Question

A solid has a structure in which $W$ atoms are located at the corners of a cubic lattice, $O$ atoms at the centre of the edges and $Na$ atoms at the centre of the cubic. The formula for the compound is:

• A. $NaW{O}_2$
• B. $NaW{O}_3$
• C. $N{a}_{2}W{O}_3$
• D. $NaW{O}_4$

Answer 1

The correct option is B $NaW{O}_3$

As $W$ atoms are located at the corners and each corner atom contributes $\frac{1}{8}$ and there are $8$ corner atoma in a cube, so the total number of $W$ atoms $=\frac{1}{8}\times 8=1$
As $Na$ is located at center and each center atom contributes fully to the unit cell, the total number of $Na$ atoms $=1$
As $O$ atom is located at edge centers and each such atom contributes $\frac{1}{4}$ and there are $12$ edge centers in a cube. the total number of $W$ atoms $=\frac{1}{4}\times 12=3$
So, the formula of compound is $NaW{O}_3$.