Answer
136 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: $4\times 192.217\ g/mol\div 6.022\times 10^{23}\ atoms/mol=1.277\times10^{-21}\ g/cell$
Volume: $1.277\times10^{-21}\ g/cell\div 22.56\ g/cm^3=5.659\times 10^{-23}\ cm^3/cell$
Side length: $\sqrt[3]{5.659\times 10^{-23}\ cm^3}=3.84\times10^{-8}\ cm=384\ pm$
The diagonal of a side equals the radius of two atoms in the vertexes plus the diameter of the one in the face, so:
$384\ pm\times \sqrt2 =4.r\rightarrow r=136\ pm$
