In a solid AB of NaCl structure, A atoms occupy the corner of the cubic unit cell. If all the corner atoms are removed then the formula of the unit cell will be

Options

A. `A_(4)B_(4)`
B. B
C. `A_(3)B_(4)`
D. AB

Answer

To solve the problem, we need to analyze the structure of the solid AB with a NaCl structure and determine the formula of the unit cell after removing all the corner atoms.

### Step-by-Step Solution:

1. **Understanding the NaCl Structure**:
- In the NaCl structure, sodium (Na) and chloride (Cl) ions are arranged in a face-centered cubic (FCC) lattice.
- In this structure, the A atoms (which we can assume to be Na) occupy the corners of the cubic unit cell, while the B atoms (which we can assume to be Cl) occupy the face centers.

2. **Counting Atoms in the Unit Cell**:
- In a cubic unit cell, there are 8 corners. Each corner atom contributes 1/8 of its volume to the unit cell because it is shared among 8 unit cells.
- Therefore, the total contribution from the corner atoms (A atoms) is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ A atom} \]
- The face-centered atoms (B atoms) contribute:
- There are 6 faces, and each face atom contributes 1/2 to the unit cell.
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \text{ B atoms} \]

3. **Initial Formula of the Unit Cell**:
- Before removing the corner atoms, the formula of the unit cell is:
\[ \text{Formula} = A_1B_3 \]

4. **Removing Corner Atoms**:
- The problem states that all corner atoms (A atoms) are removed. Since there are 8 corners, and we are removing all of them, we are effectively removing 1 A atom from the unit cell.
- After removing the corner atoms, the number of A atoms left in the unit cell is:
\[ \text{Remaining A atoms} = 1 - 1 = 0 \text{ A atoms} \]
- The number of B atoms remains unchanged at 3.

5. **Final Formula of the Unit Cell**:
- After removing all the corner A atoms, the formula of the unit cell now becomes:
\[ \text{Final Formula} = A_0B_3 \]
- Since we cannot have a formula with 0 atoms of A, we can denote it simply as \( B_3 \).

### Conclusion:
The formula of the unit cell after removing all the corner atoms is:
\[ \text{Formula} = B_3 \]