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In a pure Face-Centred Cubic (FCC) lattice, what exact fraction of the unit cell edge length is NOT Solid State Chemistry Question

Question

In a pure Face-Centred Cubic (FCC) lattice, what exact fraction of the unit cell edge length is NOT covered by the electron clouds of the corner and face-centred atoms?

Answer: C

💡 Solution & Explanation

In FCC, atoms touch along the face diagonal, so $4r=\sqrt{2}a$ and $2r/a=1/\sqrt{2}=0.707$. Along a unit-cell edge, the uncovered fraction is $1-0.707=0.293$.

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