## Q. 12.3.4

An oxide of cesium crystallizes in a tetragonal unit cell with a cesium atom on each corner and at the center, as shown to the right in the following figure. There are two oxygen atoms each on four of the edges and two oxygen atoms in the interior of the cell. What is the chemical formula of the compound?

## Verified Solution

You are asked to determine the chemical formula of a compound.
You are given the arrangement of ions in the unit cell of the compound.
Corner atoms are shared with eight cells and edge atoms with four cells. Interior atoms belong entirely to the cell.

Cs at corners: 8 $\times \frac{1}{8}$ = 1 Cs

Cs at center: = 1 Cs

O on edges: (2 × 4)(¼) = 2 O

O in interior: = 2 O
2 Cs + 4 O = Cs$_{2}$O$_{4}$
Formula: CsO$_{2}$