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If 'a' stands for the edge length of the cubic systems : simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively
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The correct answer is:
$\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}}^a$
For simple cube, $a=2 r$
or $r=\frac{a}{2}$
For BCC, $4 r=\sqrt{3} a$
or $r=\frac{\sqrt{3}}{4} a$
For FCC, $4 r=\sqrt{2} a$
or $r=\frac{a}{2 \sqrt{2}}$
Thus, the ratio is $\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
or $r=\frac{a}{2}$
For BCC, $4 r=\sqrt{3} a$
or $r=\frac{\sqrt{3}}{4} a$
For FCC, $4 r=\sqrt{2} a$
or $r=\frac{a}{2 \sqrt{2}}$
Thus, the ratio is $\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
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