Question

A compound of ‘A’ and ‘B’ crystallises in a cubic lattice in which ‘A’ atoms occupy the lattice points at the corners of the cube. The ‘B’ atoms occupy the centre of each face of the cube. The probable empirical formula of the compound is:

• A. AB\(_2\)
• B. A\(_2\)B
• C. AB
• D. AB\(_3\)

Hint:

In crystal lattice problems:

Corner atom contribution = ( frac18 )
Face-centre atom contribution = ( frac12 )
Always calculate the effective number of atoms per unit cell.

Answer 1

The Correct Option is A

Step 1: Count the contribution of atom A. Atom A occupies the corners of the cube. There are \(8\) corner atoms and each corner atom is shared by \(8\) unit cells. \[ \text{Effective number of A atoms} = 8 \times \frac{1}{8} = 1 \] Step 2: Count the contribution of atom B. Atom B occupies the face centres of the cube. There are \(6\) face-centred atoms and each face-centred atom is shared by \(2\) unit cells. \[ \text{Effective number of B atoms} = 6 \times \frac{1}{2} = 3 \] Step 3: Write the atomic ratio. \[ A : B = 1 : 3 \] Step 4: Write the empirical formula. The simplest whole number ratio gives the empirical formula: \[ \boxed{\text{AB}_3} \]