(b) Because atoms are spherical, they cannot occupy all of the space of the cube. The silver atoms pack in the solid in such a way that 74% of the volume of the solid is actually filled with the silver atoms. Calculate the volume of a single silver atom.

Verified step by step guidance

1. First, understand that the problem involves calculating the volume of a single silver atom given that 74% of the volume of the solid is filled with silver atoms. This percentage is known as the packing efficiency.
2. Next, recognize that the packing efficiency is the ratio of the volume occupied by the atoms to the total volume of the solid. In this case, the packing efficiency is 0.74 (or 74%).
3. Assume the solid is a cube with a side length 'a'. The total volume of the cube is then given by the formula: \( V_{cube} = a^3 \).
4. The volume occupied by the silver atoms is 74% of the total volume of the cube. Therefore, the volume occupied by the atoms is: \( V_{atoms} = 0.74 \times a^3 \).
5. To find the volume of a single silver atom, you need to know the number of atoms in the cube. If the crystal structure is known (e.g., face-centered cubic), you can calculate the number of atoms per unit cell and then divide the total volume occupied by the atoms by this number to find the volume of a single atom.