If an atom is present in the centre of the cube, the participation of that atom per unit cell is:

Options

A. `(1)/(4)`
B. 1
C. `(1)/(2)`
D. `(1)/(8)`

Answer

To determine the participation of an atom located at the center of a cube (body-centered cubic structure) per unit cell, we can follow these steps:

### Step 1: Understand the Structure
In a body-centered cubic (BCC) structure, there is one atom located at the center of the cube and additional atoms located at the corners of the cube.

### Step 2: Contribution of the Atom at the Center
The atom at the center of the cube is fully contained within that unit cell. Therefore, its contribution to the unit cell is considered as 1 whole atom.

### Step 3: Contribution of Corner Atoms
For completeness, we can also consider the contribution of the corner atoms. Each corner atom is shared among eight adjacent unit cells, contributing only 1/8 of an atom to each unit cell. Since there are 8 corners in a cube, the total contribution from the corner atoms would be:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

### Step 4: Total Contribution per Unit Cell
In a body-centered cubic unit cell, the total number of atoms per unit cell is:
- 1 atom from the center
- 1 atom from the corners

Thus, the total number of atoms per unit cell in a BCC structure is:
\[ \text{Total atoms per unit cell} = 1 + 1 = 2 \text{ atoms} \]

### Step 5: Final Answer
However, the question specifically asks for the participation of the atom at the center of the cube per unit cell, which is simply:
\[ \text{Participation of the atom at the center} = 1 \]

Therefore, the correct answer is:
**Option 2: 1**

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