The ratio of atoms present per unit cell in bcc to that present in fcc is

Options

A. `1:2`
B. `2:3`
C. `1:4`
D. `2:5`

Answer

To find the ratio of atoms present per unit cell in body-centered cubic (BCC) to that present in face-centered cubic (FCC), we will follow these steps:

### Step 1: Calculate the number of atoms in BCC
In a BCC unit cell:
- There are 8 atoms located at the corners of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- There is 1 atom located at the body center.

**Calculation:**
- Contribution from corner atoms: \( 8 \times \frac{1}{8} = 1 \)
- Contribution from body center atom: \( 1 \)

Total number of atoms in BCC:
\[ Z_{\text{BCC}} = 1 + 1 = 2 \]

### Step 2: Calculate the number of atoms in FCC
In an FCC unit cell:
- There are 8 atoms located at the corners of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom.

**Calculation:**
- Contribution from corner atoms: \( 8 \times \frac{1}{8} = 1 \)
- Contribution from face-centered atoms: \( 6 \times \frac{1}{2} = 3 \)

Total number of atoms in FCC:
\[ Z_{\text{FCC}} = 1 + 3 = 4 \]

### Step 3: Calculate the ratio of atoms in BCC to FCC
Now, we need to find the ratio of the number of atoms in BCC to that in FCC:
\[ \text{Ratio} = \frac{Z_{\text{BCC}}}{Z_{\text{FCC}}} = \frac{2}{4} = \frac{1}{2} \]

### Conclusion
The ratio of atoms present per unit cell in BCC to that present in FCC is \( 1:2 \).

### Final Answer
The correct option is \( 1:2 \).

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