Question

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

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

Answer 1

The correct option is D $r_{C{s}^{+}}+r_{C{l}^{-}}=\frac{\sqrt{3}}{2}a$

In a body centered cubic (bcc) lattice, oppositely charged ions touch each other along the cross - diagonal of the cube.
In case of CsCl,
$2r_{C{s}^{+}}+2r_{C{l}^{-}}=\sqrt{3}a$
or $r_{C{s}^{+}}+r_{C{l}^{-}}=\frac{\sqrt{3}}{2}a$