Atomic radius of aluminium is 125 pm. If aluminium has a fcc structure, calculate the edge length of the unit cell.

Explanation

To find the edge length of the unit cell of aluminum with a face-centered cubic (FCC) structure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the FCC Structure**:
- In a face-centered cubic (FCC) structure, atoms are located at each corner and the centers of all the faces of the cube. Each unit cell contains 4 atoms.

2. **Relate Atomic Radius to Edge Length**:
- In an FCC structure, the relationship between the atomic radius (R) and the edge length (A) can be derived from the geometry of the cube. The diagonal of the face of the cube is equal to 4 times the atomic radius (since there are two atomic radii from each atom at the corners and two from the atom at the center of the face).
- The formula for the diagonal (d) of the face of the cube is given by:
\[ d = A\sqrt{2} \]
- Therefore, we can set up the equation:
\[ d = 4R \]
- Equating the two expressions for d gives:
\[ A\sqrt{2} = 4R \]

3. **Substitute the Given Radius**:
- We know the atomic radius of aluminum (R) is 125 pm (picometers).
- Substitute R into the equation:
\[ A\sqrt{2} = 4 \times 125 \text{ pm} \]
\[ A\sqrt{2} = 500 \text{ pm} \]

4. **Solve for Edge Length (A)**:
- Now, solve for A:
\[ A = \frac{500 \text{ pm}}{\sqrt{2}} \]
- Calculate the value:
\[ A = \frac{500 \text{ pm}}{1.414} \approx 353.55 \text{ pm} \]

5. **Final Result**:
- The edge length of the unit cell of aluminum is approximately:
\[ A \approx 354 \text{ pm} \]

### Final Answer:
The edge length of the unit cell of aluminum is approximately **354 pm**.