A solid has a structure in which A atoms are located at the cube corners of the unit cell, B atoms are located at the cube edges of unit cell and the C atoms at the body centre. Formula of the compound

Options

A. `CAB_(3)`
B. `C_(2)AB_(3)`
C. `CA_(3)B`
D. `C_(2)A_(3)B`

Answer

To determine the formula of the compound based on the given arrangement of atoms in the unit cell, we need to analyze the contributions of each type of atom (A, B, and C) to the overall formula. Here are the steps to find the formula:

### Step 1: Identify the contribution of A atoms
- A atoms are located at the corners of the cube.
- In a cube, there are 8 corners.
- Each corner atom contributes 1/8th of an atom to the unit cell.

**Calculation:**
Contribution of A atoms = Number of corners × Contribution per corner
= 8 corners × (1/8) = 1 A atom

### Step 2: Identify the contribution of B atoms
- B atoms are located at the edges of the cube.
- A cube has 12 edges.
- Each edge atom contributes 1/4th of an atom to the unit cell.

**Calculation:**
Contribution of B atoms = Number of edges × Contribution per edge
= 12 edges × (1/4) = 3 B atoms

### Step 3: Identify the contribution of C atoms
- C atoms are located at the body center of the cube.
- There is only 1 body center atom, and it contributes fully to the unit cell.

**Calculation:**
Contribution of C atoms = 1 (since it is fully inside the unit cell)

### Step 4: Combine the contributions to write the formula
Now, we can combine the contributions of A, B, and C atoms to write the empirical formula of the compound.

- From Step 1: 1 A atom
- From Step 2: 3 B atoms
- From Step 3: 1 C atom

Thus, the formula of the compound is \( A_1B_3C_1 \) or simply \( AB_3C \).

### Final Answer:
The formula of the compound is \( AB_3C \).

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