Metallic rhodium crystallizes in a face-centered cubic lattice, with one Rh atom per lattice point. If the metallic radius of Rh is 134 pm, what is the volume of the unit cell in pm^{3} and in cm^{3}?

For a face-centered cubic lattice with one atom per lattice point, there are4 atoms per unit cell. The atoms are in contact along a face diagonal and 4r = (2)^{1/2}a, where r is the metallic radius and a is the edge length of the cell.

Thus: a = r / 0.354 = 134 pm /0.354 = 379 pm

For a cubic cell the volume is the edge length cubed. V = (379 pm)^{3} = 5.44E7 pm^{3}