An elementoccurring in the bcc structure has `12.08 xx 10^(23)` unit cells .The total number of atoms of the element in these cells will be

Options

A. `24.16xx10^(23)`
B. `36.18xx10^(23)`
C. `6.04xx10^(23)`
D. `12.08xx10^(23)`

Answer

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

### Step 1: Understand the BCC Structure
In a body-centered cubic (BCC) structure, each unit cell contains 2 atoms. This is because there is one atom at each of the eight corners of the cube (each corner atom is shared among 8 unit cells, contributing 1/8 of an atom per unit cell), and one atom in the center of the cube.

### Step 2: Identify the Given Data
We are given:
- Number of unit cells = \( 12.08 \times 10^{23} \)

### Step 3: Calculate the Total Number of Atoms
To find the total number of atoms in the given number of unit cells, we can use the formula:
\[ \text{Total number of atoms} = \text{Number of unit cells} \times \text{Number of atoms per unit cell} \]
Substituting the known values:
\[ \text{Total number of atoms} = 12.08 \times 10^{23} \times 2 \]

### Step 4: Perform the Calculation
Now, we perform the multiplication:
\[ \text{Total number of atoms} = 24.16 \times 10^{23} \]

### Conclusion
The total number of atoms of the element in the given BCC unit cells is:
\[ \text{Total number of atoms} = 24.16 \times 10^{23} \]

### Final Answer
The correct option is the first one: \( 24.16 \times 10^{23} \).

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