The number of atoms present per unit cell in simple, fcc and bcc are ………, ……….., and …………, respectively.

Answer

To solve the question regarding the number of atoms present per unit cell in simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC) structures, we will analyze each type of unit cell step by step.

### Step-by-Step Solution:

1. **Simple Cubic (SC) Structure:**
- In a simple cubic unit cell, there are atoms located at each of the 8 corners of the cube.
- Each corner atom is shared by 8 adjacent unit cells.
- Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
- Total contribution from all 8 corner atoms:
\[ \text{Total atoms} = 8 \times \frac{1}{8} = 1 \]
- **Number of atoms per unit cell in SC = 1.**

2. **Face-Centered Cubic (FCC) Structure:**
- In an FCC unit cell, there are also atoms at each of the 8 corners, similar to the simple cubic structure.
- Additionally, there are atoms located at the center of each of the 6 faces of the cube.
- Each face-centered atom is shared by 2 adjacent unit cells.
- Contribution from the corner atoms:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \]
- Contribution from face-centered atoms:
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \]
- Total contribution from both corners and faces:
\[ \text{Total atoms} = 1 + 3 = 4 \]
- **Number of atoms per unit cell in FCC = 4.**

3. **Body-Centered Cubic (BCC) Structure:**
- In a BCC unit cell, there are atoms at each of the 8 corners, just like in the previous structures.
- Additionally, there is one atom located at the center of the cube (body center).
- Contribution from the corner atoms:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \]
- Contribution from the body-centered atom:
\[ \text{Contribution from body center} = 1 \times 1 = 1 \]
- Total contribution from corners and body center:
\[ \text{Total atoms} = 1 + 1 = 2 \]
- **Number of atoms per unit cell in BCC = 2.**

### Final Answer:
- The number of atoms present per unit cell in:
- Simple Cubic (SC) = 1
- Face-Centered Cubic (FCC) = 4
- Body-Centered Cubic (BCC) = 2

### Summary:
- Simple Cubic: 1 atom
- FCC: 4 atoms
- BCC: 2 atoms