Question

The edge length of an fcc type unit cell of copper having atomic radius \(127.6~\text{pm}\) is equal to

• A. \(295~\text{pm}\)
• B. \(361~\text{pm}\)
• C. \(331~\text{pm}\)
• D. \(378~\text{pm}\)

Hint:

For FCC: \(\sqrt{2}a = 4r\); for BCC: \(\sqrt{3}a = 4r\).

Answer 1

The Correct Option is B

Step 1: Relation for FCC unit cell.
In an FCC lattice, atoms touch along the face diagonal. The relation between edge length \(a\) and atomic radius \(r\) is: \[ \sqrt{2}\,a = 4r \] Step 2: Substitute the given value.
\[ r = 127.6~\text{pm} \] \[ a = \frac{4r}{\sqrt{2}} = \frac{4 \times 127.6}{1.414} \] Step 3: Calculate the edge length.
\[ a \approx 361~\text{pm} \] Step 4: Conclusion.
Hence, the edge length of the unit cell is \(361~\text{pm}\).