`{:("(Unitcell)","(no of atoms per unitcell)"),("A) Simple cube","1) 4"),("B) fcc","2) 2"),("C) bcc","3) 1"):}`
The correct match is

Options

A. `{:(A,B,C),(2,3,1):}`
B. `{:(A,B,C),(2,1,3):}`
C. `{:(A,B,C),(3,1,2):}`
D. `{:(A,B,C),(1,2,3):}`

Answer

To solve the question regarding the number of atoms per unit cell for different types of cubic unit cells, we will analyze each type of unit cell step by step.

### Step 1: Understand the Types of Cubic Unit Cells
There are three types of cubic unit cells mentioned:
1. Simple Cubic (SC)
2. Face-Centered Cubic (FCC)
3. Body-Centered Cubic (BCC)

### Step 2: Analyze the Simple Cubic Unit Cell
- In a simple cubic unit cell, there is one atom located at each of the eight corners of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total number of atoms in a simple cubic unit cell is calculated as:
\[ \text{Total atoms} = 8 \times \frac{1}{8} = 1 \]
- Thus, the number of atoms per unit cell for Simple Cubic is **1**.

### Step 3: Analyze the Face-Centered Cubic Unit Cell
- In a face-centered cubic unit cell, there are atoms at each of the eight corners and one atom at the center of each of the six faces.
- The contribution from the corner atoms is the same as before:
\[ \text{Corner atoms contribution} = 8 \times \frac{1}{8} = 1 \]
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell, and there are six face-centered atoms:
\[ \text{Face-centered atoms contribution} = 6 \times \frac{1}{2} = 3 \]
- Therefore, the total number of atoms in a face-centered cubic unit cell is:
\[ \text{Total atoms} = 1 + 3 = 4 \]
- Thus, the number of atoms per unit cell for Face-Centered Cubic is **4**.

### Step 4: Analyze the Body-Centered Cubic Unit Cell
- In a body-centered cubic unit cell, there are atoms at each of the eight corners and one atom at the center of the cube.
- The contribution from the corner atoms is:
\[ \text{Corner atoms contribution} = 8 \times \frac{1}{8} = 1 \]
- The body-centered atom contributes \( 1 \) atom to the unit cell:
\[ \text{Body-centered atom contribution} = 1 \]
- Therefore, the total number of atoms in a body-centered cubic unit cell is:
\[ \text{Total atoms} = 1 + 1 = 2 \]
- Thus, the number of atoms per unit cell for Body-Centered Cubic is **2**.

### Step 5: Match the Results
Now we can summarize the findings:
- Simple Cubic (A) has **1 atom** per unit cell.
- Face-Centered Cubic (B) has **4 atoms** per unit cell.
- Body-Centered Cubic (C) has **2 atoms** per unit cell.

### Final Matching:
- A (Simple Cubic) matches with **3** (1 atom).
- B (FCC) matches with **1** (4 atoms).
- C (BCC) matches with **2** (2 atoms).

Thus, the correct match is:
- A → 3
- B → 1
- C → 2

### Conclusion:
The correct match is:
- A) Simple Cube → 1 atom
- B) FCC → 4 atoms
- C) BCC → 2 atoms