Number of atoms per unit cell, if atoms are present at the corner of unit cell and 2 atoms at each body diagonal

Options

A. 9
B. 10
C. 6
D. 4

Answer

To determine the number of atoms per unit cell when atoms are present at the corners of the unit cell and 2 atoms are located on each body diagonal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atoms at the Corners**:
- A cube has 8 corners.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 unit cells.
- Therefore, the contribution from the corner atoms is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

2. **Identify the Body Diagonal Atoms**:
- A cube has 4 body diagonals.
- Each body diagonal has 2 atoms that are not shared with any other unit cell (since they are located entirely within the unit cell).
- Therefore, the contribution from the body diagonal atoms is:
\[ \text{Contribution from body diagonals} = 4 \times 2 = 8 \text{ atoms} \]

3. **Calculate the Total Number of Atoms**:
- Now, we can sum the contributions from the corner atoms and the body diagonal atoms:
\[ \text{Total number of atoms} = \text{Contribution from corners} + \text{Contribution from body diagonals} \]
\[ \text{Total number of atoms} = 1 + 8 = 9 \text{ atoms} \]

### Final Answer:
The total number of atoms per unit cell is **9 atoms**.

---