Question

If $AgI$ crystallises in zinc blende structure with ${I^ - }$ ions at lattice points. What fraction of tetrahedral voids is occupied by $A{g^ + }$ ions
A.$25\%$
B.$50\%$
C.$100\%$
D.$75\%$

Answer 1

First we know that crystals are classified into three types based on their structures. The three types of structures are primitive cubic also called a simple cubic, Body centered cubic (BCC) and Face centered cubic (FCC) is also called cubic close packed (CCP). Zinc blende has FCC structure.

Complete answer:
Given $AgI$ crystallises in zinc blende structure with ${I^ - }$ ions at lattice points.
Since zinc blende structure is the FCC structure where anions are present at the lattice points and cations are present in alternate tetrahedral voids. Then in $AgI$, ${I^ - }$anions are present at the lattice points and $A{g^ + }$ cations are present in alternate tetrahedral voids.
Hence the number of $A{g^ + }$ ions are equal to ${I^ - }$ ions i.e., If there is $n$ number of ${I^ - }$ ions, there will be $n$ number of $A{g^ + }$ ions.
We know that the number of tetrahedral voids is twice the number of atoms forming the cubic/crystal lattice.
Then the number of tetrahedral voids $= 2n$
Thus, the fraction of tetrahedral voids occupied by $A{g^ + }$ ions $= \dfrac{n}{{2n}} \times 100 = 50\%$
Hence the correct option is (C) $50\%$.

Note:
Note that the crystal lattice is the symmetrical 3D-structural arrangements of constituent particles such as atoms, ions or molecules inside a crystalline solid as points. These points are called lattice points.
Unit cell is the simplest repeating unit in a crystal structure and the entire lattice is generated by the repetition of the unit cell in different directions.