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Question

# Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

A
65%
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B
90%
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C
75%
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D
45%
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Solution

## The correct option is B 90%Packing efficiency = Volume occupied by sphereVolume of cube×100 taking rA as the radius of atom A rB as the radius of atom B a1 is the edge length of solid 1 and a2 is the edge length of solid 2 Given, rB=2rA a2=a1+50100=1.5a1 For bcc lattice: 4rA=√3a1 rA=√3a14 a1=4rA√3 a2=1.54rA√3 =32(4rA√3) a2=2√3rA Packing efficiency =(43πr3A×1)+(43πr3B×1)a32×100 = (43πr3A)+(43πr3B)(2√3rA)3×100 = 43πr3A×98×3√3r3A×100 = π2√3×100 = 90.72% = 90%

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