If the crystallises in zinc blende structure with `I^-` ions at lattice points. What fraction of tetrahedral voids is occupied by `Ag^+` ions ?

Options

A. 25%
B. 50%
C. 100%
D. 75%.

Answer

To solve the problem of determining the fraction of tetrahedral voids occupied by Ag⁺ ions in a zinc blende structure with I⁻ ions at the lattice points, we can follow these steps:

### Step 1: Understand the Structure
The zinc blende structure is a face-centered cubic (FCC) lattice where the anions (I⁻) occupy the lattice points. The cations (Ag⁺) occupy the tetrahedral voids.

**Hint:** Remember that in a zinc blende structure, the anions are at the lattice points and the cations fill the tetrahedral voids.

### Step 2: Determine the Number of I⁻ Ions
Let’s denote the number of I⁻ ions at the lattice points as \( n \). In the FCC structure, there are \( n \) lattice points, and thus \( n \) I⁻ ions.

**Hint:** The number of lattice points in an FCC structure corresponds to the number of anions in the structure.

### Step 3: Calculate the Number of Tetrahedral Voids
In a face-centered cubic (FCC) structure, the number of tetrahedral voids is twice the number of atoms (or ions) in the lattice. Therefore, the number of tetrahedral voids is given by:

\[ \text{Number of tetrahedral voids} = 2n \]

**Hint:** Remember that for every atom in an FCC lattice, there are two tetrahedral voids.

### Step 4: Determine the Number of Ag⁺ Ions
Since the number of Ag⁺ ions is equal to the number of I⁻ ions in the structure, we also have \( n \) Ag⁺ ions occupying the tetrahedral voids.

**Hint:** The stoichiometry of the compound AgI indicates that the number of cations equals the number of anions.

### Step 5: Calculate the Fraction of Tetrahedral Voids Occupied by Ag⁺ Ions
The fraction of tetrahedral voids occupied by Ag⁺ ions can be calculated using the formula:

\[ \text{Fraction occupied} = \frac{\text{Number of Ag}^+ \text{ ions}}{\text{Number of tetrahedral voids}} = \frac{n}{2n} \]

This simplifies to:

\[ \text{Fraction occupied} = \frac{1}{2} \]

### Step 6: Convert to Percentage
To express this fraction as a percentage, we multiply by 100:

\[ \text{Percentage occupied} = \frac{1}{2} \times 100 = 50\% \]

### Conclusion
Thus, the fraction of tetrahedral voids occupied by Ag⁺ ions in the zinc blende structure is 50%.

**Final Answer:** 50%

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