How many number of atom effectively present in a cubic unit formed by arrangement of eight B.C.C unit cell

Answer

To determine the number of atoms effectively present in a cubic unit formed by the arrangement of eight Body-Centered Cubic (BCC) unit cells, we can follow these steps:

### Step 1: Understand the Structure of a BCC Unit Cell
A BCC unit cell consists of:
- 8 atoms located at the corners of the cube.
- 1 atom located at the center of the cube.

### Step 2: Calculate the Contribution of Corner Atoms
Each corner atom is shared among 8 adjacent unit cells. Therefore, the contribution of each corner atom to one unit cell is:
\[ \text{Contribution from one corner atom} = \frac{1}{8} \]
Since there are 8 corners in a BCC unit cell, the total contribution from the corner atoms is:
\[ \text{Total contribution from corner atoms} = 8 \times \frac{1}{8} = 1 \]

### Step 3: Calculate the Contribution of the Body-Centered Atom
The atom at the body center is entirely contained within the unit cell, so its contribution is:
\[ \text{Contribution from body-centered atom} = 1 \]

### Step 4: Calculate Total Atoms in One BCC Unit Cell
Now, we can find the total number of atoms effectively present in one BCC unit cell by adding the contributions from the corner atoms and the body-centered atom:
\[ \text{Total atoms in one BCC unit cell} = \text{Contribution from corner atoms} + \text{Contribution from body-centered atom} = 1 + 1 = 2 \]

### Step 5: Calculate Total Atoms in Eight BCC Unit Cells
To find the total number of atoms effectively present in the arrangement of 8 BCC unit cells, we multiply the number of atoms in one BCC unit cell by the number of unit cells:
\[ \text{Total atoms in 8 BCC unit cells} = 8 \times 2 = 16 \]

### Final Answer
Thus, the total number of atoms effectively present in a cubic unit formed by the arrangement of eight BCC unit cells is **16 atoms**.

---