Question

Silver crystallises in face centred cubic structure. If radius of silver atom is 144.5 pm, what is the edge length of unit cell?

• A. 408.6 pm
• B. 289.0 pm
• C. 428.6 pm
• D. 333.7 pm

Hint:

For FCC lattice, atoms touch along the face diagonal, leading to the relation \(a = 2\sqrt{2}r\).

Answer 1

The Correct Option is A

Step 1: Recall the relation between atomic radius and edge length for FCC lattice.
In face centred cubic (FCC) structure:
\[ a = 2\sqrt{2}\,r \]
Step 2: Substitute the given value of radius.
\[ r = 144.5\ \text{pm} \]
\[ a = 2\sqrt{2} \times 144.5 \]
Step 3: Calculate the edge length.
\[ a = 2.828 \times 144.5 \approx 408.6\ \text{pm} \]
Step 4: Conclusion.
The edge length of the unit cell is 408.6 pm.