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CsCl has a body-centred cubic arrangement. If the unit cell edge is denoted by a, which relation between the ionic radii is correct?

1. rCs+ + rCl− = 3a
2. rCs+ + rCl− = 3a/2
3. rCs+ + rCl− = (√3/2)a
4. rCs+ + rCl− = √3a

Correct answer: rCs+ + rCl− = (√3/2)a

Solution

In a body-centered cubic structure like CsCl, the ions touch along the body diagonal of the cube. The length of the body diagonal is equal to the sum of the ionic radii multiplied by the square root of 3, leading to the relation rCs+ + rCl− = (√3/2)a.

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