Question:
What is the packing efficiency in BCC unit cell ?
What is the packing efficiency in BCC unit cell ?
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BCC has 2 atoms per cell, and the atoms touch along the body diagonal.
Updated On: Nov 12, 2026
- \(24\ \%\)
- \(32\ \%\)
- \(68\ \%\)
- \(74\ \%\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
A BCC cell has 8 corner atoms and 1 body-centre atom, so \(Z = 8\times\dfrac{1}{8}+1 = 2\).
Step 2: Relation between r and a
Atoms touch along the body diagonal, so \(4r = \sqrt{3}a\), that is \(r = \dfrac{\sqrt{3}a}{4}\).
Step 3: Packing efficiency
\(\dfrac{2\times\frac{4}{3}\pi r^3}{a^3}\times 100 = \dfrac{\sqrt{3}\,\pi}{8}\times 100 \approx 68\ \%\).
Final Answer:
The packing efficiency of BCC is about 68%. \[ \boxed{\text{(C) }68\ \%} \]
A BCC cell has 8 corner atoms and 1 body-centre atom, so \(Z = 8\times\dfrac{1}{8}+1 = 2\).
Step 2: Relation between r and a
Atoms touch along the body diagonal, so \(4r = \sqrt{3}a\), that is \(r = \dfrac{\sqrt{3}a}{4}\).
Step 3: Packing efficiency
\(\dfrac{2\times\frac{4}{3}\pi r^3}{a^3}\times 100 = \dfrac{\sqrt{3}\,\pi}{8}\times 100 \approx 68\ \%\).
Final Answer:
The packing efficiency of BCC is about 68%. \[ \boxed{\text{(C) }68\ \%} \]
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