In a face centered lattice of X and Y, X atoms are present at the corners while Y atoms are at face centres.
(a) What is the formula of the compound ?
(b) What would be the formula of the compound if (i) one of the X atoms is missing from a corner in each unit cell
(ii) one of the X atoms at from a corner is replaced by Z atom. (also monovalent) ?

Explanation

To solve the given problem, we will break it down into two parts as specified in the question.

### Part (a): Determine the formula of the compound

1. **Identify the number of X atoms in the unit cell:**
- In a face-centered cubic lattice, X atoms are located at the corners.
- There are 8 corners in the unit cell, and each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution from X atoms is:
\[ \text{Number of X atoms} = 8 \times \frac{1}{8} = 1 \]

2. **Identify the number of Y atoms in the unit cell:**
- Y atoms are located at the face centers.
- There are 6 faces in the unit cell, and each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Therefore, the total contribution from Y atoms is:
\[ \text{Number of Y atoms} = 6 \times \frac{1}{2} = 3 \]

3. **Write the formula of the compound:**
- From the contributions calculated, we have:
- X: 1 atom
- Y: 3 atoms
- Thus, the formula of the compound is:
\[ XY_3 \]

### Part (b): Determine the new formulas under different conditions

#### (i) If one of the X atoms is missing from a corner in each unit cell:

1. **Recalculate the number of X atoms:**
- If one X atom is missing from the corners, then instead of 8 corners, we have 7 effective corners.
- The contribution now becomes:
\[ \text{Number of X atoms} = 7 \times \frac{1}{8} = \frac{7}{8} \]

2. **Y atoms remain the same:**
- The number of Y atoms is still 3.

3. **Write the new formula:**
- The new formula becomes:
\[ X_{\frac{7}{8}}Y_3 \]
- To express this in whole numbers, multiply by 8:
\[ X_7Y_{24} \]

#### (ii) If one of the X atoms at a corner is replaced by a Z atom (also monovalent):

1. **Recalculate the number of X and Z atoms:**
- The number of X atoms remains \( \frac{7}{8} \) (as one X atom is still missing).
- The contribution from the Z atom, which replaces one of the corner X atoms, is:
\[ \text{Number of Z atoms} = \frac{1}{8} \]

2. **Y atoms remain the same:**
- The number of Y atoms is still 3.

3. **Write the new formula:**
- The new formula becomes:
\[ X_{\frac{7}{8}}Y_3Z_{\frac{1}{8}} \]
- To express this in whole numbers, multiply by 8:
\[ X_7Y_{24}Z_1 \]

### Final Answers:
- (a) The formula of the compound is \( XY_3 \).
- (b)
- (i) If one X atom is missing: \( X_7Y_{24} \)
- (ii) If one X atom is replaced by Z: \( X_7Y_{24}Z_1 \)