Answer
197 pm
Work Step by Step
For a face-centered cubic arrangement there are $8 \times 1/8$ atoms in the corners and $6\times1/2$ in the faces, so 4 atoms per unit cell:
Mass: $4\times 40.078\ g/mol\div 6.022\times 10^{23}\ atoms/mol=2.662\times10^{-22}\ g/cell$
Volume: $2.662\times10^{-22}\ g/cell\div 1.54\ g/cm^3=1.729\times 10^{-22}\ cm^3/cell$
Side length: $\sqrt[3]{1.729\times 10^{-22}\ cm^3}=5.57\times10^{-8}\ cm=557\ pm$
The diagonal of a side equals the radius of two atoms in the vertexes plus the diameter of the one in the face, so:
$557\ pm\times \sqrt2 =4.r\rightarrow r=197\ pm$
