A crystalline solid `XY_(3)` has ccp arrangement for its element Y. X occupies _______.

Options

A. 66% of tetrahedral voids
B. 33% of tetrahedral voids
C. 66% of octahedral voids
D. 33% of octahedral voids

Answer

To solve the problem regarding the crystalline solid \( XY_3 \) with a ccp arrangement for the element \( Y \), we will follow these steps:

### Step 1: Understand the arrangement
In a cubic close-packed (ccp) structure, also known as face-centered cubic (fcc), the atoms of \( Y \) are arranged in a way that there are 4 atoms of \( Y \) per unit cell. This is because there are 8 corner atoms (1/8 contribution each) and 6 face-centered atoms (1/2 contribution each):
\[ \text{Total Y atoms} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

**Hint:** Remember that in a ccp arrangement, the number of atoms per unit cell can be calculated based on the contributions from corner and face-centered positions.

### Step 2: Determine the ratio of \( X \) to \( Y \)
The formula of the compound is \( XY_3 \). This indicates that for every 1 atom of \( X \), there are 3 atoms of \( Y \). Since we have 4 atoms of \( Y \) in the unit cell, we need to find how many \( X \) atoms are required to maintain the ratio of 1:3.

**Hint:** Use the ratio from the formula to find the number of \( X \) atoms needed based on the number of \( Y \) atoms.

### Step 3: Calculate the number of \( X \) atoms
From the ratio \( 1:3 \), if there are 4 atoms of \( Y \), then the number of \( X \) atoms required can be calculated as follows:
\[ \text{Number of } X = \frac{1}{3} \times \text{Number of } Y = \frac{1}{3} \times 4 = \frac{4}{3} \]

**Hint:** The number of \( X \) atoms must be a fraction that maintains the stoichiometric ratio with \( Y \).

### Step 4: Identify the voids in the ccp structure
In a ccp structure, there are two types of voids:
- **Octahedral voids:** There are 4 octahedral voids per unit cell.
- **Tetrahedral voids:** There are 8 tetrahedral voids per unit cell.

Since we have determined that \( X \) occupies \( \frac{4}{3} \) of the octahedral voids to maintain the ratio with \( Y \), we can conclude that \( X \) occupies the octahedral voids.

**Hint:** Remember that the type of voids (octahedral or tetrahedral) can be determined based on the stoichiometry of the compound.

### Step 5: Conclusion
Thus, in the crystalline solid \( XY_3 \), the element \( X \) occupies the octahedral voids.

**Final Answer:** \( X \) occupies the **octahedral voids**.