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In a primitive simple cubic unit cell, what is the geometric distance between the next-nearest neighSolid State Chemistry Question

Question

In a primitive simple cubic unit cell, what is the geometric distance between the next-nearest neighbours (atoms across a face diagonal)?

Answer: B

💡 Solution & Explanation

In a primitive simple cubic lattice, nearest neighbours are along the edge at distance $a$. Next-nearest neighbours lie across the face diagonal. The face diagonal distance is $\sqrt{a^2+a^2}=\sqrt{2}a$.

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