard spheres that touch each other, the fraction of volume occupied is
(a)$\frac{\pi \sqrt{2}}{6}$
(b)$\frac{\pi \sqrt{3}}{6}$
(c)$\frac{\pi}{6}$
(d)$\frac{2 \pi}{6}$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
fcc: 4 atoms of radius a√2/4; fraction = 4 × (4/3)π(√2a/4)³/a³ = π√2/6 = 0.74.

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