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

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$N a W O_{2}$

$N a W O_{3}$

${NaWO}_{4}$

${Na}_{2} {WO}_{3}$

answer is B.

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Detailed Solution

Because there are eight corner atoms in a cube and W atoms are found there, the total number of $W$ atoms is equal to $\frac{1}{8}$ (the number of corner atoms). Since $N$ an is in the Centre and each Centre atom fully contributes to the unit cell, the total number of $N$ an atoms equals $= \frac{1}{8} \times 8 = 1$ .

$O$ atom is at the edge Centre, and each of these atoms contributes $\frac{1}{4}$ there are 12 edge center's in a cube; therefore, the total number of $W$ atoms is $= \frac{1}{4} \times 12 = 3$ . ${NaWO}_{3}$ is the compound's chemical formula.