Final answer:
The planar density for the (0 1 0) plane is 1/(0.334 nm)^2 and for the (0 2 0) plane is 2/(0.334 nm)^2. The planar packing fraction for both planes is 1.
Step-by-step explanation:
In a simple cubic structure, the planar density is the ratio of the number of atoms in a plane to the area of that plane. For the (0 1 0) plane, there is one atom in the plane, and the area of the plane is the square of the lattice parameter, so the planar density is 1/(0.334 nm)^2. Similarly, for the (0 2 0) plane, there are two atoms in the plane, so the planar density is 2/(0.334 nm)^2.
The planar packing fraction is the ratio of the size of the atoms to the area of the plane. Since polonium is a simple cubic structure, the atoms touch each other along the edges of the unit cell. The edge length of the unit cell is the lattice parameter, so the size of the atoms is 0.334 nm. Therefore, the planar packing fraction is (0.334 nm)/(0.334 nm) = 1.