In a face centred cubic unit cell of close packed atoms, the radius of atom (r) is related to the edge length ‘a’ of the unit cell by the expression

\(r = \frac{a}{2\sqrt{2}}\)

The correct answer is 3. \(r = \frac{a}{2\sqrt{2}}\).

In a face-centered cubic arrangement, the three atoms along the face diagonal touch each other.

Therefore, Distance between the nearest neighbours, \(d = \frac{AC}{2}\)

Now in right angled \(\Delta ABC\)

\(AC^2 = AB^2  + BC^2\)

or, \(AC^2 = a^2  + a^2 = 2a^2\)

or, \(AC = \sqrt{2}a\)

∴  \(d = \frac{\sqrt{2}a}{2} = \frac{a}{\sqrt{2}}\)

Radius, \(r = \frac{d}{2} = \frac{a}{2\sqrt{2}}\)