Question

Copper crystallises as face centered cubic lattice, with edge length of unit cell 361 pm. Calculate the radius of copper atom.

• A. 108.6 pm
• B. 127.65 pm
• C. 181.6 pm
• D. 157.6 pm

Hint:

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

Answer 1

The Correct Option is B

Step 1: Relation for FCC lattice.
In an FCC unit cell, atoms touch along the face diagonal. The relation is:
\[ \sqrt{2}a = 4r \]

Step 2: Substituting given value.
\[ r = \frac{\sqrt{2} \times 361}{4} \]

Step 3: Calculating atomic radius.
\[ r = \frac{1.414 \times 361}{4} = 127.65 \, \text{pm} \]

Step 4: Conclusion.
Hence, the radius of copper atom is 127.65 pm.