An AB solid has `CsCl` type of structure, where A occupies corner. If the atoms from corners along one of the body diagonal are removed , the formula of a the solid would be

Options

A. `A_7B_8`
B. `A_5B_6`
C. `A_3B_4`
D. `A_4B_3`

Answer

To solve the problem, we need to analyze the structure of the AB solid with a CsCl-type arrangement and determine the new formula after removing certain atoms.

### Step-by-Step Solution:

1. **Understanding the CsCl Structure**:
- In a CsCl-type structure, the cation (A) occupies the corners of the cube, and the anion (B) is located at the body center of the cube.
- In a unit cell of this structure, there are 8 corner atoms and 1 body-centered atom.

2. **Counting Atoms in the Unit Cell**:
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because each corner is shared by 8 adjacent unit cells.
- Therefore, the total contribution from the corner atoms (A) is:
\[ 8 \times \frac{1}{8} = 1 \text{ atom of A} \]
- The body-centered atom (B) contributes:
\[ 1 \text{ atom of B} \]

3. **Removing Atoms Along the Body Diagonal**:
- The question states that atoms from corners along one of the body diagonals are removed.
- A body diagonal connects two opposite corners of the cube. In a cube, there are 4 corners along a body diagonal (2 at each end).
- Removing these 4 corner atoms means we are removing 4 contributions of \( \frac{1}{8} \) each from the total count of A atoms:
\[ 4 \times \frac{1}{8} = \frac{4}{8} = \frac{1}{2} \text{ atom of A} \]
- Thus, the remaining contribution from the corners will be:
\[ 1 - \frac{1}{2} = \frac{1}{2} \text{ atom of A} \]

4. **Final Count of Atoms**:
- After removing the corner atoms, we have:
- A: \( \frac{1}{2} \) atom
- B: \( 1 \) atom
- Therefore, the new formula of the solid becomes:
\[ A_{\frac{1}{2}}B_1 \]

5. **Simplifying the Formula**:
- To express the formula in whole numbers, we can multiply through by 2:
\[ A_1B_2 \]
- This means the final formula of the solid after the removal of the corner atoms is:
\[ AB_2 \]

### Final Answer:
The formula of the solid after removing the atoms along one of the body diagonals is \( AB_2 \).