A solid is made up of two types of atoms "X" and "Y". Atoms of "X" occupy all the tetrahedral sites while the atoms of "Y" have FCC arrangement. Its formula is

Options

A. XY
B. `X_(2)Y`
C. `XY_(2)`
D. `XY_(4)`

Answer

To determine the formula of the solid made up of two types of atoms "X" and "Y", where atoms of "X" occupy all the tetrahedral sites and atoms of "Y" have a face-centered cubic (FCC) arrangement, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the arrangement of Y in FCC:**
- In a face-centered cubic (FCC) structure, the effective number of atoms (Z) is 4. This is calculated as follows:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom (total contribution from corners = \( 8 \times \frac{1}{8} = 1 \)).
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom (total contribution from faces = \( 6 \times \frac{1}{2} = 3 \)).
- Therefore, the total number of atoms in the unit cell is \( 1 + 3 = 4 \).

2. **Calculate the number of tetrahedral voids:**
- The number of tetrahedral voids in a structure is given by the formula \( 2n \), where \( n \) is the number of atoms present in the FCC unit cell.
- Since we have 4 atoms of Y in the FCC, the number of tetrahedral voids is \( 2 \times 4 = 8 \).

3. **Determine the ratio of X to Y:**
- Atoms of X occupy all the tetrahedral sites, which we calculated to be 8.
- Atoms of Y in the FCC arrangement are 4.
- Therefore, the ratio of X to Y is \( 8:4 \) or simplified to \( 2:1 \).

4. **Write the formula:**
- Based on the ratio of X to Y, the formula of the compound can be represented as \( X_2Y \).

### Final Answer:
The formula of the solid is \( X_2Y \).

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