If the anions (X) form hexagonal closed packing and cations (Y) occupy only 3/8th of octahedral voids in it, then the general formula of the compound is

Options

A. `XY`
B. `YX_2`
C. `X_8 Y_3`
D. `X_3 Y_4`

Answer

To solve the problem, we need to determine the general formula of the compound formed by anions (X) and cations (Y) based on the given information about their arrangement in a hexagonal closed packing (HCP) structure.

### Step-by-Step Solution:

1. **Understanding Hexagonal Closed Packing (HCP)**:
- In hexagonal closed packing, the coordination number of each particle is 12.
- The number of atoms per unit cell in HCP is 6.

2. **Identifying the Number of Anions (X)**:
- Since the anions (X) form the hexagonal closed packing, there will be 6 anions in one unit cell.
- Therefore, \( n_X = 6 \).

3. **Determining the Number of Octahedral Voids**:
- In a unit cell with \( n \) atoms, the number of octahedral voids is equal to the number of atoms.
- Since there are 6 anions (X), there will be 6 octahedral voids in the unit cell.
- Thus, the number of octahedral voids \( n_{oct} = 6 \).

4. **Calculating the Number of Cations (Y)**:
- It is given that cations (Y) occupy only \( \frac{3}{8} \) of the octahedral voids.
- Therefore, the number of cations (Y) can be calculated as follows:
\[ n_Y = \frac{3}{8} \times n_{oct} = \frac{3}{8} \times 6 = \frac{18}{8} = 2.25 \]
- Since we need whole numbers for the formula, we can express this in a simpler ratio.

5. **Finding the Ratio of X to Y**:
- We have \( n_X = 6 \) and \( n_Y = 2.25 \).
- To find the simplest whole number ratio, we can multiply both by 8 (to eliminate the fraction):
\[ n_X : n_Y = 6 \times 8 : 2.25 \times 8 = 48 : 18 \]
- Simplifying this ratio:
\[ n_X : n_Y = 48 : 18 = 8 : 3 \]

6. **Writing the General Formula**:
- Based on the ratio of anions to cations, the general formula of the compound can be expressed as:
\[ \text{General Formula} = X_8Y_3 \]

### Conclusion:
The general formula of the compound is \( X_8Y_3 \).