Solid State - Result Question 29
####29. Consider an ionic solid $M X$ with $NaCl$ structure. Construct a new structure $(Z)$ whose unit cell is constructed from the unit cell of $M X$ following the sequential instruction given below. Neglect the charge balance.
(2018 Adv.)
(a) Remove all the anions $(X)$ except the central one
(b) Replace all the face centered cations $(M)$ by anions $(X)$
(c) Remove all the corner cations $(M)$
(d) Replace the central anion $(X)$ with cation $(M)$
The value of $\left(\frac{\text { Number of anions }}{\text { Number of cations }}\right)$ in $Z$ is
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Answer:
Correct Answer: 29. (3)
Solution:
- The unit cell of initial structure of ionic solid $M X$ looks like
In $NaCl$ type of solids cations $\left(Na^{+}\right)$occupy the octahedral voids while anions $\left(Cl^{-}\right)$occupy the face centre positions.
However, as per the demand of problem the position of cations and anions are swapped.
We also know that (for 1 unit cell)
(A) Total number of atoms at $FCC=4$
(B) Total number of octahedral voids $=4$
(as no. of atoms at $FCC=$ No. of octahedral voids)
Now taking the conditions one by one
(i) If we remove all the anions except the central one than number of left anions.
$$ =4-3=1 $$
(ii) If we replace all the face centred cations by anions than effective number of cations will be $=4-3=1$
Likewise effective number of anions will be $=1+3=4$
(iii) If we remove all the corner cations then effective number of cations will be $1-1=0$
(iv) If we replace central anion with cation then effective number of cations will be $0+1=1$
Likewise effective number of anions will be $4-1=3$
Thus, as the final outcome, total number of cations present in $Z$ after fulfilling all the four sequential instructions $=1$
Likewise, total number of anions $=3$
Hence, the value of $\frac{\text { Number of anions }}{\text { Number of cations }}=\frac{3}{1}=3$
