Given: Atomic radius (r) of gold = 0.144 nm

To find: Edge length (a) of the unit cell

Formula: a = \(\sqrt{8}\) r = 2\(\sqrt{2}\) r

Calculation: For fcc unit cell,

\(a=2\sqrt{2}\,r=2\sqrt{2}\times0.144=0.407\,nm\)

Ans: The length of a side of the cell is 0.407 nm.

For fcc,
Edge length of unit cell a = 2√2r
= 2 x 1.414 x 0.144 nm
= 0.407 nm

For FCC , ` a = 2 sqrt2 r = 2 xx 1.414 xx 0.144 nm = 0.407 nm ` ]