Discussion Forum



1)

Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose   unit cell is constructed from the unit cell of MX following the sequential instruction  given  below. Neglect the charge balance.

(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  ( Number of anions/ Number of cations )  in Z  is ..............


A) 4

B) 5

C) 3

D) 2

Answer:

Option C

Explanation:

The unit cell of initial structure of ionic solid MX looks like 

288201911_face.JPG

In NaCl type of solids cations (Na+ ) occupy the octahedral voids white anions (Cl- ) 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

                 Number of anions/ Number of cations = $\frac{3}{1}=3$