Question: The atomic radius is determined from the edge length, ℓ. The edge length is determined from the volume. The volume is found from the mass of the number of atoms in the unit cell and the density. Potassium has a density of 0.856 g/and crystallizes with a body-centered cubic unit cell structure. What is the atomic radius of the atom?

(a) Determining an Atom Radius from Lattice Dimensions: Gold has a face-centered unit cell, and its density is 19.32 g/cm3. Calculate the radius of a gold atom. (b) The Structure of Solid Iron: Iron has a density of 7.8740 g/cm3, and the radius of an iron atom is 126 pm. Verify that solid iron has a body-centered cubic unit cell. (Be sure to note that the atoms in a body-centered cubic unit cell touch along the diagonal across the cell. They do not touch along the edges of the cell.) (Hint: The diagonal distance across the unit cell = edge 3.)

Iridium metal, Ir, crystallizes in a face-centered cubic (close-packed) structure. The edge length of the unit cell was found by x-ray diffraction to be 383.9 pm. The density of iridium is 22.42 g/cm3. Calculate the mass of an iridium atom. Use Avogadros number to calculate the atomic mass of iridium.

Metallic barium has a body-centered cubic structure (all atoms at the lattice points) and a density of 3.51 g/cm3. Assume barium atoms to be spheres. The spheres in a body-centered array occupy 68.0% of the total space. Find the atomic radius of barium. (See Problem 11.93.)