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NEET 2008
Exam
NEET
Year
2008
Subject
Chemistry
Chapter
Solid State

NEET 2008 · Chemistry · Solid State

Percentage of free space in a body centred cubic unit cell is

Percentage of free space in a body centred cubic unit cell is

Options

  1. A30%30 \%
  2. B32%32 \%
  3. C34%34 \%
  4. D28%28 \%

Correct answer

B. 32%32 \%

Step-by-step solution

Key Idea : Packing fraction = Volume occupied by atoms in a unit cell  Volume of the unit cell =\frac{\text{ Volume occupied by atoms in a unit cell }}{\text{ Volume of the unit cell }} For body centred cube, Packing fraction =2×43πr3(4r3)3=3π8=0.68=\frac{2 \times \frac{4}{3} \pi r^3}{\left(\frac{4 r}{\sqrt{3}}\right)^3}=\frac{\sqrt{3} \pi}{8}=0.68 where, edge length a=4r3∴a=\frac{4 r}{\sqrt{3}} \therefore Volume occupied =68%=68 \% and volume vacant =32%=32 \%
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