[eliarae]

The density of an unknown metal is 12.3 g/cm3 with an atomic radius of 0.134 nm. It has a face-centered cubic unit cell. Find the atomic weight of this metal.

I've actually seen this worked out more than once by others with different answers, so I'm a little confused if I figured this out correctly.
Anyway, here was my attempt and solution:

1.34x10^-8 cm = (√2 x edge)/4
edge length = 3.79x10^-8 cm
volume = (3.79x10^-8)^3 = 5.44x10^-23 cm3

12.3 g/cm3 x 5.44x10^-23 cm3 = 6.69x10^-22 g

(6.022x10^23 atoms/mol) x (1 unit cell/4 atoms) x (6.69x10^-22 g/unit cell)

= 101 g/mol

Thanks in advance!

[Enthalpy]

I cheat:
https://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)
There are many definitions of the "atomic radius", but here the metallic one must fit.

Ruthenium fits: 12370kg/m³, 134pm, 101g/mol.
It's hexagonal close-packed but the packing density equals the face-centred cubic crystal.
https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres