Question

A solid $‘A{B}^{\prime }$ has the $NaCl$ structure, and $‘A^{\prime }$ atoms occupy the corners of the cubic unit cell. If all the face-centred atoms along one of the axes are removed, then the resultant formula of the of the unit cell of the solid will be:

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

Answer 1

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


$NaCl$ structure ${\Rightarrow }^{\prime }{A}^{\prime }$ occupies all the corners and face centred.
${}^{\prime }{B}^{\prime }$ occupies all edge centres and bodycentred.
$\Rightarrow A_{(8\times \frac{1}{8}+6\times \frac{1}{2})}{B}_{(12\times \frac{1}{4}+1)}=A_4{B}_4$
When face-centred atoms along an axis are removed; 2 atoms of ${}^{\prime }{A}^{\prime }$ will be removed.
$A_{(8\times \frac{1}{8}+4\times \frac{1}{2})}{B}_4\Rightarrow A_3{B}_4$