Question

Copper crystallises in a structure of face centered cubic unit cell. The atomic radius of copper is $1.28$$A^{\circ }$. What is edge length of the unit cell?

• A. $2.16A^{\circ }$
• B. $3.62A^{\circ }$
• C. $3.94A^{\circ }$
• D. $4.15A^{\circ }$

Answer 1

The correct option is B $3.62A^{\circ }$

In fcc struture, atoms are touching along the face diagonal.
The face diagonal contains two atoms of copper or four atomic radius of copper atom.
Thus,
$\text{Length of face diagonal}=4r=4\times 1.28\stackrel{\circ }{A}$
Length of face diagonal is related to the edge length(a) by,
4r = $a\sqrt{2}$
$a=\frac{4r}{\sqrt{2}}=\frac{4\times 1.28}{\sqrt{2}}\stackrel{\circ }{A}=3.62\stackrel{\circ }{A}$