Question

A compound is formed by elements, A and B. This crystallises in the cubic structure where A atoms occupies the corners of the cube and B atoms are at the body centers. The simplest formula of the compound is :

• A. $A_8{B}_4$
• B. $A^{}{B}_6$
• C. $A^{}{B}^{}$
• D. $A_6{B}^{}$

Answer 1

Answer: (C)

$A^{}{B}^{}$

In simple cube, contribution of one corner $=\frac{1}{8}$
Total number of corner in a cube is $8$.
So, effective number of atoms per unit cell $=\frac{1}{8}\times 8=1$
Number of body centers in simple cubic $=1$

Number of atoms in body center $=1$
So, the simplest formula is $AB$.