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NEET 2008
Exam
NEET
Year
2008
Subject
Chemistry
Chapter
Solid State

NEET 2008 · Chemistry · Solid State

If 'a' stands for the edge length of the cubic systems : simple...

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

Options

  1. A1a:3a:2a1 a: \sqrt{3} a: \sqrt{2} a
  2. B12a:34a:122a\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}}^a
  3. C12a:3a:12a\frac{1}{2} a: \sqrt{3} a: \frac{1}{\sqrt{2}} \mathrm{a}
  4. D12a:32a:22a\frac{1}{2} \mathrm{a}: \frac{\sqrt{3}}{2} \mathrm{a}: \frac{\sqrt{2}}{2} \mathrm{a}

Correct answer

B. 12a:34a:122a\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}}^a

Step-by-step solution

For simple cube, a=2ra=2 r or r=a2r=\frac{a}{2} For BCC, 4r=3a4 r=\sqrt{3} a or r=34ar=\frac{\sqrt{3}}{4} a For FCC, 4r=2a4 r=\sqrt{2} a or r=a22r=\frac{a}{2 \sqrt{2}} Thus, the ratio is 12a:34a:122a\frac{1}{2} a: \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a
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