Question

A compound is formed by atoms of $Na,O,X$ which has a cubic structure . $X-$atoms are located at the corners of the unit cell, $O-$atoms are located at the edges and the $Na-$ atoms at the body centres. The simplest formula of the compound is :

• A. $N{a}_{2}X{O}_3$
• B. $Na{X}_4{O}_3$
• C. $N{a}_{2}X{O}_3$
• D. $NaX{O}_3$

Answer 1

The correct option is D $NaX{O}_3$

Atom 'X' located at the corners of the cell. Each atom at corners are shared by 8 unit cells
Therefore,
$\text{No. of X atoms}=\frac{1}{8}\times 8=1$

Atom 'O' is located at cube edges. Each atom at edge is shared by 4 other unit cells
Therefore,
$\text{No. of O atoms}=\frac{1}{4}\times 12=3$

Atom 'Na' is located at centre of cube. Atom at centre is shared only be 1 unit cell.
$\text{No. of Na atoms}=\frac{1}{1}\times 1=1$
Thus, the simplest formula of the compound is $NaX{O}_3$