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12 grade chemistry others

What is the number of atoms in the unit cell of the body centred cubic crystal?(A) 1(B) 3(C) 4(D) 2

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1 Year agoGrade
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1 Answer

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1 Year ago

To determine the number of atoms in the unit cell of a body-centered cubic (BCC) crystal, let's break down the structure.

### BCC Structure:
- In a body-centered cubic crystal, atoms are positioned at:
1. The **corners** of the unit cell.
2. **One atom** at the **center** of the unit cell.

#### Contribution of Atoms:
1. **Corner atoms:**
- A cubic unit cell has 8 corners.
- Each atom at the corner is shared by 8 adjacent unit cells.
- Thus, each corner atom contributes **1/8th** of an atom to the given unit cell.
- Contribution of all 8 corner atoms:
\[
8 \times \frac{1}{8} = 1 \text{ atom}
\]

2. **Body-centered atom:**
- The atom in the center of the unit cell is completely inside the unit cell.
- So, this atom contributes **1 full atom** to the unit cell.

#### Total number of atoms in the unit cell:
- Contribution from corner atoms = 1 atom
- Contribution from the body-centered atom = 1 atom
- Total atoms in the unit cell = 1 + 1 = **2 atoms**

### Answer:
The number of atoms in the unit cell of a body-centered cubic crystal is **(D) 2**.