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 formula of the compound, let's analyze the given information:
Explanation of how atoms are arranged in the unit cell
- In a cubic solid lattice:
- A atoms are at the corners, contributing \( \frac{1}{8} \) of an atom per corner to the unit cell.
- B atoms are at the cubic centres, contributing 1 atom per unit cell.
- C atoms are at the centres of the edges, contributing \( \frac{1}{4} \) of an atom per edge to the unit cell.
Now, calculating the total number of atoms per unit cell:
- There are 8 corners, so \( 8 \times \frac{1}{8} = 1 \) A atom.
- There is 1 B atom at the centre.
- There are 12 edges, so \( 12 \times \frac{1}{4} = 3 \) C atoms.
Thus, the formula of the compound is ABC.