Crystal Structure of Sodium Chloride

The ionic radius of the sodium ion is 1.16 Å and that of the chloride ion is 1.67 Å. The ratio of radii for the cation and anion is thus r₊/r_- = 1.16/1.67 = 0.695.
With a radius ratio of 0.695, the cubic holes are too large (r_hole/r = 0.732) to be suitable. The sodium ions will prefer to occupy octahedral holes in a closest-packed structure. As it happens, the chloride ions in NaCl pack in a cubic closest-packed structure.
The images below depict the structure of NaCl. The green spheres represent the chloride ions and the red spheres represent the sodium ions.
Examine the images and note how the sulfide ions lie in an expanded cubic closest-packed structure. The sodium ions, which are smaller than the chloride ions, are inserted into octahedral holes and push the chloride ions apart so that no two chloride ions are in contact with each other. The resulting structure has (6,6)-coordination. Observe that none of the tetrahedral holes are occupied.
The dimensions of the NaCl unit cell are a = b = c = 5.406 Å.

1. How many chloride ions lie inside the unit cell? (Portions of a chloride ion lying outside the unit cell do not count.)
2. How many sodium ions like inside the unit cell? The structure as a whole is electrically neutral and thus the unit cell must be electrically neutral. Therefore Na⁺ and Cl^- ions must be present in a 1:1 ratio.
3. What is the volume of the NaCl unit cell (in cm³)?
4. What is the density of crystalline NaCl (in g cm^-3)?
5. The measured density of halite (the mineral name for naturally occurring crystalline NaCl) is 2.168 g cm^-3. How does your calculated density compare with the experimental values?