Match the following columns. Which of the following is correct?

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A - 1 ; B - 2 ; C - 3

A - 3 ; B - 2 ; C - 1

A - 1 ; B - 3 ; C - 2

A - 3 ; B - 1 ; C - 2

answer is C.

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Detailed Solution

A→1;B→3;C→2The Packing efficiency=Total volume of spherevolume of cube×100 (1) It represents simple cubic latticeIn simple cubic structures, each unit cell has only one atom,Packing efficiency =(43)πr3 × 100(2r)3 = 52.4% (since a=2r)(2) It represents hcp (or) ccp structure.Volume of the cube = a3 = (8r)3Volume of the sphere = (4/3) π r3No. of Sphere present in one FCC (or) ccp unit cell =4The volume of the sphere = 4 x (4/3) π r3 The packing efficiency =163πr388r3×100= 74%(3) It represents bcc structureIn body centered cubic structures, each unit cell has two atoms,Packing efficiency = 2 × (43)πr3 × 100(43r)3 = 68% (since a=4r3)

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