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Question

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in%) of the resultant solid is closest to

A
25
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B
55
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C
35
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D
75
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Solution

The correct option is C 35
No. of atoms per unit cell :
Z=8 [corner] 18+6 [Face] 12+4 [Alternate TV]

Z=1+3+4
Z=8

It is diamond like structure in which
2r=3a4

a=(8r3)

Packing efficiency = (Z x Volume of single lattice point x 100) / volume of the unit cell
Packing efficiency=8×43πr3[8r3]3×100=35% (roughly)

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