What is the approximate numerical value of the atomic packing factor for a simple cubic lattice?

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Multiple Choice

What is the approximate numerical value of the atomic packing factor for a simple cubic lattice?

Explanation:
APF is the fraction of space filled by the atoms inside a unit cell. For a simple cubic lattice there is effectively one atom per unit cell, since the eight corner atoms contribute 1 whole atom. The edge length a relates to the atomic radius by a = 2r, so the cell volume is a^3 = 8r^3. The volume of the single atom is (4/3)πr^3. Therefore APF = (4/3)πr^3 / 8r^3 = π/6 ≈ 0.5236. This value is lower than the packing factors of more efficiently packed structures (fcc around 0.74, bcc around 0.68), reflecting the looser packing in simple cubic.

APF is the fraction of space filled by the atoms inside a unit cell. For a simple cubic lattice there is effectively one atom per unit cell, since the eight corner atoms contribute 1 whole atom. The edge length a relates to the atomic radius by a = 2r, so the cell volume is a^3 = 8r^3. The volume of the single atom is (4/3)πr^3. Therefore APF = (4/3)πr^3 / 8r^3 = π/6 ≈ 0.5236. This value is lower than the packing factors of more efficiently packed structures (fcc around 0.74, bcc around 0.68), reflecting the looser packing in simple cubic.

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