Question

In a solid AB having the $NaCl$ structure, 'A' atoms occupy the corners of the cubic unit cell. If all the face centred atoms along one of the axes are removed, the resultant stoichiometry of the solid is:

• A. $A{B}_2$
• B. $A_{2}B$
• C. $A_4{B}_3$
• D. $A_3{B}_4$

Answer 1

The correct option is D $A_3{B}_4$

Face centred atoms along one of the axis = 2

Effective number of $A^{-}orC{l}^{-}$ (normally) $=(8\times \frac{1}{8})+(6\times \frac{1}{2})=4$

Effective number of $A^{-}$ after removing atoms along one axes $=(8\times \frac{1}{8})+(4\times \frac{1}{2})=3$

Effective number of $B^{+}orN{a}^{+}=(12\times \frac{1}{4})+1=4$
$\therefore$ The formula is $A_3{B}_4.$
Hence (D) is correct option.