Question

If three elements A, B and C crystallize in a cubic solid lattice with A atoms at the corners, B atoms at the cube centre and C atoms at the centre of the face of the cube, then the formula of the compound will be:

• A. $A{B}_{3}C$
• B. $A_{3}BC$
• C. $AB{C}_3$
• D. $ABC$

Answer 1

Answer: (C)

$AB{C}_3$

Three elements A, B and C crystallize in a cubic solid lattice.

A atoms are present at the corners of the cube.
There are a total of $8$ corners in the cube.
Each atom contributes $\frac{1}{8}$th to the cube.
Number of A atoms $=8\times \frac{1}{8}=1$

B atoms are present at the cubic center.
There is only one cubic center.
Each atom contributes $1$ to the cube.
Number of B atoms $=1$

C atoms are present at the center of the face of the cube.
There are $6$ face centers.
Each atom contributes $\frac{1}{2}$ to the cube.
Number of C atoms $=6\times \frac{1}{2}=3$

Hence, the formula of the compound will be $AB{C}_3$.