Question

CsCl crystallizes in body centred cubic lattice. If a is its edge length, then which of the following expressions is correct?
  (A) ${{r}_{C{{s}^{+}}}}+{{r}_{C{{l}^{-}}}}=\dfrac{\sqrt{3}}{2}a$
  (B) ${{r}_{C{{s}^{+}}}}+{{r}_{C{{l}^{-}}}}=\sqrt{3}a$
  (C) ${{r}_{C{{s}^{+}}}}+{{r}_{C{{l}^{-}}}}=3a$
  (D) ${{r}_{C{{s}^{+}}}}+{{r}_{C{{l}^{-}}}}=\dfrac{3a}{2}$

Answer 1

Hint: In Caesium chloride, each Caesium ion is surrounded by 8 chloride ions at the corners of the cube. The cation is located at the center of the body centered cube and anions are at the corners. In the bcc unit cell of Caesium chloride, we have the Caesium ion in touch with the two chloride ions diagonally arranged.

Complete step by step answer:
  -Its given as the Caesium chloride (CsCl) occupies body centered cubic lattice. Thus the chloride ions will occupy the corners of the cube and the Caesium ion occupy the cubic void present in the centre of the cubic unit cell.
  - The coordination number of both Caesium and chloride ions is eight and the total number of cations and anions in the Caesium chloride crystal is one. This type of structure is also exhibited by Caesium bromide, Caesium iodide and also by many binary metallic alloys.
  - The cubic structure of Caesium chloride is given below
  

  -As we can see from the structure along the body diagonal both chloride and Caesium ion touch each other. The edge length is given as ‘a’ and hence we can write the equation for edge length in CsCl as follows,
\[Edge\text{ }length\text{ }a=\dfrac{2}{\sqrt{3}}\left( {{r}_{C{{s}^{+}}}}+{{r}_{C{{l}^{-}}}} \right)\]
 Or we can write as follows
\[{{r}_{C{{s}^{+}}}}+{{r}_{C{{l}^{-}}}}=\dfrac{\sqrt{3}}{2}a\]

Thus we can say that in Caesium chloride, the Caesium ion is in contact with chloride ion at a nearest distance equal to $\dfrac{\sqrt{3}a}{2}$.
So, the correct answer is “Option A”.

Note: Some people might confuse the structure of sodium chloride with Caesium chloride. But they are different; Caesium chloride is more stable than sodium chloride, for it produces a more stable crystal and more energy is released. Also keep in mind that on application of high pressure, the sodium chloride structure changes into Caesium chloride structure.