Question

$KCl$ has a rock salt lattice with edge length $=628pm$. Pick the incorrect option(s).

• A. In an unit cell, number of effective KCl molecules are 6
• B. Second nearest neighbours of $K^{+}$ are 12, their sign is negative, with a distance of 364 pm
• C. Third nearest neighbours of $K^{+}$ are 8, their sign is negative, with a distance of 544 pm
• D. Second nearest neighbours of $K^{+}$ are 12, their sign is positive, with a distance of 444 pm

Answer 1

Answer: (A), (B)

Second nearest neighbours of $K^{+}$ are 12, their sign is negative, with a distance of 364 pm

Edge length $=a=628pm$

$1^{st}$ neighbour of $K^{+}=C{l}^{-}=6\text{at}\frac{a}{2}=314pm$

6 first neighbours located at the distance of $\frac{a}{2}$. [For $K^{+}$ at body centre, these first neighbours are $6C{l}^{-}$ present at faces.]

$2^{nd}$ neighbour of $K^{+}=K^{+}=12$ at $\frac{a}{\sqrt{2}}=\frac{628}{\sqrt{2}}=444pm$

12 second neighbours located at the distance of $\frac{a}{\sqrt{2}}$[For $K^{+}$ at body centre, these second neighbours are $12K^{+}$ present at the edges].

$3^{rd}$ neighbour of $K^{+}=C{l}^{-}=8$ at $\frac{\sqrt{3a}}{2}=\frac{\sqrt{3}\times 628}{2}=544pm$

8 Third neighbours located at the distance of $\frac{\sqrt{3}a}{2}$ [For $K^{+}$ at body centre, these third neighbours are $8C{l}^{-}$ present at the corners].

In an unit cell, number of effective KCl molecules are 4.