Question

$CsCl$ crystallizes in B.C.C lattice. If ‘a’ is its edge length then which of the following expressions is correct?

• A. $r_{Cs}+r_{C{l}^{-}}=\frac{\sqrt{3}}{2}a$
• B. $r_{C{l}^{-}}+r_{Cs}=\sqrt{3}a$
• C. $r_{Cs}+r_{C{l}^{-}}=3a$
• D. $r_{Cs}+r_{C{l}^{-}}=\frac{3a}{2}$

Answer 1

Correct option: (A)

• ​Cesium chloride occupies a body-centered cubic lattice. Thus, the chloride ions will occupy the corners of the cube and the Cesium ion occupy the cubic void present at the center of the cubic unit cell.
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• As we can see from the structure along the body diagonal both chloride and Caesium ion touch each other.

Using the Pythagoras theorem

$\sqrt{3}a=2(r_{C{s}^{+}}+r_{C{l}^{-}})$

$r_{C{s}^{+}}+r_{C{l}^{-}}=\frac{\sqrt{3}a}{2}$

Hence, the correct option is A.