Q35 / 180 · KCET 2023 · Chemistry
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
- A$1 a: \sqrt{3} a: \sqrt{2} a$
- Correct answerB$\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
- 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
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
$\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
Hence, the correct answer is option: 'B'.