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Which of the following statements is not correct?
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The correct answer is:
The fraction of the total volume occupied by the atoms in a primitive cell is 0.48
Key Idea: Packing fraction of lattice structure or fraction of total volume occupied
$=\frac{\text { Volume occupied by atoms in a unit cell }}{\text { Volume of the unit cell }}$
Packing fraction of simple cube
$\begin{gathered}
=\frac{1 \times \frac{4}{3} \pi r^3}{a^3}=\frac{1 \times \frac{4}{3} \pi r^3}{(2 r)^3} \\
=0.52
\end{gathered}$
($\because$ For primitive cell $a=2 r$)
$\therefore$ Volume occupied $=52 \%$
$=\frac{\text { Volume occupied by atoms in a unit cell }}{\text { Volume of the unit cell }}$
Packing fraction of simple cube
$\begin{gathered}
=\frac{1 \times \frac{4}{3} \pi r^3}{a^3}=\frac{1 \times \frac{4}{3} \pi r^3}{(2 r)^3} \\
=0.52
\end{gathered}$
($\because$ For primitive cell $a=2 r$)
$\therefore$ Volume occupied $=52 \%$
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