Question

Barium titanate has the perovskite structure, i.e., a cubic lattice with $ B{a^{2 + }} $ ions at the corners of the unit cell, oxide ions at the face centres and titanium ions at the body center. The molecular formula of barium titanate is:
(A) $ BaTi{O_3} $
(B) $ BaTi{O_4} $
(C) $ BaTi{O_2} $
(D) $ BaTiO $

Answer 1

Hint: To answer this question, you must recall the formula for finding the total number of atoms in a unit cell. The perovskite structure is found in a cubic lattice, i.e. substances with a cubic unit cell. The corners contain $ \dfrac{1}{8} $ atoms, the face centres have $ \dfrac{1}{2} $ atoms and the body centre has 1 atom.

Complete step by step solution
In the perovskite structure for barium titanate, it is given that barium ions are present at the corners of the unit cell, oxide ions are present at the face centres and titanium ions are present at the body center.
Each corner in a lattice is shared by 8 other cubes. So the effective amount of a particle present at the corner in one unit cell is equal to $ \dfrac{1}{8} $ . There are 8 such corners in every cube. So the total number of barium ions in the unit cell is given by $ n = 1 $
Each face in the crystal lattice is shared by two cubic unit cells. So the effective number of the particles present at the face center in one unit cell is equal to $ \dfrac{1}{2} $ . There are 6 such faces in a cubic unit cell. So the total number of oxide ions present in the unit cell are $ n = 3 $
The body center of a cubic unit cell is not shared by any other cube. So the effective number of the particles present at the body center in one unit cell is equal to $ 1 $ . There is only one body center in an atom so, the total number of titanium ions present in the unit cell are $ n = 1 $ .
Thus, the molecular formula of barium titanate is given by $ BaTi{O_3} $ .
Thus, the correct answer is A.

Note
The edge in a cubic crystal lattice is shared by 4 other cubes. So the effective amount of a particle present at the edge in one unit cell is equal to $ \dfrac{1}{4} $ . There are 12 such edges in every cube.