An element having bcc structure has `12.8xx10^(23)` unit cells. The number of atoms in these cells is

Options

A. `12.08xx10^(23)`
B. `24.16xx10^(23)`
C. `48.38xx10^(23)`
D. `12.08xx10^(22)`

Answer

To find the number of atoms in the given number of body-centered cubic (BCC) unit cells, we can follow these steps:

### Step-by-Step Solution

1. **Understand the BCC Structure**:
- A body-centered cubic (BCC) unit cell contains 2 atoms. This is because there is 1 atom at the center of the cube and 1/8 of an atom at each of the 8 corners (totaling 1 atom from the corners).

2. **Identify the Given Data**:
- The number of unit cells is given as \( 12.8 \times 10^{23} \).

3. **Calculate the Total Number of Atoms**:
- To find the total number of atoms in the given unit cells, multiply the number of unit cells by the number of atoms per unit cell:
\[ \text{Total Atoms} = \text{Number of Unit Cells} \times \text{Number of Atoms per Unit Cell} \]
- Substituting the values:
\[ \text{Total Atoms} = (12.8 \times 10^{23}) \times 2 \]

4. **Perform the Calculation**:
- Calculate the total:
\[ \text{Total Atoms} = 25.6 \times 10^{23} \]

5. **Final Result**:
- The total number of atoms in \( 12.8 \times 10^{23} \) BCC unit cells is \( 25.6 \times 10^{23} \).

### Summary
The number of atoms in \( 12.8 \times 10^{23} \) unit cells of a BCC structure is \( 25.6 \times 10^{23} \).

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