The atomic radius of metal x is 125 picometers (pm) and a crystal of metal x has a unit cell that is face-centered cubic. calculate the density of metal x (atomic weight = 42.3 g/mol).

I guess you mean 1.40 x 10^2 pm. An FCC cell contains 4 atoms, and the face diagonal embraces two atomic diameters. So the face diagonal of the Metal X cell is 560 pm, and the edge of this cell is 560 pm/sqrt(2) = 396 pm. The volume of the cell is 6.21 x 10^(-29) m^3, and the mass of the cell is 4*42.3 g/(6.022E23) = 2.81 x 10^(-22) grams or 2.81 x 10^(-25) kg. The density of metal X is:
2.81E(-25)kg/6.21E(-29)m^3 = 4525 kg/m^3 or 4.525 g/cm^3.

It could possibly be beneficial if the experiment is successful.

Ithink that one is (c)