JEE Main · 2014 · 06 Apr 2014 · Offline · Solid State

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CsCl crystallises in body centred cubic lattice. If 'a' is its edge length then which of the following expressions is correct?

(A) $r_{Cs^{+}} + r_{Cl^{-}} = \frac{3}{2} a$ ✓ Correct
(B) $r_{Cs^{+}} + r_{Cl^{-}} = 3 a$
(C) $r_{Cs^{+}} + r_{Cl^{-}} = 3 a$
(D) $r_{Cs^{+}} + r_{Cl^{-}} = \frac{3 a}{2}$

Answer: (A)

Solution

In the caesium chloride lattice one ion sits at the body centre and the others at the corners, and the two kinds of ion touch along the body diagonal of the cube. That diagonal has length

3 a

and runs from one corner through the centre to the opposite corner; over half its length it spans one cation radius and one anion radius. Hence

r_{Cs X^{+}} + r_{Cl X^{-}} = \frac{3}{2} a

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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