Chemistry - Solid State Question with Solution | TestHub

P) Cations form CCP lattice and anions in alternate tetrahedral voids:

Number of Ions: Cations in CCP = $4$. Anions in alternate (half) tetrahedral voids = $\frac{1}{2}\times 8=4$.

Ratio: Cation : Anion = $4:4=1:1$ (Matches 1).

Coordination Geometry: Both ions have an identical tetrahedral ($4:4$) coordination geometry (Matches 2).

Formula Units ($Z$): Number of formula units per unit cell is $4$ (Matches 4).

Match: $P\to 1,2,4$

Q) Cations occupy all corners of cube and anions located at body centre:

Number of Ions: Cations at $8$ corners = $8\times \frac{1}{8}=1$. Anion at body center = $1$.

Ratio: Cation : Anion = $1:1$ (Matches 1).

Coordination Geometry: Both ions have an identical cubic ($8:8$) coordination geometry (Matches 2).

Match: $Q\to 1,2$

R) Anions form CCP lattice and cations located in all tetrahedral voids:

Number of Ions: Anions in CCP = $4$. Cations in all tetrahedral voids = $8$.

Coordination Geometry: Cations have tetrahedral coordination ($4$) and anions have cubic coordination ($8$), meaning they have different geometries (Matches 3).

Formula Units ($Z$): The compound formula is A₂B, giving $4$ formula units per unit cell (Matches 4).

Match: $R\to 3,4$

S) Cations form CCP lattice and anions located in all octahedral voids:

Ratio & Geometry: Cation : Anion ratio is $1:1$ (Matches 1) and both have an identical octahedral ($6:6$) coordination geometry (Matches 2).

Shortest Distance: In a CCP (FCC) array, the shortest distance between any two identical ions (e.g., from corner to face-center) is half of the face diagonal:

$$Shortestdistance=\frac{\sqrt{2}a}{2}=\frac{a}{\sqrt{2}}$$

(Matches 5).

Match: $S\to 1,2,5$