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JIPMER 2014

Exam: JIPMER
Year: 2014
Subject: Chemistry
Chapter: Solid State

JIPMER 2014 · Chemistry · Solid State

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

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

Options

A $30 \%$
B $32 \%$
C $34 \%$
D $28 \%$

Correct answer

B. $32 \%$

Step-by-step solution

Packing fraction

=\frac{\text{ Volume occupied by atoms in a unit cell }}{\text{ Volume of the unit cell }}

For body centred cube, Packing fraction

=\frac{2 \times \frac{4}{3} \pi r^3}{\left(\frac{4 r}{\sqrt{3}}\right)^3}=\frac{\sqrt{3} \pi}{8}=0.68 \therefore \quad

Volume occupied

=68 \%

and volume vacant

=32 \%

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