Question

Aluminium crystallises in face centred cubic structure, having atomic radius 125 pm. The edge length of the unit cell of aluminium is

• A. 253.5 pm
• B. 353.5 pm
• C. 465.0 pm
• D. 250.0 pm

Hint:

For FCC lattice: \( a = \dfrac{4r}{\sqrt{2}} \).

Answer 1

The Correct Option is B

Step 1: Relation for FCC lattice.
In a face centred cubic (fcc) structure, atoms touch along the face diagonal. The relation between edge length \( a \) and atomic radius \( r \) is:
\[ \sqrt{2}\,a = 4r \]

Step 2: Substituting given value.
\[ a = \frac{4r}{\sqrt{2}} = \frac{4 \times 125}{1.414} \]

Step 3: Calculation.
\[ a \approx 353.5 \, \text{pm} \]

Step 4: Conclusion.
Thus, the edge length of the unit cell of aluminium is 353.5 pm.