If the anion (A) form hexagonal closet packing and cation (C ) occupy only 2/3 octahedral voids in it, then the general formula of the comound is:

Options

A. CA
B. `CA_(2)`
C. `C_(2)A_(3)`
D. `C_(3)A_(2)`

Answer

To solve the problem, we need to determine the general formula of a compound formed by anions (A) arranged in hexagonal close packing (HCP) and cations (C) occupying 2/3 of the octahedral voids. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Hexagonal Close Packing (HCP)
In hexagonal close packing, the arrangement of atoms is such that there are layers of atoms stacked in an AB-AB pattern. Each unit cell of HCP contains a specific number of atoms.

### Step 2: Calculate the Number of Atoms in HCP
In a unit cell of HCP:
- There are 12 corner atoms, each contributing 1/6 to the unit cell (since they are shared by 6 unit cells).
- There are 2 face-centered atoms, each contributing 1/2 to the unit cell (since they are shared by 2 unit cells).
- There is 1 body-centered atom that belongs entirely to the unit cell.

Calculating the contributions:
- Contribution from corner atoms: \(12 \times \frac{1}{6} = 2\)
- Contribution from face-centered atoms: \(2 \times \frac{1}{2} = 1\)
- Contribution from body-centered atoms: \(1\)

Total number of atoms in HCP = \(2 + 1 + 3 = 6\).

### Step 3: Determine the Number of Octahedral Voids
In HCP, the number of octahedral voids is equal to the number of atoms in the unit cell. Therefore, the number of octahedral voids = 6.

### Step 4: Calculate the Number of Cations (C)
According to the problem, cations (C) occupy 2/3 of the octahedral voids:
\[ \text{Number of cations (C)} = \frac{2}{3} \times 6 = 4 \]

### Step 5: Determine the Ratio of Anions (A) to Cations (C)
We have:
- Number of anions (A) = 6 (from HCP)
- Number of cations (C) = 4 (from above calculation)

The ratio of anions to cations is:
\[ \text{Ratio of A to C} = 6 : 4 = 3 : 2 \]

### Step 6: Write the General Formula
From the ratio of anions to cations, we can write the general formula of the compound as:
\[ \text{General Formula} = A_3C_2 \]

### Final Answer
The general formula of the compound is \(A_3C_2\).

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