If the atomic radius of metallic ytterbium is 193.92 pm..?

Question

If the atomic radius of metallic ytterbium is 193.92 pm, and the density of the metal is 6.96 g/mL, what type of unit cell does metallic ytterbium contain?

Answer 1

you'll also need to know that the molar mass of ytterbium is 173.04 g/mol

therefore the molar density of the metal is

6.96/173.04 = 0.0402 mol/mL

or

0.0402*6.022e23*1e6 (mL/m^3) = 2.42e28 particles/m^3

the volume of the ytterbium atom alone is

4/3*PI*(193.92*1e-12)^3 = 3.05e-29 m^3

so the fraction of the volume occupied by the atom (packing efficiency) is

2.42e28 * 3.05e-29 = 0.740

this is characteristic of face-centered cubic or hexagonal unit cells.

Answer 2

the first link will help you. see the table. atomic radius of lithium is somewhat average (I think).