In the rock salt AB, if C introduced in tetrahedral voids such that no distoration occurss, then fromula of resultant compound is :

Options

A. ABC
B. `ABC_(2)`
C. `A_(4)B_(4)C`
D. `ABC_(8)`

Answer

To solve the problem, we need to determine the formula of the resultant compound when element C is introduced into the tetrahedral voids of the rock salt structure AB without causing any distortion. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Rock Salt Structure
In the rock salt structure (AB), the anions (let's denote them as A) are arranged in a cubic close-packed (CCP) or face-centered cubic (FCC) lattice. The cations (denote as B) occupy the octahedral voids.

### Step 2: Count the Atoms in the Unit Cell
1. **Anions (A)**:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) to the unit cell.
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) to the unit cell.
- Total contribution from A:
\[ \text{Total A} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

2. **Cations (B)**:
- There is 1 atom at the body center.
- There are 12 edge-centered atoms, each contributing \( \frac{1}{4} \) to the unit cell.
- Total contribution from B:
\[ \text{Total B} = 1 + 12 \times \frac{1}{4} = 1 + 3 = 4 \]

### Step 3: Count the Tetrahedral Voids
In a cubic close-packed structure, the number of tetrahedral voids is twice the number of atoms in the unit cell. Since we have 4 atoms of A (and thus also 4 atoms of B), the number of tetrahedral voids is:
\[ \text{Number of Tetrahedral Voids} = 2 \times \text{Number of A atoms} = 2 \times 4 = 8 \]

### Step 4: Introduce C into Tetrahedral Voids
Now, when C is introduced into the tetrahedral voids, we have:
- 8 atoms of C occupying the tetrahedral voids.

### Step 5: Determine the Ratio of A, B, and C
Now we have:
- Number of A = 4
- Number of B = 4
- Number of C = 8

To find the simplest ratio, we divide each by 4:
\[ \text{Ratio of A:B:C} = \frac{4}{4} : \frac{4}{4} : \frac{8}{4} = 1 : 1 : 2 \]

### Step 6: Write the Formula
From the ratio, we can write the formula of the resultant compound as:
\[ \text{Formula} = ABC_2 \]

### Final Answer
The formula of the resultant compound is \( ABC_2 \).

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