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?
Silver crystallises in face centred cubic structure. If radius of silver atom is 144.5 pm, what is the edge length of unit cell?
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For FCC lattice, atoms touch along the face diagonal, leading to the relation \(a = 2\sqrt{2}r\).
Updated On: Feb 11, 2026
- 408.6 pm
- 289.0 pm
- 428.6 pm
- 333.7 pm
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The Correct Option is A
Solution and Explanation
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.
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.
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