Question

AgI crystallizes in the ccp (cubic closed packed), zinc blende structure. Assuming that ${{I}^{-}}$ ions occupy the lattice points, the fraction of tetrahedral voids occupied by $A{{g}^{+}}$ ions is:

Answer 1

So, here the question is talking about solid state chapter. We have to put AgI in ccp. Then we have to check how many voids are there in which $A{{g}^{+}}$ can occupy.

Complete step by step answer:
Here ccp is cubic closed packed. Ccp (cubic closed packing) is another name given to FCC (face centered cubic) but HCP is not the same. Although they both have closest possible packing of atoms.
Zinc Blende is the name given to the mineral ZnS. It has a cubic close packed (face centred cubic) array of S and the Zn (II) sit in tetrahedral (1/2 occupied) sites in the lattice. Silver iodide is an inorganic compound with the formula AgI.
If there is an ‘n’ number of ${{I}^{-}}$ ions then there are ‘n’ $A{{g}^{+}}$ ions. ${{I}^{-}}$ ions form the lattice points and $A{{g}^{+}}$ ions occupy tetrahedral voids. Now, we have to find the number of tetrahedral voids in ccp (cubic closed packed). Effective number of tetrahedral holes = 8, in Fcc.
Number of tetrahedral voids is twice the number of atoms forming the cubic lattice.
So, the number of tetrahedral voids occupied by $A{{g}^{+}}$ion = 50% of total tetrahedral voids.

Note: The ccp system involves two types of voids – tetrahedral voids and octahedral voids. The tetrahedral void has four spheres adjacent to it while the octahedral void has six spheres adjacent to it. These voids are only found in either fcc or Hexagonal Primitive unit cells.