In a cubic unit cell, seven of the eight corners are occupied by atoms A and centres of faces are occupied by atoms B. The general formula of the compound is:

Options

A. `A_(7)B_(6)`
B. `A_(7)B_(12)`
C. `A_(7)B_(24)`
D. `A_(24)B_(7)`

Answer

To find the general formula of the compound in a cubic unit cell where 7 of the 8 corners are occupied by atoms A and the centers of the faces are occupied by atoms B, we can follow these steps:

### Step 1: Determine the contribution of corner atoms (A)
In a cubic unit cell, there are 8 corners. Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 adjacent unit cells.

- Since 7 out of the 8 corners are occupied by atoms A:

\[ \text{Total contribution of A} = 7 \times \frac{1}{8} = \frac{7}{8} \]

### Step 2: Determine the contribution of face-centered atoms (B)
In a cubic unit cell, there are 6 faces. Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell because it is shared between two adjacent unit cells.

- Since all 6 face centers are occupied by atoms B:

\[ \text{Total contribution of B} = 6 \times \frac{1}{2} = 3 \]

### Step 3: Write the general formula
Now we can express the general formula of the compound based on the contributions calculated:

- The total number of A atoms is \( \frac{7}{8} \).
- The total number of B atoms is \( 3 \).

Thus, the general formula can be represented as:

\[ \text{General formula} = A_{\frac{7}{8}}B_{3} \]

### Step 4: Convert to integer form
To express this formula in integer form, we can multiply both parts of the formula by 8 (the denominator of the fraction for A):

\[ A_{\frac{7}{8} \times 8}B_{3 \times 8} = A_{7}B_{24} \]

### Final Answer
The general formula of the compound is:

\[ \text{A}_7\text{B}_{24} \]