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 cube. The formula of 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 atoms in a cube, so the total number of $W$ atoms $=\frac{1}{8}\times 8=1$. As $Na$ is located at centre, and each centre atom contributes fully to the unit cell, the total number of $Na$ atoms $=1$.

As $O$ atom is located at edge centre, 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 $NaW{O}_3$.