Question

Three elements A,B and C crystalize in a cubic lattice with A atoms at the corners, B atoms at the cube center and C atoms at the centre of the face of the cube.The simplest formula for the compound will be:

• A. $ABC$
• B. $A_{8}B{C}_6$
• C. $AB{C}_3$
• D. $A_2{B}_3{C}_5$

Answer 1

The correct option is C $AB{C}_3$

Three elements A, B and C crystalize in a cubic solid lattice
A atoms are present at the corners of the cube.
$\text{Number of A atoms}=8\times \frac{1}{8}=1$

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

C atoms are present at the center of the face of the cube.
$\text{Number of C atoms}=6\times \frac{1}{2}=3$
Formula is :
$AB{C}_3$