The number of atoms in bcc and fcc arrangement are respectively :

Options

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

Answer

To determine the number of atoms in body-centered cubic (BCC) and face-centered cubic (FCC) arrangements, we can follow these steps:

### Step 1: Understanding BCC Structure
- In a BCC unit cell, there is:
- 1 atom at the center of the body.
- 8 atoms at the corners of the cube.

### Step 2: Contribution of Atoms in BCC
- The contribution of the atom at the center is 1 (since it is not shared).
- The contribution of each corner atom is \( \frac{1}{8} \) (since each corner atom is shared by 8 unit cells).
- Total contribution from corner atoms:
\[ 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]
- Therefore, the total number of atoms in a BCC unit cell is:
\[ 1 \text{ (center)} + 1 \text{ (from corners)} = 2 \text{ atoms} \]

### Step 3: Understanding FCC Structure
- In an FCC unit cell, there is:
- 6 atoms at the face centers.
- 8 atoms at the corners of the cube.

### Step 4: Contribution of Atoms in FCC
- The contribution of each face-centered atom is 1 (since it is not shared).
- The contribution of each corner atom is \( \frac{1}{8} \).
- Total contribution from face-centered atoms:
\[ 6 \text{ faces} \times 1 = 6 \text{ atoms} \]
- Total contribution from corner atoms:
\[ 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]
- Therefore, the total number of atoms in an FCC unit cell is:
\[ 6 \text{ (from faces)} + 1 \text{ (from corners)} = 4 \text{ atoms} \]

### Final Answer
- The number of atoms in BCC is **2**.
- The number of atoms in FCC is **4**.

### Summary
Thus, the respective number of atoms in BCC and FCC arrangements are **2 and 4**.

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