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Question: Answered & Verified by Expert
If ' $a$ ' stands for the edge length of the cubic systems. The ratio of radii in simple cubic, body centred cubic and face centred cubic unit cells is
ChemistrySolid StateKCETKCET 2023
Options:
  • A $1 a: \sqrt{3} a: \sqrt{2} a$
  • B $\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
  • C $\frac{1}{2} a: \frac{\sqrt{3}}{2} a: \frac{\sqrt{2}}{2} a$
  • D $\frac{1}{2} a: \sqrt{3} a: \frac{1}{\sqrt{2}} a$
Solution:
2379 Upvotes Verified Answer
The correct answer is: $\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
For simple cube,
$r=\frac{a}{2}$
For bcc, $r=\frac{a \sqrt{3}}{4}$
For $f c c, r=\frac{a}{2 \sqrt{2}}$
where, $a=$ edge length, $r=$ radius
Thus, ratio of radii of the three unit cells will be
$\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$

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