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Question

Packing density in identical solid spheres is 74% in:

A
simple cubic
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B
fcc
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C
hcp
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D
bcc
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Solution

The correct options are
B hcp
C fcc
For fcc:
4R=2aR=24a
Packing factor=VsVc=4×4π3R3a3=4×4π3×(24a)3a3
=2π6=74.05%

For hcp:
c=83a,R=a2
Packing factor =VsVc=6×4π3R36×12×32a2×c=6×4π3×(a2)26×12×32a2×83a
=2π6=74.05%

1491009_213022_ans_02ae1ed9e136467c9fb7569a578657ff.PNG

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