Question

Aluminium crystallises in a face-centred cubic structure, its atomic radius is 125 pm. What is the edge length of unit cell?

• A. 280 pm
• B. 353.5 pm
• C. 335.5 pm
• D. 288.6 pm

Hint:

For FCC crystals, use the formula \( a = \frac{4r}{\sqrt{2}} \) to calculate the edge length of the unit cell.

Answer 1

The Correct Option is B

Step 1: Formula for edge length of unit cell.
For a face-centred cubic (FCC) structure, the relationship between the atomic radius \( r \) and the edge length \( a \) of the unit cell is given by: \[ a = \frac{4r}{\sqrt{2}} \] Where \( r = 125 \, \text{pm} \).
Step 2: Calculation.
Substitute the given value of \( r \): \[ a = \frac{4 \times 125}{\sqrt{2}} = 353.5 \, \text{pm} \] Step 3: Conclusion.
The correct answer is (B) 353.5 pm.