Question

The mineral perovskite has a calcium atom at each corner of the unit cell, a titanium atom at the center of the unit cell, and an oxygen atom at the center of each face. What is the chemical formula of this compound?

Short answer

The chemical formula of this compound is$CaTi{O}_3$

Step-by-step solution

The contribution of calciumatom in one unit cell.

There are 8 corners in one cube and the contribution of one atom to the unit cell is$\frac{1}{8}$; as each atom contributes to 4 unit cells up and 4 unit cells down

Therefore, the 8 calcium atoms on the corners contribute;

$8\times \frac{1}{8}=1$

The contribution of Titanium atom in one unit cell.

In the center contribution of one atom is completely 1 to one unit cell.

Therefore, as seen, the dark ball titanium contributes to one unit cell as: 1

The contribution of Oxygen atoms in one unit cell.

There are 6 faces in one cube and the contribution of one atom to the unit cell is $\frac{1}{2}$s each atom contributes to 2 unit cells

Therefore, the six (6) dark balls of oxygen atoms on the faces contribute;

$6\times \frac{1}{2}=3$

The chemical formula of the given compound.

The contribution of Ca atoms in one unit cell;

$8\times \frac{1}{8}=1$

The contribution of Ti atoms in one unit cell; 1

The contribution of O atoms in one unit cell;

$6\times \frac{1}{2}=3$

Therefore, the chemical formula becomes$CaTi{O}_3$ .