Question

In the $NaCl$ type structure shortest distance between two nearest neighbours is 100 pm, then the distance between two next nearest neighbours in the same unit cell will be:

• A. $100/\sqrt{2}$pm
• B. $100\sqrt{2}$pm
• C. $200$ pm
• D. $200\sqrt{2}$

Answer 1

The correct option is B $100\sqrt{2}$pm

$\begin{array}{c}\text{NaCl structure}\Rightarrow \\ \text{Cl- ions in FCC lattice and}{Na}^{+}\text{in octahedral void.}\\ \text{Shortest distance between nearest neighbours}=2r=\frac{a}{\sqrt{2}}\\ \text{Distance between two next nearest neighbour}=a\\ \text{Given,}\frac{a}{\sqrt{2}}=100pm\Rightarrow a=100\sqrt{2}pm\end{array}$