Question

Metallic gold crystallizes in fcc lattice. The length of the cubic unit cell is $4.242\stackrel{\circ }{A}$. The closest distance between two gold atoms is:

• A. $4\stackrel{\circ }{A}$
• B. $3\stackrel{\circ }{A}$
• C. $2\stackrel{\circ }{A}$
• D. $6\stackrel{\circ }{A}$

Answer 1

The correct option is B $3\stackrel{\circ }{A}$

We know that for FCC lattice,

$a=2\sqrt{2}r$

So,

Closest distance, $d=2r=\frac{a}{\sqrt{2}}$ and $\sqrt{2}a=4r$

$2r=\frac{4.242}{1.414}\approx 3\stackrel{o}{A}$