Question

A compound formed by elements A and B has a cubic structure in which A atoms are at the corners of the cube and B atoms are at the face centres. The formula of the compound will be ___________.

• A. $A_4{B}_3$
• B. $A_{2}B$
• C. $A{B}_3$
• D. $A_2{B}_3$

Answer 1

The correct option is C

$A{B}_3$

The explanation for the correct answer:-

Option (C) $A{B}_3$

Step 1: Given data

The compound has a cubic structure in which A atoms are at the corners of the cube and B atoms are at the face centres.

Step 2: Calculating the number of atoms of components

Number of atoms A present per unit cell

= $(1/8)x8$

$=1$

Number of atoms B present per unit cell = $6x(1/2)$

$=3$

Step 3: Deriving components formula

So, the ratio of A: B = $1:3$

Therefore, the formula is ${\mathrm{AB}}_3$, option (C) is the correct answer.