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) and face-centered cubic (fcc) structures, we can follow these steps:

### Step 1: Determine the number of atoms in a bcc unit cell.
In a body-centered cubic (bcc) unit cell:
- There is 1 atom at the center of the cube.
- Each of the 8 corners of the cube contributes 1/8 of an atom (since each corner atom is shared by 8 adjacent unit cells).

Calculating the total number of atoms in a bcc unit cell:
- Contribution from the center atom = 1
- Contribution from the corner atoms = 8 corners × (1/8) atom per corner = 1

Total number of atoms in bcc = 1 (center) + 1 (from corners) = 2 atoms.

### Step 2: Determine the number of atoms in an fcc unit cell.
In a face-centered cubic (fcc) unit cell:
- There are 6 face-centered atoms, each contributing 1/2 of an atom (since each face atom is shared by 2 adjacent unit cells).
- Each of the 8 corners contributes 1/8 of an atom.

Calculating the total number of atoms in an fcc unit cell:
- Contribution from the face-centered atoms = 6 faces × (1/2) atom per face = 3
- Contribution from the corner atoms = 8 corners × (1/8) atom per corner = 1

Total number of atoms in fcc = 3 (from faces) + 1 (from corners) = 4 atoms.

### Step 3: Calculate the ratio of atoms in bcc to fcc.
Now, we can find the ratio of the number of atoms in bcc to the number of atoms in fcc:
\[ \text{Ratio} = \frac{\text{Number of atoms in bcc}}{\text{Number of atoms in fcc}} = \frac{2}{4} = \frac{1}{2} \]

### Final Answer:
The ratio of atoms present per unit cell in bcc to that present in fcc is \(1:2\).