Formula of a Compound and Number of Voids Filled

When particles are close-packed resulting in either ccp or hcp structure, two types of voids are generated. While the number of octahedral voids present in a lattice is equal to the number of close packed particles, the number of tetrahedral voids generated is twice this number. In ionic solids, the bigger ions (usually anions) form the close packed structure and the smaller ions (usually cations) occupy the voids. If the latter ion is small enough then tetrahedral voids are occupied, if bigger, then octahedral voids. All octahedral or tetrahedral voids are not occupied. In a given compound, the fraction of octahedral or tetrahedral voids that are occupied, depends upon the chemical formula of the compound.

A solid has structure in which 'W' atoms are located at corners of the unit cell. Oxygen atoms are at the edge centres and Na atoms are at the centre of cube. What is the formula of the unit cell?

NaWO₃

The correct answer is option 2. NaWO₃

'W' atoms are located at corners of the unit cell

Total number of 'W' atoms \(= \frac{1}{8}\times 8 = 1\)

Oxygen atoms are at the edge centres 

Total number of 'O' atoms \(= \frac{1}{4} \times 12 = 3\)

Na atoms are at the centre of cube

Total number of 'Na' atoms \(= 1 \times 1 = 1\)

Hence, the chemical formula of the compound is NaWO₃.