In a compound, atoms of elementsY form ccp lattice and those of element X occupy 2/3 rd of tetrahedral voids. The formula of the compound can be

Options

A. `X_(4) Y_(3)`
B. `X_(2) Y_(3)`
C. `X_(2)Y`
D. `X_(2)Y_(4)`

Answer

To determine the formula of the compound formed by elements X and Y, we need to follow these steps:

### Step 1: Understand the Structure
- Element Y forms a cubic close-packed (ccp) lattice, which is also known as face-centered cubic (FCC). In this lattice, there are 4 atoms of Y per unit cell.

**Hint:** Recall that in a face-centered cubic lattice, the number of atoms per unit cell is 4.

### Step 2: Determine the Number of Tetrahedral Voids
- In a face-centered cubic lattice, there are 8 tetrahedral voids per unit cell.

**Hint:** Remember that the number of tetrahedral voids in a FCC lattice is always 2 times the number of atoms present in the unit cell.

### Step 3: Calculate the Number of Tetrahedral Voids Occupied by X
- According to the problem, element X occupies 2/3 of the tetrahedral voids. Since there are 8 tetrahedral voids, the number of tetrahedral voids occupied by X is:
\[ \text{Number of voids occupied by X} = \frac{2}{3} \times 8 = \frac{16}{3} \]

**Hint:** Make sure to multiply the total number of voids by the fraction given in the problem.

### Step 4: Determine the Ratio of X to Y
- From the previous steps, we have:
- Number of Y atoms = 4 (from the FCC structure)
- Number of X atoms = \( \frac{16}{3} \)

### Step 5: Write the Empirical Formula
- The ratio of X to Y can be expressed as:
\[ \text{Ratio of X to Y} = \frac{\frac{16}{3}}{4} = \frac{16}{3} \div 4 = \frac{16}{12} = \frac{4}{3} \]
- This means for every 4 atoms of X, there are 3 atoms of Y. Thus, the empirical formula can be written as:
\[ X_4Y_3 \]

### Final Answer
The formula of the compound is \( X_4Y_3 \).

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