Please make sure to display your thought process? It is imperative to be able to follow how the answer was deduced. Please be as thorough as possible. Please address all parts as they are critical to answering this question correctly:

1) Determine the inter-particle distance of spherical inclusions as a function of particle size and volume fraction. Consider a size range of 20 nm to 200 m in diameter and volume fractions as high as 0.5.