In a body centred unit cell, the number of atoms present is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the number of atoms present in a body-centered cubic (BCC) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure of BCC**:
In a body-centered cubic unit cell, there is one atom located at the center of the cube and one atom at each of the eight corners of the cube.

2. **Count the Atoms at the Corners**:
Each corner of the cube has an atom, and since there are 8 corners, we initially have 8 atoms from the corners.

3. **Determine the Contribution of Corner Atoms**:
Each corner atom is shared among 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
- Total contribution from corner atoms = Number of corner atoms × Contribution per corner atom
- Total contribution from corner atoms = \( 8 \times \frac{1}{8} = 1 \) atom.

4. **Count the Atom at the Center**:
The atom located at the center of the cube is not shared with any other unit cell. Therefore, its contribution is 1.

5. **Calculate the Total Number of Atoms**:
Now, we can sum the contributions from the corner atoms and the center atom:
- Total number of atoms in BCC = Contribution from corner atoms + Contribution from center atom
- Total number of atoms in BCC = \( 1 + 1 = 2 \).

### Final Answer:
The number of atoms present in a body-centered cubic unit cell is **2**.

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