Search any question & find its solution
Question:
Answered & Verified by Expert
Percentage of free space in a body centre cubic unit cell is
Options:
Solution:
2112 Upvotes
Verified Answer
The correct answer is:
$32 \%$
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 $=32 \%$
$=\frac{\text { Volume occupied by atoms in a unit cell }}{\text { Volume of the unit cell }}$
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 $=32 \%$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.