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Choose the Best Answer · Q16

Q.If 'a' stands for the edge length of the cubic system; sc, bcc, and fcc. Then the ratio of radii of spheres in these systems will be respectively.

(a) 12a:32a:22a\dfrac{1}{2}a : \dfrac{\sqrt{3}}{2}a : \dfrac{\sqrt{2}}{2}a
(b) 1a:3a:2a\sqrt{1}a : \sqrt{3}a : \sqrt{2}a
(c) 12a:34a:122a\dfrac{1}{2}a : \dfrac{\sqrt{3}}{4}a : \dfrac{1}{2\sqrt{2}}a
(d) 12a:3a:12a\dfrac{1}{2}a : \sqrt{3}a : \dfrac{1}{\sqrt{2}}a
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Step 1. Simple cubic: atoms touch along the edge, a=2r⇒rsc=a2a = 2r \Rightarrow r_{sc} = \dfrac{a}{2}.

Step 2. Body-centred cubic: atoms touch along the body diagonal, 3a=4r⇒rbcc=34a\sqrt{3}a = 4r \Rightarrow r_{bcc} = \dfrac{\sqrt{3}}{4}a.

Step 3. Face-centred cubic: atoms touch along the face diagonal, 2a=4r⇒rfcc=a22=122a\sqrt{2}a = 4r \Rightarrow r_{fcc} = \dfrac{a}{2\sqrt{2}} = \dfrac{1}{2\sqrt{2}}a. …

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