Question

A and B atoms in a crystal are positioned at the corners and face centers respectively. What is the formula of the crystal?

• A. \(A_2B_3\)
• B. \(AB_2\)
• C. \(AB_3\)
• D. \(A_2B_3\)

Hint:

In a cubic unit cell, a corner atom contributes \(\frac{1}{8}\), a face-centered atom contributes \(\frac{1}{2}\), an edge-centered atom contributes \(\frac{1}{4}\), and a body-centered atom contributes \(1\).

Answer 1

The Correct Option is C

Step 1: Calculate effective atoms from lattice positions.
Corners: 8 × 1/8 = 1 A atom. Face centers: 6 × 1/2 = 3 B atoms. Simplest ratio A:B = 1:3.

Step 2: Final Answer:
AB₃ (option 3).