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An element crystallizes in a structure where its constituent atoms touch each other strictly along tSolid State Chemistry Question

Question

An element crystallizes in a structure where its constituent atoms touch each other strictly along the body diagonal. The overall packing efficiency of this unit cell is:

Answer: B

💡 Solution & Explanation

Atoms touching strictly along the body diagonal identifies a BCC unit cell. For BCC, $4r=\sqrt{3}a$ and $Z=2$. Packing efficiency $=\frac{2\cdot\frac43\pi r^3}{a^3}=\frac{\sqrt{3}\pi}{8}\approx0.68$, i.e. $68\%$.

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