Discussion
The packing efficiency (in %) of spheres for a body-centered cubic (bcc) lattice is approximately
Answer: B
The packing efficiency of a bcc lattice is about 68%.
A bcc cell of edge a holds 2 atoms, and they touch along the body diagonal, so \(4r = \sqrt{3}a\):
\[ \begin{aligned} f &= \frac{2 \times \tfrac{4}{3}\pi r^{3}}{a^{3}} = \frac{\sqrt{3}\pi}{8} \\ &\approx 0.680 \end{aligned} \]
74% is the value for the close-packed fcc (ccp) and hcp structures, and 52% is the simple cubic value (\(\pi/6\)). 60% matches no common lattice.
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