Final answer:
The fraction of vacant atom sites in a substance is calculated by the total number of vacant sites divided by the total atomic sites, but the question doesn't provide enough information to perform this calculation. The percentage of free space in cubic lattices is found by volume comparison, with the FCC structure being the most efficient. Cadmium sulfide crystallizes with a 1:1 ratio of cadmium to sulfide ions, resulting in the formula CdS.
Step-by-step explanation:
Calculating the Fraction of Vacant Atom Sites
To calculate the fraction of vacant atom sites in a substance, the number of vacant sites within the structure must be known relative to the total number of atomic sites. This information is not directly provided in the reference, so a calculation that would allow us to deduce this figure is not possible here. However, it is important to note that vacant sites, or vacancies, can affect the properties of materials. Vacancies are often deliberately introduced into materials through processes like doping to change electrical and thermal properties.
Regarding the percentage of free space within cubic lattices, it involves subtracting the volume occupied by atoms in a unit cell from the total volume of the unit cell. Then, to find the percentage, you divide the free volume by the total volume and multiply by 100. Efficient packing is determined by which cubic lattice has the smallest percentage of free space. For example, in the face-centered cubic (FCC) lattice, atoms are most efficiently packed compared to body-centered cubic (BCC) or simple cubic (SC) structures.
As for determining the formula of a compound like cadmium sulfide, the structural arrangement of atoms within its crystal lattice needs to be analyzed. In a closest packed array, the number of tetrahedral holes is equal to twice the number of atoms forming the close-packed layers. Since cadmium occupies half of these holes, there is a 1:1 ratio of cadmium to sulfide ions, leading to the formula CdS for cadmium sulfide.