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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=4rA3

a2=1.54rA3

=32(4rA3)
a2=23rA

Packing efficiency =(43πr3A×1)+(43πr3B×1)a32×100

= (43πr3A)+(43πr3B)(23rA)3×100

= 43πr3A×98×33r3A×100

= π23×100

= 90.72%

= 90%

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