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

Hint: 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.