A unit cell consists of a cube in which the atoms A are occupying the corners while the atoms B are present at the centre of each face. If the atoms A are missing from 2 corners, what is the simplest formuls of the compound ?

Explanation

To find the simplest formula of the compound given the arrangement of atoms in the unit cell, we can follow these steps:

### Step 1: Identify the positions of atoms A and B in the unit cell
- Atoms A are located at the corners of the cube.
- Atoms B are located at the center of each face of the cube.

### Step 2: Calculate the contribution of atoms A
- In a cube, there are 8 corners. Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Since 2 corners are missing atoms A, we have:
- Total corners = 8
- Corners occupied by A = 8 - 2 = 6
- Contribution from A = \( 6 \times \frac{1}{8} = \frac{6}{8} = \frac{3}{4} \)

### Step 3: Calculate the contribution of atoms B
- There are 6 faces on the cube. Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Contribution from B = \( 6 \times \frac{1}{2} = 3 \)

### Step 4: Write the formula based on the contributions
- We have \( \frac{3}{4} \) of atom A and 3 of atom B.
- The formula can be represented as \( A_{\frac{3}{4}}B_3 \).

### Step 5: Simplify the formula
- To simplify, we can multiply the entire formula by 4 to eliminate the fraction:
- \( 4 \times A_{\frac{3}{4}}B_3 = A_3B_{12} \)
- Now, we can divide by 3 to simplify further:
- \( A_3B_{12} = A_1B_4 \)

### Final Answer
The simplest formula of the compound is \( AB_4 \).

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