Question

If three elements A, B, C crystallize in a cubic solid lattice with B atoms at the cubic centres, C atoms at the centre of edges, and A atoms at the corners, then the formula of the compound is:

• A. AB₃
• B. A₃BC
• C. ABC
• D. ABC₃

Hint:

Tip about crystallography and counting atoms In crystallography problems, always remember how atoms are arranged in the unit cell and how to count their contributions based on their positions. Atoms at corners contribute \( \frac{1{8 \), at edges \( \frac{1{4 \), at face centres \( \frac{1{2 \), and at body centres contribute 1 full atom.

Answer 1

The Correct Option is C

To determine the compound's formula, we analyze the information:
Arrangement of atoms in the unit cell:
- In a cubic solid lattice:
- A atoms are at the corners, contributing \( \frac{1}{8} \) per corner.
- B atoms are at the cubic centers, contributing 1 atom.
- C atoms are at the edge centers, contributing \( \frac{1}{4} \) per edge.
Calculating the atoms per unit cell:
- A atoms: 8 corners × \( \frac{1}{8} \) = 1 atom.
- B atoms: 1 atom.
- C atoms: 12 edges × \( \frac{1}{4} \) = 3 atoms.
The compound's formula is ABC.