Let's determine the effective number of atoms for each element in one unit cell of the cubic lattice:
A atoms :
Atoms are placed at the 8 corners of the cube.
Each corner atom is shared by 8 neighboring unit cells.
Effective atoms per unit cell:
8×‌=1.
B atoms :
B atoms are located at the center of the cube, which is entirely within the unit cell.
Effective atoms per unit cell: 1.
C atoms :
Atoms are positioned at the center of each of the 12 edges.
Each edge-centered atom is shared by 4 unit cells.
Effective atoms per unit cell:
12×‌=3.
With these contributions, the total number of atoms per unit cell is:
‌A=1,‌B=1,‌C=3.Thus, the formula of the compound is:
ABC3.
The correct option is Option C.